Initial commit

.gitignore

@@ -0,0 +1,5 @@
+.pio
+.vscode/.browse.c_cpp.db*
+.vscode/c_cpp_properties.json
+.vscode/launch.json
+.vscode/ipch

.vscode/extensions.json

@@ -0,0 +1,10 @@
+{
+    // See http://go.microsoft.com/fwlink/?LinkId=827846
+    // for the documentation about the extensions.json format
+    "recommendations": [
+        "platformio.platformio-ide"
+    ],
+    "unwantedRecommendations": [
+        "ms-vscode.cpptools-extension-pack"
+    ]
+}

README.md

@@ -0,0 +1,30 @@
+## About RippleCore
+
+RippleCore is a portable C++ library which provides classes for adding multi-hop packet routing to embedded projects typically employing packet radios like LoRa.
+
+It is commercially known as the 'R2' protocol, and is the successor LoRa routing engine to the ['Ripple' project](https://buymeacoffee.com/ripplebiz).
+
+At present it is mostly aimed at Arduino projects, using the [PlatformIO](https://docs.platformio.org) tools, but could potentially be integrated into other environments.
+
+## Getting Started
+
+You'll need to install PlatformIO, and an IDE in which it runs, like VSCode. Once installed, you should just be able to open this folder as a project, and it will read the platformio.ini file, and bring in all the required dependencies.
+
+There are a number of build environments defined in the platformio.ini file, all targeting the Heltec V3 LoRa boards. For example, **[env:Heltec_v3_chat_alice]** is the target for building/running the 'secure chat' sample app as the user 'Alice'. There is a similar env, configured to run the secure chat as the user 'Bob'.
+
+Try running these two examples first, flashing to two separate Heltec V3's, and use the Serial Monitor to interact with the *very basic* command-line interface.
+
+## Other Example Apps
+
+There is also a pair of examples, **'ping_client'** and **'ping_server'** which has some very basic constructs for setting up a node in a 'server'-like role, and another as client.
+
+There is also a **'simple_repeater'** example, which should function as a basic repeater to ALL of the various samples, like the chat ones. It also defines a few examples of some 'remote admin', like setting the clock. The **'test_admin'** example is an example of an app that remotely monitors and sends commands to the 'simple_repeater' nodes.
+
+## To-Do's
+
+Will hopefully figure out how to make this a registered PlatformIO library, so it can just be added in **lib_deps** in your own project.
+
+## Acknowledgments
+
+This project is insipired from/by the [Reticulum project, by Mark Qvist](https://reticulum.network/start.html). I recommend having a look at RNS (Reticulum Network Stack) and study, almost as a pre-requisite to this project.
+

examples/ping_client/main.cpp

@@ -0,0 +1,149 @@
+#include <Arduino.h>   // needed for PlatformIO
+#include <Mesh.h>
+#include <SPIFFS.h>
+
+#define RADIOLIB_STATIC_ONLY 1
+#include <RadioLib.h>
+#include <helpers/RadioLibWrappers.h>
+#include <helpers/ArduinoHelpers.h>
+#include <helpers/StaticPoolPacketManager.h>
+#include <helpers/SimpleSeenTable.h>
+
+/* ------------------------------ Config -------------------------------- */
+
+#ifdef HELTEC_LORA_V3
+  #include <helpers/HeltecV3Board.h>
+  static HeltecV3Board board;
+#else
+  #error "need to provide a 'board' object"
+#endif
+
+/* ------------------------------ Code -------------------------------- */
+
+class MyMesh : public mesh::Mesh {
+  SimpleSeenTable* _table;
+  uint32_t last_advert_timestamp = 0;
+  mesh::Identity server_id;
+  uint8_t server_secret[PUB_KEY_SIZE];
+  int server_path_len = -1;
+  uint8_t server_path[MAX_PATH_SIZE];
+  bool got_adv = false;
+
+protected:
+  int searchPeersByHash(const uint8_t* hash) override {
+    if (got_adv && server_id.isHashMatch(hash)) {
+      return 1;
+    }
+    return 0;  // not found
+  }
+
+  void onAdvertRecv(mesh::Packet* packet, const mesh::Identity& id, uint32_t timestamp, const uint8_t* app_data, size_t app_data_len) override {
+    if (memcmp(app_data, "PING", 4) == 0) {
+      Serial.println("Received advertisement from a PING server");
+
+      // check for replay attacks
+      if (timestamp > last_advert_timestamp) {
+        last_advert_timestamp = timestamp;
+
+        server_id = id;
+        self_id.calcSharedSecret(server_secret, id);  // calc ECDH shared secret
+        got_adv = true;
+      }
+    }
+  }
+
+  void onPeerDataRecv(mesh::Packet* packet, uint8_t type, int sender_idx, uint8_t* data, size_t len) override {
+    if (type == PAYLOAD_TYPE_RESPONSE) {
+      if (_table->hasSeenPacket(packet)) return;
+
+      Serial.println("Received PING Reply!");
+
+      if (packet->isRouteFlood()) {
+        // let server know path TO here, so they can use sendDirect() for future ping responses
+        mesh::Packet* path = createPathReturn(server_id, server_secret, packet->path, packet->path_len, 0, NULL, 0);
+        if (path) sendFlood(path);
+      }
+    }
+  }
+
+  void onPeerPathRecv(mesh::Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) override {
+    if (_table->hasSeenPacket(packet)) return;
+
+    // must be from server_id 
+    Serial.printf("PATH to server, path_len=%d\n", (uint32_t) path_len);
+
+    memcpy(server_path, path, server_path_len = path_len);  // store a copy of path, for sendDirect()
+
+    if (packet->isRouteFlood()) {
+      // send a reciprocal return path to sender, but send DIRECTLY!
+      mesh::Packet* rpath = createPathReturn(server_id, server_secret, packet->path, packet->path_len, 0, NULL, 0);
+      if (rpath) sendDirect(rpath, path, path_len);
+    }
+
+    if (extra_type == PAYLOAD_TYPE_RESPONSE) {
+      Serial.println("Received PING Reply!");
+    }
+  }
+
+public:
+  MyMesh(mesh::Radio& radio, mesh::RNG& rng, mesh::RTCClock& rtc, SimpleSeenTable& table)
+     : mesh::Mesh(radio, *new ArduinoMillis(), rng, rtc, *new StaticPoolPacketManager(16)), _table(&table)
+  {
+  }
+
+  void sendPingPacket() {
+    if (!got_adv) return;   // have not received Advert yet
+
+    uint32_t now = getRTCClock()->getCurrentTime(); // important, need timestamp in packet, so that packet_hash will be unique
+    mesh::Packet* ping = createDatagram(PAYLOAD_TYPE_ANON_REQ, server_id, server_secret, (uint8_t *) &now, sizeof(now));
+
+    if (ping) {
+      if (server_path_len < 0) {
+        sendFlood(ping);
+      } else {
+        sendDirect(ping, server_path, server_path_len);
+      }
+    }
+  }
+
+};
+
+SPIClass spi;
+StdRNG fast_rng;
+SimpleSeenTable table;
+SX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY, spi);
+MyMesh the_mesh(*new RadioLibWrapper(radio, board), fast_rng, *new VolatileRTCClock(), table);
+unsigned long nextPing;
+
+void halt() {
+  while (1) ;
+}
+
+void setup() {
+  Serial.begin(115200);
+
+  board.begin();
+  spi.begin(P_LORA_SCLK, P_LORA_MISO, P_LORA_MOSI);
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+  if (status != RADIOLIB_ERR_NONE) {
+    Serial.print("ERROR: radio init failed: ");
+    Serial.println(status);
+    halt();
+  }
+  fast_rng.begin(radio.random(0x7FFFFFFF));
+  the_mesh.begin();
+
+  RadioNoiseListener true_rng(radio);
+  the_mesh.self_id = mesh::LocalIdentity(&true_rng);  // create new random identity
+
+  nextPing = 0;
+}
+
+void loop() {
+  if (the_mesh.millisHasNowPassed(nextPing)) {
+    the_mesh.sendPingPacket();
+
+    nextPing = the_mesh.futureMillis(10000);  // attempt ping every 10 seconds
+  }
+  the_mesh.loop();
+}

examples/ping_server/main.cpp

@@ -0,0 +1,174 @@
+#include <Arduino.h>   // needed for PlatformIO
+#include <Mesh.h>
+#include <SPIFFS.h>
+
+#define RADIOLIB_STATIC_ONLY 1
+#include <RadioLib.h>
+#include <helpers/RadioLibWrappers.h>
+#include <helpers/ArduinoHelpers.h>
+#include <helpers/StaticPoolPacketManager.h>
+
+/* ------------------------------ Config -------------------------------- */
+
+#ifdef HELTEC_LORA_V3
+  #include <helpers/HeltecV3Board.h>
+  static HeltecV3Board board;
+#else
+  #error "need to provide a 'board' object"
+#endif
+
+/* ------------------------------ Code -------------------------------- */
+
+struct ClientInfo {
+  mesh::Identity id;
+  uint32_t last_timestamp;
+  uint8_t secret[PUB_KEY_SIZE];
+  int out_path_len;
+  uint8_t out_path[MAX_PATH_SIZE];
+};
+
+#define MAX_CLIENTS   4
+
+class MyMesh : public mesh::Mesh {
+  int num_clients;
+  ClientInfo known_clients[MAX_CLIENTS];
+
+  ClientInfo* putClient(const mesh::Identity& id) {
+    for (int i = 0; i < num_clients; i++) {
+      if (id.matches(known_clients[i].id)) return &known_clients[i];  // already known
+    }
+    if (num_clients < MAX_CLIENTS) {
+      auto newClient = &known_clients[num_clients++];
+      newClient->id = id;
+      newClient->out_path_len = -1;  // initially out_path is unknown
+      newClient->last_timestamp = 0;
+      self_id.calcSharedSecret(newClient->secret, id);   // calc ECDH shared secret
+      return newClient;
+    }
+    return NULL;  // table is full
+  }
+
+protected:
+  void onAnonDataRecv(mesh::Packet* packet, uint8_t type, const mesh::Identity& sender, uint8_t* data, size_t len) override {
+    if (type == PAYLOAD_TYPE_ANON_REQ) {  // received a PING!
+      uint32_t timestamp;
+      memcpy(&timestamp, data, 4);
+
+      auto client = putClient(sender);  // add to known clients (if not already known)
+      if (client == NULL || timestamp <= client->last_timestamp) {
+        return;  // FATAL: client table is full -OR- replay attack -OR- have seen this packet before
+      }
+
+      client->last_timestamp = timestamp;
+
+      uint32_t now = getRTCClock()->getCurrentTime(); // response packets always prefixed with timestamp
+
+      if (packet->isRouteFlood()) {
+        // let this sender know path TO here, so they can use sendDirect(), and ALSO encode the Ping response
+        mesh::Packet* path = createPathReturn(sender, client->secret, packet->path, packet->path_len,
+                                              PAYLOAD_TYPE_RESPONSE, (uint8_t *) &now, sizeof(now));
+        if (path) sendFlood(path);
+      } else {
+        mesh::Packet* reply = createDatagram(PAYLOAD_TYPE_RESPONSE, sender, client->secret, (uint8_t *) &now, sizeof(now));
+        if (reply) {
+          if (client->out_path_len >= 0) {  // we have an out_path, so send DIRECT
+            sendDirect(reply, client->out_path, client->out_path_len);
+          } else {
+            sendFlood(reply);
+          }
+        }
+      }
+    }
+  }
+
+  int  matching_peer_indexes[MAX_CLIENTS];
+
+  int searchPeersByHash(const uint8_t* hash) override {
+    int n = 0;
+    for (int i = 0; i < num_clients; i++) {
+      if (known_clients[i].id.isHashMatch(hash)) {
+        matching_peer_indexes[n++] = i;  // store the INDEXES of matching contacts (for subsequent 'peer' methods)
+      }
+    }
+    return n;
+  }
+
+  // not needed for this example, but for sake of 'completeness' of Mesh impl
+  void getPeerSharedSecret(uint8_t* dest_secret, int peer_idx) override {
+    if (peer_idx >= 0 && peer_idx < MAX_CLIENTS) {
+      // lookup pre-calculated shared_secret
+      int i = matching_peer_indexes[peer_idx];
+      memcpy(dest_secret, known_clients[i].secret, PUB_KEY_SIZE);
+    } else {
+      MESH_DEBUG_PRINTLN("Invalid peer_idx: %d", peer_idx);
+    }
+  }
+
+  void onPeerPathRecv(mesh::Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) override {
+    if (sender_idx >= 0 && sender_idx < MAX_CLIENTS) {
+      Serial.printf("PATH to client, path_len=%d\n", (uint32_t) path_len);
+
+      // TODO: prevent replay attacks
+
+      int i = matching_peer_indexes[sender_idx];
+      if (i >= 0 && i < num_clients) {
+        auto client = &known_clients[i];  // get from our known_clients table (sender SHOULD already be known in this context)
+        memcpy(client->out_path, path, client->out_path_len = path_len);  // store a copy of path, for sendDirect()
+      }
+    } else {
+      MESH_DEBUG_PRINTLN("Invalid sender_idx: %d", sender_idx);
+    }
+
+    // NOTE: no reciprocal path send!!
+  }
+
+public:
+  MyMesh(mesh::Radio& radio, mesh::MillisecondClock& ms, mesh::RNG& rng, mesh::RTCClock& rtc)
+     : mesh::Mesh(radio, ms, rng, rtc, *new StaticPoolPacketManager(16))
+  {
+    num_clients = 0;
+  }
+};
+
+SPIClass spi;
+StdRNG fast_rng;
+SX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY, spi);
+MyMesh the_mesh(*new RadioLibWrapper(radio, board), *new ArduinoMillis(), fast_rng, *new VolatileRTCClock());
+
+unsigned long nextAnnounce;
+
+void halt() {
+  while (1) ;
+}
+
+void setup() {
+  Serial.begin(115200);
+
+  board.begin();
+  spi.begin(P_LORA_SCLK, P_LORA_MISO, P_LORA_MOSI);
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+  if (status != RADIOLIB_ERR_NONE) {
+    Serial.print("ERROR: radio init failed: ");
+    Serial.println(status);
+    halt();
+  }
+  fast_rng.begin(radio.random(0x7FFFFFFF));
+  the_mesh.begin();
+
+  RadioNoiseListener true_rng(radio);
+  the_mesh.self_id = mesh::LocalIdentity(&true_rng);  // create new random identity
+
+  nextAnnounce = 0;
+}
+
+void loop() {
+  if (the_mesh.millisHasNowPassed(nextAnnounce)) {
+    mesh::Packet* pkt = the_mesh.createAdvert(the_mesh.self_id, (const uint8_t *)"PING", 4);
+    if (pkt) the_mesh.sendFlood(pkt);
+
+    nextAnnounce = the_mesh.futureMillis(30000);  // announce every 30 seconds (test only, don't do in production!)
+  }
+  the_mesh.loop();
+
+  // TODO: periodically check for OLD entries in known_clients[], and evict
+}

examples/simple_repeater/main.cpp

@@ -0,0 +1,338 @@
+#include <Arduino.h>   // needed for PlatformIO
+#include <Mesh.h>
+#include <SPIFFS.h>
+
+#define RADIOLIB_STATIC_ONLY 1
+#include <RadioLib.h>
+#include <helpers/CustomSX1262Wrapper.h>
+#include <helpers/ArduinoHelpers.h>
+#include <helpers/StaticPoolPacketManager.h>
+#include <helpers/SimpleMeshTables.h>
+#include <helpers/IdentityStore.h>
+
+/* ------------------------------ Config -------------------------------- */
+
+#define  ANNOUNCE_DATA   "repeater:v1"
+
+#define  ADMIN_PASSWORD  "h^(kl@#)"
+
+#if defined(HELTEC_LORA_V3)
+  #include <helpers/HeltecV3Board.h>
+  static HeltecV3Board board;
+#else
+  #error "need to provide a 'board' object"
+#endif
+
+/* ------------------------------ Code -------------------------------- */
+
+#define CMD_GET_STATS      0x01
+#define CMD_SET_CLOCK      0x02
+#define CMD_SEND_ANNOUNCE  0x03
+#define CMD_SET_CONFIG     0x04
+
+struct RepeaterStats {
+  uint16_t batt_milli_volts;
+  uint16_t curr_tx_queue_len;
+  uint16_t curr_free_queue_len;
+  int16_t  last_rssi;
+  uint32_t n_packets_recv;
+  uint32_t n_packets_sent;
+  uint32_t total_air_time_secs;
+  uint32_t total_up_time_secs;
+};
+
+struct ClientInfo {
+  mesh::Identity id;
+  uint32_t last_timestamp;
+  uint8_t secret[PUB_KEY_SIZE];
+  int out_path_len;
+  uint8_t out_path[MAX_PATH_SIZE];
+};
+
+#define MAX_CLIENTS   4
+
+class MyMesh : public mesh::Mesh {
+  RadioLibWrapper* my_radio;
+  mesh::MeshTables* _tables;
+  float airtime_factor;
+  uint8_t reply_data[MAX_PACKET_PAYLOAD];
+  int num_clients;
+  ClientInfo known_clients[MAX_CLIENTS];
+
+  ClientInfo* putClient(const mesh::Identity& id) {
+    for (int i = 0; i < num_clients; i++) {
+      if (id.matches(known_clients[i].id)) return &known_clients[i];  // already known
+    }
+    if (num_clients < MAX_CLIENTS) {
+      auto newClient = &known_clients[num_clients++];
+      newClient->id = id;
+      newClient->out_path_len = -1;  // initially out_path is unknown
+      newClient->last_timestamp = 0;
+      self_id.calcSharedSecret(newClient->secret, id);   // calc ECDH shared secret
+      return newClient;
+    }
+    return NULL;  // table is full
+  }
+
+  int handleRequest(ClientInfo* sender, uint8_t* payload, size_t payload_len) { 
+    uint32_t now = getRTCClock()->getCurrentTime();
+    memcpy(reply_data, &now, 4);   // response packets always prefixed with timestamp
+
+    switch (payload[0]) {
+      case CMD_GET_STATS: {
+        uint32_t max_age_secs;
+        if (payload_len >= 5) {
+          memcpy(&max_age_secs, &payload[1], 4);    // first param in request pkt
+        } else {
+          max_age_secs = 12*60*60;   // default, 12 hours
+        }
+
+        RepeaterStats stats;
+        stats.batt_milli_volts = board.getBattMilliVolts();
+        stats.curr_tx_queue_len = _mgr->getOutboundCount();
+        stats.curr_free_queue_len = _mgr->getFreeCount();
+        stats.last_rssi = (int16_t) my_radio->getLastRSSI();
+        stats.n_packets_recv = my_radio->getPacketsRecv();
+        stats.n_packets_sent = my_radio->getPacketsSent();
+        stats.total_air_time_secs = getTotalAirTime() / 1000;
+        stats.total_up_time_secs = _ms->getMillis() / 1000;
+
+        memcpy(&reply_data[4], &stats, sizeof(stats));
+
+        return 4 + sizeof(stats);  //  reply_len
+      }
+      case CMD_SET_CLOCK: {
+        if (payload_len >= 5) {
+          uint32_t curr_epoch_secs;
+          memcpy(&curr_epoch_secs, &payload[1], 4);    // first param is current UNIX time
+
+          if (curr_epoch_secs > now) {   // time can only go forward!!
+            getRTCClock()->setCurrentTime(curr_epoch_secs);
+            memcpy(&reply_data[4], "OK", 2);
+          } else {
+            memcpy(&reply_data[4], "ER", 2);
+          }
+          return 4 + 2;   //  reply_len
+        }
+        return 0;  // invalid request 
+      }
+      case CMD_SEND_ANNOUNCE: {
+        // broadcast another self Advertisement
+        auto adv = createAdvert(self_id, (const uint8_t *)ANNOUNCE_DATA, strlen(ANNOUNCE_DATA));
+        if (adv) sendFlood(adv, 1500);   // send after slight delay
+
+        memcpy(&reply_data[4], "OK", 2);
+        return 4 + 2;  // reply_len
+      }
+      case CMD_SET_CONFIG: {
+        if (payload_len >= 4 && payload_len < 32 && memcmp(&payload[1], "AF", 2) == 0) {
+          payload[payload_len] = 0;  // make it a C string
+          airtime_factor = atof((char *) &payload[3]);
+
+          memcpy(&reply_data[4], "OK", 2);
+          return 4 + 2;  // reply_len
+        }        
+        return 0;  // unknown config var
+      }
+    }
+    // unknown command
+    return 0;  // reply_len
+  }
+
+protected:
+  float getAirtimeBudgetFactor() const override {
+    return airtime_factor;
+  }
+
+  bool allowPacketForward(mesh::Packet* packet) override {
+    uint8_t hash[MAX_HASH_SIZE];
+    packet->calculatePacketHash(hash);
+
+    if (_tables->hasForwarded(hash)) return false;  // has already been forwarded
+
+    _tables->setHasForwarded(hash);  // mark packet as forwarded
+    return true;   // Yes, allow packet to be forwarded
+  }
+
+  void onAnonDataRecv(mesh::Packet* packet, uint8_t type, const mesh::Identity& sender, uint8_t* data, size_t len) override {
+    if (type == PAYLOAD_TYPE_ANON_REQ) {  // received an initial request by a possible admin client (unknown at this stage)
+      uint32_t timestamp;
+      memcpy(&timestamp, data, 4);
+
+      if (memcmp(&data[4], ADMIN_PASSWORD, 8) == 0) {  // check for valid password
+        auto client = putClient(sender);  // add to known clients (if not already known)
+        if (client == NULL || timestamp <= client->last_timestamp) {
+          return;  // FATAL: client table is full -OR- replay attack -OR- have seen this packet before
+        }
+
+        client->last_timestamp = timestamp;
+
+        uint32_t now = getRTCClock()->getCurrentTime();
+        memcpy(reply_data, &now, 4);   // response packets always prefixed with timestamp
+        memcpy(&reply_data[4], "OK", 2);
+
+        if (packet->isRouteFlood()) {
+          // let this sender know path TO here, so they can use sendDirect(), and ALSO encode the response
+          mesh::Packet* path = createPathReturn(sender, client->secret, packet->path, packet->path_len,
+                                                PAYLOAD_TYPE_RESPONSE, reply_data, 4 + 2);
+          if (path) sendFlood(path);
+        } else {
+          mesh::Packet* reply = createDatagram(PAYLOAD_TYPE_RESPONSE, sender, client->secret, reply_data, 4 + 2);
+          if (reply) {
+            if (client->out_path_len >= 0) {  // we have an out_path, so send DIRECT
+              sendDirect(reply, client->out_path, client->out_path_len);
+            } else {
+              sendFlood(reply);
+            }
+          }
+        }
+      }
+    }
+  }
+
+  int  matching_peer_indexes[MAX_CLIENTS];
+
+  int searchPeersByHash(const uint8_t* hash) override {
+    int n = 0;
+    for (int i = 0; i < num_clients; i++) {
+      if (known_clients[i].id.isHashMatch(hash)) {
+        matching_peer_indexes[n++] = i;  // store the INDEXES of matching contacts (for subsequent 'peer' methods)
+      }
+    }
+    return n;
+  }
+
+  void getPeerSharedSecret(uint8_t* dest_secret, int peer_idx) override {
+    int i = matching_peer_indexes[peer_idx];
+    if (i >= 0 && i < num_clients) {
+      // lookup pre-calculated shared_secret
+      memcpy(dest_secret, known_clients[i].secret, PUB_KEY_SIZE);
+    } else {
+      MESH_DEBUG_PRINTLN("getPeerSharedSecret: Invalid peer idx: %d", i);
+    }
+  }
+
+  void onPeerDataRecv(mesh::Packet* packet, uint8_t type, int sender_idx, uint8_t* data, size_t len) override {
+     if (type == PAYLOAD_TYPE_REQ) {  // request (from a Known admin client!)
+      int i = matching_peer_indexes[sender_idx];
+
+      if (i >= 0 && i < num_clients) {  // get from our known_clients table (sender SHOULD already be known in this context)
+        auto client = &known_clients[i];
+
+        uint32_t timestamp;
+        memcpy(&timestamp, data, 4);
+
+        if (timestamp > client->last_timestamp) {  // prevent replay attacks AND receiving via multiple paths
+          int reply_len = handleRequest(client, &data[4], len - 4);
+          if (reply_len == 0) return;  // invalid command
+
+          client->last_timestamp = timestamp;
+
+          if (packet->isRouteFlood()) {
+            // let this sender know path TO here, so they can use sendDirect(), and ALSO encode the response
+            mesh::Packet* path = createPathReturn(client->id, client->secret, packet->path, packet->path_len,
+                                                  PAYLOAD_TYPE_RESPONSE, reply_data, reply_len);
+            if (path) sendFlood(path);
+          } else {
+            mesh::Packet* reply = createDatagram(PAYLOAD_TYPE_RESPONSE, client->id, client->secret, reply_data, reply_len);
+            if (reply) {
+              if (client->out_path_len >= 0) {  // we have an out_path, so send DIRECT
+                sendDirect(reply, client->out_path, client->out_path_len);
+              } else {
+                sendFlood(reply);
+              }
+            }
+          }
+        }
+      } else {
+        MESH_DEBUG_PRINTLN("onPeerDataRecv: invalid peer idx: %d", i);
+      }
+    }
+  }
+
+  void onPeerPathRecv(mesh::Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) override {
+    // TODO: prevent replay attacks
+    int i = matching_peer_indexes[sender_idx];
+
+    if (i >= 0 && i < num_clients) {  // get from our known_clients table (sender SHOULD already be known in this context)
+      Serial.printf("PATH to client, path_len=%d\n", (uint32_t) path_len);
+      auto client = &known_clients[i];
+      memcpy(client->out_path, path, client->out_path_len = path_len);  // store a copy of path, for sendDirect()
+    } else {
+      MESH_DEBUG_PRINTLN("onPeerPathRecv: invalid peer idx: %d", i);
+    }
+
+    // NOTE: no reciprocal path send!!
+  }
+
+public:
+  MyMesh(RadioLibWrapper& radio, mesh::MillisecondClock& ms, mesh::RNG& rng, mesh::RTCClock& rtc, mesh::MeshTables& tables)
+     : mesh::Mesh(radio, ms, rng, rtc, *new StaticPoolPacketManager(32)), _tables(&tables)
+  {
+    my_radio = &radio;
+    airtime_factor = 5.0;   // 1/6th
+    num_clients = 0;
+  }
+
+  void sendSelfAdvertisement() {
+    mesh::Packet* pkt = createAdvert(self_id, (const uint8_t *)ANNOUNCE_DATA, strlen(ANNOUNCE_DATA));
+    if (pkt) {
+      sendFlood(pkt);
+    } else {
+      MESH_DEBUG_PRINTLN("ERROR: unable to create advertisement packet!");
+    }
+  }
+};
+
+#if defined(P_LORA_SCLK)
+SPIClass spi;
+CustomSX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY, spi);
+#else
+CustomSX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY);
+#endif
+StdRNG fast_rng;
+SimpleMeshTables tables;
+MyMesh the_mesh(*new CustomSX1262Wrapper(radio, board), *new ArduinoMillis(), fast_rng, *new VolatileRTCClock(), tables);
+
+void halt() {
+  while (1) ;
+}
+
+void setup() {
+  Serial.begin(115200);
+  delay(5000);
+
+  board.begin();
+#if defined(P_LORA_SCLK)
+  spi.begin(P_LORA_SCLK, P_LORA_MISO, P_LORA_MOSI);
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+#else
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+#endif
+  if (status != RADIOLIB_ERR_NONE) {
+    Serial.print("ERROR: radio init failed: ");
+    Serial.println(status);
+    halt();
+  }
+
+  SPIFFS.begin(true);
+  IdentityStore store(SPIFFS, "/identity");
+  if (!store.load("_main", the_mesh.self_id)) {
+    the_mesh.self_id = mesh::LocalIdentity(the_mesh.getRNG());  // create new random identity
+    store.save("_main", the_mesh.self_id);
+  }
+
+  Serial.print("Repeater ID: ");
+  mesh::Utils::printHex(Serial, the_mesh.self_id.pub_key, PUB_KEY_SIZE); Serial.println();
+
+  the_mesh.begin();
+
+  // send out initial Advertisement to the mesh
+  the_mesh.sendSelfAdvertisement();
+}
+
+void loop() {
+  the_mesh.loop();
+
+  // TODO: periodically check for OLD/inactive entries in known_clients[], and evict
+}

examples/simple_secure_chat/main.cpp

@@ -0,0 +1,334 @@
+#include <Arduino.h>   // needed for PlatformIO
+#include <Mesh.h>
+#include <SPIFFS.h>
+
+#define RADIOLIB_STATIC_ONLY 1
+#include <RadioLib.h>
+#include <helpers/RadioLibWrappers.h>
+#include <helpers/ArduinoHelpers.h>
+#include <helpers/StaticPoolPacketManager.h>
+#include <helpers/SimpleSeenTable.h>
+
+/* ---------------------------------- CONFIGURATION ------------------------------------- */
+
+//#define RUN_AS_ALICE    true
+
+#if RUN_AS_ALICE
+  const char* alice_private = "B8830658388B2DDF22C3A508F4386975970CDE1E2A2A495C8F3B5727957A97629255A1392F8BA4C26A023A0DAB78BFC64D261C8E51507496DD39AFE3707E7B42";
+#else
+  const char *bob_private = "30BAA23CCB825D8020A59C936D0AB7773B07356020360FC77192813640BAD375E43BBF9A9A7537E4B9614610F1F2EF874AAB390BA9B0C2F01006B01FDDFEFF0C";
+#endif
+  const char *alice_public = "106A5136EC0DD797650AD204C065CF9B66095F6ED772B0822187785D65E11B1F";
+  const char *bob_public = "020BCEDAC07D709BD8507EC316EB5A7FF2F0939AF5057353DCE7E4436A1B9681";
+
+#ifdef HELTEC_LORA_V3
+  #include <helpers/HeltecV3Board.h>
+  static HeltecV3Board board;
+#else
+  #error "need to provide a 'board' object"
+#endif
+
+#define FLOOD_SEND_TIMEOUT_MILLIS   4000
+#define DIRECT_SEND_TIMEOUT_MILLIS  2000
+
+/* -------------------------------------------------------------------------------------- */
+
+static unsigned long txt_send_timeout;
+
+#define MAX_CONTACTS         1
+#define MAX_SEARCH_RESULTS   1
+
+#define MAX_TEXT_LEN    (10*CIPHER_BLOCK_SIZE)  // must be LESS than (MAX_PACKET_PAYLOAD - 4 - CIPHER_MAC_SIZE - 1)
+
+struct ContactInfo {
+  mesh::Identity id;
+  const char* name;
+  int out_path_len;
+  uint8_t out_path[MAX_PATH_SIZE];
+  uint32_t last_advert_timestamp;
+  uint8_t shared_secret[PUB_KEY_SIZE];
+};
+
+class MyMesh : public mesh::Mesh {
+public:
+  SimpleSeenTable* _table;
+  mesh::LocalIdentity self_id;
+  ContactInfo contacts[MAX_CONTACTS];
+  int num_contacts;
+
+  void addContact(const char* name, const mesh::Identity& id) {
+    if (num_contacts < MAX_CONTACTS) {
+      contacts[num_contacts].id = id;
+      contacts[num_contacts].name = name;
+      contacts[num_contacts].last_advert_timestamp = 0;
+      contacts[num_contacts].out_path_len = -1;
+      // only need to calculate the shared_secret once, for better performance
+      self_id.calcSharedSecret(contacts[num_contacts].shared_secret, id);
+      num_contacts++;
+    }
+  }
+
+protected:
+  int  matching_peer_indexes[MAX_SEARCH_RESULTS];
+
+  int searchPeersByHash(const uint8_t* hash) override {
+    int n = 0;
+    for (int i = 0; i < num_contacts && n < MAX_SEARCH_RESULTS; i++) {
+      if (contacts[i].id.isHashMatch(hash)) {
+        matching_peer_indexes[n++] = i;  // store the INDEXES of matching contacts (for subsequent 'peer' methods)
+      }
+    }
+    return n;
+  }
+
+  void onAdvertRecv(mesh::Packet* packet, const mesh::Identity& id, uint32_t timestamp, const uint8_t* app_data, size_t app_data_len) override {
+    Serial.print("Valid Advertisement -> ");
+    mesh::Utils::printHex(Serial, id.pub_key, PUB_KEY_SIZE);
+    Serial.println();
+
+    for (int i = 0; i < num_contacts; i++) {
+      ContactInfo& from = contacts[i];
+      // check for replay attacks 
+      if (id.matches(from.id) && timestamp > from.last_advert_timestamp) {  // is from one of our contacts
+        from.last_advert_timestamp = timestamp;
+        Serial.printf("   From contact: %s\n", from.name);
+      }
+    }
+  }
+
+  void getPeerSharedSecret(uint8_t* dest_secret, int peer_idx) override {
+    int i = matching_peer_indexes[peer_idx];
+    if (i >= 0 && i < num_contacts) {
+      // lookup pre-calculated shared_secret
+      memcpy(dest_secret, contacts[i].shared_secret, PUB_KEY_SIZE);
+    } else {
+      MESH_DEBUG_PRINTLN("getPeerSHharedSecret: Invalid peer idx: %d", i);
+    }
+  }
+
+  void onPeerDataRecv(mesh::Packet* packet, uint8_t type, int sender_idx, uint8_t* data, size_t len) override {
+    if (type == PAYLOAD_TYPE_TXT_MSG) {
+      if (_table->hasSeenPacket(packet)) return;
+
+      int i = matching_peer_indexes[sender_idx];
+      if (i < 0 && i >= num_contacts) {
+        MESH_DEBUG_PRINTLN("onPeerDataRecv: Invalid sender idx: %d", i);
+        return;
+      }
+
+      ContactInfo& from = contacts[i];
+
+      uint32_t timestamp;
+      memcpy(&timestamp, data, 4);  // timestamp (by sender's RTC clock - which could be wrong)
+
+      // len can be > original length, but 'text' will be padded with zeroes
+      data[len] = 0; // need to make a C string again, with null terminator
+
+      Serial.print("MSG -> from ");
+      Serial.print(from.name);
+      Serial.print(": ");
+      Serial.println((const char *) &data[4]);
+
+      uint32_t ack_hash;    // calc truncated hash of the message timestamp + text + sender pub_key, to prove to sender that we got it
+      mesh::Utils::sha256((uint8_t *) &ack_hash, 4, data, len, from.id.pub_key, PUB_KEY_SIZE);
+
+      if (packet->isRouteFlood()) {
+        // let this sender know path TO here, so they can use sendDirect(), and ALSO encode the ACK
+        mesh::Packet* path = createPathReturn(from.id, from.shared_secret, packet->path, packet->path_len,
+                                              PAYLOAD_TYPE_ACK, (uint8_t *) &ack_hash, 4);
+        if (path) sendFlood(path);
+      } else {
+        mesh::Packet* ack = createAck(ack_hash);
+        if (ack) {
+          if (from.out_path_len < 0) {
+            sendFlood(ack);
+          } else {
+            sendDirect(ack, from.out_path, from.out_path_len);
+          }
+        }
+      }
+    }
+  }
+
+  void onPeerPathRecv(mesh::Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) override {
+    if (_table->hasSeenPacket(packet)) return;
+
+    int i = matching_peer_indexes[sender_idx];
+    if (i < 0 && i >= num_contacts) {
+      MESH_DEBUG_PRINTLN("onPeerPathRecv: Invalid sender idx: %d", i);
+      return;
+    }
+
+    ContactInfo& from = contacts[i];
+    Serial.printf("PATH to: %s, path_len=%d\n", from.name, (uint32_t) path_len);
+
+    memcpy(from.out_path, path, from.out_path_len = path_len);  // store a copy of path, for sendDirect()
+
+    if (packet->isRouteFlood()) {
+      // send a reciprocal return path to sender, but send DIRECTLY!
+      mesh::Packet* rpath = createPathReturn(from.id, from.shared_secret, packet->path, packet->path_len, 0, NULL, 0);
+      if (rpath) sendDirect(rpath, path, path_len);
+    }
+
+    if (extra_type == PAYLOAD_TYPE_ACK && extra_len >= 4) {
+      // also got an encoded ACK!
+      processAck(extra);
+    }
+  }
+
+  void onAckRecv(mesh::Packet* packet, uint32_t ack_crc) override {
+    processAck((uint8_t *)&ack_crc);
+  }
+
+  void processAck(const uint8_t *data) {
+    if (memcmp(data, &expected_ack_crc, 4) == 0) {     // got an ACK from recipient
+      Serial.println("Got ACK!");
+      // NOTE: the same ACK can be received multiple times!
+      expected_ack_crc = 0;  // reset our expected hash, now that we have received ACK
+      txt_send_timeout = 0;
+    }
+  }
+
+public:
+  uint32_t expected_ack_crc;
+
+  MyMesh(mesh::Radio& radio, mesh::RNG& rng, mesh::RTCClock& rtc, SimpleSeenTable& table)
+     : mesh::Mesh(radio, *new ArduinoMillis(), rng, rtc, *new StaticPoolPacketManager(16)), _table(&table)
+  {
+    num_contacts = 0;
+  }
+
+  mesh::Packet* composeMsgPacket(ContactInfo& recipient, const char *text) {
+    int text_len = strlen(text);
+    if (text_len > MAX_TEXT_LEN) return NULL;
+
+    uint8_t temp[4+MAX_TEXT_LEN+1];
+    uint32_t timestamp = getRTCClock()->getCurrentTime();
+    memcpy(temp, &timestamp, 4);   // mostly an extra blob to help make packet_hash unique
+    memcpy(&temp[4], text, text_len);
+
+    // calc expected ACK reply
+    mesh::Utils::sha256((uint8_t *)&expected_ack_crc, 4, (const uint8_t *) temp, 4 + text_len, self_id.pub_key, PUB_KEY_SIZE);
+
+    return createDatagram(PAYLOAD_TYPE_TXT_MSG, recipient.id, recipient.shared_secret, temp, 4 + text_len);
+  }
+
+  void sendSelfAnnounce() {
+    mesh::Packet* announce = createAdvert(self_id);
+    if (announce) {
+      sendFlood(announce);
+      Serial.println("   (advert sent).");
+    } else {
+      Serial.println("   ERROR: unable to create packet.");
+    }
+  }
+};
+
+SPIClass spi;
+StdRNG fast_rng;
+SimpleSeenTable table;
+SX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY, spi);
+MyMesh the_mesh(*new RadioLibWrapper(radio, board), fast_rng, *new VolatileRTCClock(), table);
+
+void halt() {
+  while (1) ;
+}
+
+static char command[MAX_TEXT_LEN+1];
+
+void setup() {
+  Serial.begin(115200);
+
+  board.begin();
+  spi.begin(P_LORA_SCLK, P_LORA_MISO, P_LORA_MOSI);
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+  if (status != RADIOLIB_ERR_NONE) {
+    Serial.print("ERROR: radio init failed: ");
+    Serial.println(status);
+    halt();
+  }
+
+  fast_rng.begin(radio.random(0x7FFFFFFF));
+
+#if RUN_AS_ALICE
+  Serial.println("   --- user: Alice ---");
+  the_mesh.self_id = mesh::LocalIdentity(alice_private, alice_public);
+  the_mesh.addContact("Bob", mesh::Identity(bob_public));
+#else
+  Serial.println("   --- user: Bob ---");
+  the_mesh.self_id = mesh::LocalIdentity(bob_private, bob_public);
+  the_mesh.addContact("Alice", mesh::Identity(alice_public));
+#endif
+  Serial.println("Help:");
+  Serial.println("  enter 'ann' to announce presence to mesh");
+  Serial.println("  enter 'send {message text}' to send a message");
+
+  the_mesh.begin();
+
+  command[0] = 0;
+  txt_send_timeout = 0;
+
+  // send out initial Announce to the mesh
+  the_mesh.sendSelfAnnounce();
+}
+
+void loop() {
+  int len = strlen(command);
+  while (Serial.available() && len < sizeof(command)-1) {
+    char c = Serial.read();
+    if (c != '\n') { 
+      command[len++] = c;
+      command[len] = 0;
+    }
+    Serial.print(c);
+  }
+  if (len == sizeof(command)-1) {  // command buffer full
+    command[sizeof(command)-1] = '\r';
+  }
+
+  if (len > 0 && command[len - 1] == '\r') {  // received complete line
+    command[len - 1] = 0;  // replace newline with C string null terminator
+
+    if (memcmp(command, "send ", 5) == 0) {
+      // TODO: some way to select recipient??
+      ContactInfo& recipient = the_mesh.contacts[0];  // just send to first contact for now
+
+      const char *text = &command[5];
+      mesh::Packet* pkt = the_mesh.composeMsgPacket(recipient, text);
+      if (pkt) {
+        if (recipient.out_path_len < 0) {
+          the_mesh.sendFlood(pkt);
+          txt_send_timeout = the_mesh.futureMillis(FLOOD_SEND_TIMEOUT_MILLIS);
+        } else {
+          the_mesh.sendDirect(pkt, recipient.out_path, recipient.out_path_len);
+          txt_send_timeout = the_mesh.futureMillis(DIRECT_SEND_TIMEOUT_MILLIS);
+        }
+        Serial.println("   (message sent)");
+      } else {
+        Serial.println("   ERROR: unable to create packet.");
+      }
+    } else if (strcmp(command, "ann") == 0) {
+      the_mesh.sendSelfAnnounce();
+    } else if (strcmp(command, "key") == 0) {
+      mesh::LocalIdentity new_id(the_mesh.getRNG());
+      new_id.printTo(Serial);
+    } else {
+      Serial.print("   ERROR: unknown command: "); Serial.println(command);
+    }
+
+    command[0] = 0;  // reset command buffer
+  }
+
+  if (txt_send_timeout && the_mesh.millisHasNowPassed(txt_send_timeout)) {
+    // failed to get an ACK
+    ContactInfo& recipient = the_mesh.contacts[0];  // just the one contact for now
+    Serial.println("   ERROR: timed out, no ACK.");
+
+    // path to our contact is now possibly broken, fallback to Flood mode
+    recipient.out_path_len = -1;
+
+    txt_send_timeout = 0;
+  }
+
+  the_mesh.loop();
+}

examples/test_admin/main.cpp

@@ -0,0 +1,304 @@
+#include <Arduino.h>   // needed for PlatformIO
+#include <Mesh.h>
+#include <SPIFFS.h>
+
+#define RADIOLIB_STATIC_ONLY 1
+#include <RadioLib.h>
+#include <helpers/CustomSX1262Wrapper.h>
+#include <helpers/ArduinoHelpers.h>
+#include <helpers/SimpleSeenTable.h>
+#include <helpers/StaticPoolPacketManager.h>
+
+/* ---------------------------------- CONFIGURATION ------------------------------------- */
+
+#define  ADMIN_PASSWORD  "h^(kl@#)"
+
+#ifdef HELTEC_LORA_V3
+  #include <helpers/HeltecV3Board.h>
+  static HeltecV3Board board;
+#else
+  #error "need to provide a 'board' object"
+#endif
+
+/* -------------------------------------------------------------------------------------- */
+
+#define MAX_TEXT_LEN    (10*CIPHER_BLOCK_SIZE)  // must be LESS than (MAX_PACKET_PAYLOAD - FROM_HASH_LEN - CIPHER_MAC_SIZE - 1)
+
+#define CMD_GET_STATS      0x01
+#define CMD_SET_CLOCK      0x02
+#define CMD_SEND_ANNOUNCE  0x03
+#define CMD_SET_CONFIG     0x04
+
+struct RepeaterStats {
+  uint16_t batt_milli_volts;
+  uint16_t curr_tx_queue_len;
+  uint16_t curr_free_queue_len;
+  int16_t  last_rssi;
+  uint32_t n_packets_recv;
+  uint32_t n_packets_sent;
+  uint32_t total_air_time_secs;
+  uint32_t total_up_time_secs;
+};
+
+class MyMesh : public mesh::Mesh {
+  SimpleSeenTable* _table;
+  uint32_t last_advert_timestamp = 0;
+  mesh::Identity server_id;
+  uint8_t server_secret[PUB_KEY_SIZE];
+  int server_path_len = -1;
+  uint8_t server_path[MAX_PATH_SIZE];
+  bool got_adv = false;
+
+protected:
+  int searchPeersByHash(const uint8_t* hash) override {
+    if (got_adv && server_id.isHashMatch(hash)) {
+      return 1;
+    }
+    return 0;  // not found
+  }
+
+  void onAdvertRecv(mesh::Packet* packet, const mesh::Identity& id, uint32_t timestamp, const uint8_t* app_data, size_t app_data_len) override {
+    if (memcmp(app_data, "repeater:", 9) == 0) {
+      Serial.println("Received advertisement from a repeater!");
+
+      // check for replay attacks
+      if (timestamp > last_advert_timestamp) {
+        last_advert_timestamp = timestamp;
+
+        server_id = id;
+        self_id.calcSharedSecret(server_secret, id);  // calc ECDH shared secret
+        got_adv = true;
+
+        // 'login' to repeater. (mainly lets it know our public key)
+        uint32_t now = getRTCClock()->getCurrentTime(); // important, need timestamp in packet, so that packet_hash will be unique
+        uint8_t temp[4 + 8];
+        memcpy(temp, &now, 4);
+        memcpy(&temp[4], ADMIN_PASSWORD, 8);
+
+        mesh::Packet* login = createDatagram(PAYLOAD_TYPE_ANON_REQ, server_id, server_secret, temp, sizeof(temp));
+        if (login) sendFlood(login);  // server_path won't be known yet
+      }
+    }
+  }
+
+  void handleResponse(const uint8_t* reply, size_t reply_len) {
+    if (reply_len >= 4 + sizeof(RepeaterStats)) {      // got an GET_STATS reply from repeater
+      RepeaterStats stats;
+      memcpy(&stats, &reply[4], sizeof(stats));
+      Serial.println("Repeater Stats:");
+      Serial.printf("  battery: %d mV\n", (uint32_t) stats.batt_milli_volts);
+      Serial.printf("  tx queue: %d\n", (uint32_t) stats.curr_tx_queue_len);
+      Serial.printf("  free queue: %d\n", (uint32_t) stats.curr_free_queue_len);
+      Serial.printf("  last RSSI: %d\n", (int) stats.last_rssi);
+      Serial.printf("  num recv: %d\n", stats.n_packets_recv);
+      Serial.printf("  num sent: %d\n", stats.n_packets_sent);
+      Serial.printf("  air time (secs): %d\n", stats.total_air_time_secs);
+      Serial.printf("  up time (secs): %d\n", stats.total_up_time_secs);
+    } else if (reply_len > 4) {   // got an SET_* reply from repeater
+      char tmp[MAX_PACKET_PAYLOAD];
+      memcpy(tmp, &reply[4], reply_len - 4);
+      tmp[reply_len - 4] = 0;  // make a C string of reply
+
+      Serial.print("Reply: "); Serial.println(tmp);
+    }
+  }
+
+  void onPeerDataRecv(mesh::Packet* packet, uint8_t type, int sender_idx, uint8_t* data, size_t len) override {
+    if (type == PAYLOAD_TYPE_RESPONSE) {
+      if (_table->hasSeenPacket(packet)) return;
+
+      handleResponse(data, len);
+
+      if (packet->isRouteFlood()) {
+        // let server know path TO here, so they can use sendDirect() for future ping responses
+        mesh::Packet* path = createPathReturn(server_id, server_secret, packet->path, packet->path_len, 0, NULL, 0);
+        if (path) sendFlood(path);
+      }
+    }
+  }
+
+  void onPeerPathRecv(mesh::Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) override {
+    if (_table->hasSeenPacket(packet)) return;
+
+    // must be from server_id 
+    Serial.printf("PATH to repeater, path_len=%d\n", (uint32_t) path_len);
+
+    memcpy(server_path, path, server_path_len = path_len);  // store a copy of path, for sendDirect()
+
+    if (packet->isRouteFlood()) {
+      // send a reciprocal return path to sender, but send DIRECTLY!
+      mesh::Packet* rpath = createPathReturn(server_id, server_secret, packet->path, packet->path_len, 0, NULL, 0);
+      if (rpath) sendDirect(rpath, path, path_len);
+    }
+
+    if (extra_type == PAYLOAD_TYPE_RESPONSE) {
+      handleResponse(extra, extra_len);
+    }
+  }
+
+public:
+  MyMesh(mesh::Radio& radio, mesh::RNG& rng, mesh::RTCClock& rtc, SimpleSeenTable& table)
+     : mesh::Mesh(radio, *new ArduinoMillis(), rng, rtc, *new StaticPoolPacketManager(16)), _table(&table)
+  {
+  }
+
+  mesh::Packet* createStatsRequest(uint32_t max_age) {
+    uint8_t payload[9];
+    uint32_t now = getRTCClock()->getCurrentTime();
+    memcpy(payload, &now, 4);
+    payload[4] = CMD_GET_STATS;
+    memcpy(&payload[5], &max_age, 4);
+
+    return createDatagram(PAYLOAD_TYPE_REQ, server_id, server_secret, payload, sizeof(payload));
+  }
+
+  mesh::Packet* createSetClockRequest(uint32_t timestamp) {
+    uint8_t payload[9];
+    uint32_t now = getRTCClock()->getCurrentTime();
+    memcpy(payload, &now, 4);
+    payload[4] = CMD_SET_CLOCK;
+    memcpy(&payload[5], &now, 4);  // repeated :-(
+
+    return createDatagram(PAYLOAD_TYPE_REQ, server_id, server_secret, payload, sizeof(payload));
+  }
+
+  mesh::Packet* createSetAirtimeFactorRequest(float airtime_factor) {
+    uint8_t payload[16];
+    uint32_t now = getRTCClock()->getCurrentTime();
+    memcpy(payload, &now, 4);
+    payload[4] = CMD_SET_CONFIG;
+    sprintf((char *) &payload[5], "AF%f", airtime_factor);
+
+    return createDatagram(PAYLOAD_TYPE_REQ, server_id, server_secret, payload, sizeof(payload));
+  }
+
+  mesh::Packet* createAnnounceRequest() {
+    uint8_t payload[5];
+    uint32_t now = getRTCClock()->getCurrentTime();
+    memcpy(payload, &now, 4);
+    payload[4] = CMD_SEND_ANNOUNCE;
+
+    return createDatagram(PAYLOAD_TYPE_REQ, server_id, server_secret, payload, sizeof(payload));
+  }
+
+  mesh::Packet* parseCommand(char* command) {
+    if (strcmp(command, "stats") == 0) {
+      return createStatsRequest(60*60);    // max_age = one hour
+    } else if (memcmp(command, "setclock ", 9) == 0) {
+      uint32_t timestamp = atol(&command[9]);
+      return createSetClockRequest(timestamp);
+    } else if (memcmp(command, "set AF=", 7) == 0) {
+      float factor = atof(&command[7]);
+      return createSetAirtimeFactorRequest(factor);
+    } else if (strcmp(command, "ann") == 0) {
+      return createAnnounceRequest();
+    }
+    return NULL;  // unknown command
+  }
+
+  void sendCommand(mesh::Packet* pkt) {
+    if (server_path_len < 0) {
+      sendFlood(pkt);
+    } else {
+      sendDirect(pkt, server_path, server_path_len);
+    }
+  }
+};
+
+StdRNG fast_rng;
+SimpleSeenTable table;
+#if defined(P_LORA_SCLK)
+SPIClass spi;
+CustomSX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY, spi);
+#else
+CustomSX1262 radio = new Module(P_LORA_NSS, P_LORA_DIO_1, P_LORA_RESET, P_LORA_BUSY);
+#endif
+MyMesh the_mesh(*new CustomSX1262Wrapper(radio, board), fast_rng, *new VolatileRTCClock(), table);
+
+void halt() {
+  while (1) ;
+}
+
+static char command[MAX_TEXT_LEN+1];
+
+#include <SHA256.h>
+
+void setup() {
+  Serial.begin(115200);
+  delay(5000);
+
+  board.begin();
+#if defined(P_LORA_SCLK)
+  spi.begin(P_LORA_SCLK, P_LORA_MISO, P_LORA_MOSI);
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+#else
+  int status = radio.begin(915.0, 250, 9, 5, RADIOLIB_SX126X_SYNC_WORD_PRIVATE, 22);
+#endif
+  if (status != RADIOLIB_ERR_NONE) {
+    Serial.print("ERROR: radio init failed: ");
+    Serial.println(status);
+    halt();
+  }
+
+  fast_rng.begin(radio.random(0x7FFFFFFF));
+
+/* add this to tests
+  uint8_t mac_encrypted[CIPHER_MAC_SIZE+CIPHER_BLOCK_SIZE];
+  const char *orig_msg = "original";
+  int enc_len = mesh::Utils::encryptThenMAC(mesh.admin_secret, mac_encrypted, (const uint8_t *) orig_msg, strlen(orig_msg));
+  char decrypted[CIPHER_BLOCK_SIZE*2];
+  int len = mesh::Utils::MACThenDecrypt(mesh.admin_secret, (uint8_t *)decrypted, mac_encrypted, enc_len);
+  if (len > 0) {
+    decrypted[len] = 0;
+    Serial.print("decrypted text: "); Serial.println(decrypted);
+  } else {
+    Serial.println("MACs DONT match!");
+  }
+*/
+
+  Serial.println("Help:");
+  Serial.println("  enter 'key' to generate new keypair");
+  Serial.println("  enter 'stats' to request repeater stats");
+  Serial.println("  enter 'setclock {unix-epoch-seconds}' to set repeater's clock");
+  Serial.println("  enter 'set AF={factor}' to set airtime budget factor");
+  Serial.println("  enter 'ann' to make repeater re-announce to mesh");
+
+  the_mesh.begin();
+
+  command[0] = 0;
+}
+
+void loop() {
+  int len = strlen(command);
+  while (Serial.available() && len < sizeof(command)-1) {
+    char c = Serial.read();
+    if (c != '\n') { 
+      command[len++] = c;
+      command[len] = 0;
+    }
+    Serial.print(c);
+  }
+  if (len == sizeof(command)-1) {  // command buffer full
+    command[sizeof(command)-1] = '\r';
+  }
+
+  if (len > 0 && command[len - 1] == '\r') {  // received complete line
+    command[len - 1] = 0;  // replace newline with C string null terminator
+
+    if (strcmp(command, "key") == 0) {
+      mesh::LocalIdentity new_id(the_mesh.getRNG());
+      new_id.printTo(Serial);
+    } else {
+      mesh::Packet* pkt = the_mesh.parseCommand(command);
+      if (pkt) { 
+        the_mesh.sendCommand(pkt);
+        Serial.println("   (request sent)");
+      } else {
+        Serial.print("   ERROR: unknown command: "); Serial.println(command);
+      }
+    }
+    command[0] = 0;  // reset command buffer
+  }
+
+  the_mesh.loop();
+}

include/README

@@ -0,0 +1,39 @@
+
+This directory is intended for project header files.
+
+A header file is a file containing C declarations and macro definitions
+to be shared between several project source files. You request the use of a
+header file in your project source file (C, C++, etc) located in `src` folder
+by including it, with the C preprocessing directive `#include'.
+
+```src/main.c
+
+#include "header.h"
+
+int main (void)
+{
+ ...
+}
+```
+
+Including a header file produces the same results as copying the header file
+into each source file that needs it. Such copying would be time-consuming
+and error-prone. With a header file, the related declarations appear
+in only one place. If they need to be changed, they can be changed in one
+place, and programs that include the header file will automatically use the
+new version when next recompiled. The header file eliminates the labor of
+finding and changing all the copies as well as the risk that a failure to
+find one copy will result in inconsistencies within a program.
+
+In C, the usual convention is to give header files names that end with `.h'.
+It is most portable to use only letters, digits, dashes, and underscores in
+header file names, and at most one dot.
+
+Read more about using header files in official GCC documentation:
+
+* Include Syntax
+* Include Operation
+* Once-Only Headers
+* Computed Includes
+
+https://gcc.gnu.org/onlinedocs/cpp/Header-Files.html

lib/README

@@ -0,0 +1,46 @@
+
+This directory is intended for project specific (private) libraries.
+PlatformIO will compile them to static libraries and link into executable file.
+
+The source code of each library should be placed in a an own separate directory
+("lib/your_library_name/[here are source files]").
+
+For example, see a structure of the following two libraries `Foo` and `Bar`:
+
+|--lib
+|  |
+|  |--Bar
+|  |  |--docs
+|  |  |--examples
+|  |  |--src
+|  |     |- Bar.c
+|  |     |- Bar.h
+|  |  |- library.json (optional, custom build options, etc) https://docs.platformio.org/page/librarymanager/config.html
+|  |
+|  |--Foo
+|  |  |- Foo.c
+|  |  |- Foo.h
+|  |
+|  |- README --> THIS FILE
+|
+|- platformio.ini
+|--src
+   |- main.c
+
+and a contents of `src/main.c`:
+```
+#include <Foo.h>
+#include <Bar.h>
+
+int main (void)
+{
+  ...
+}
+
+```
+
+PlatformIO Library Dependency Finder will find automatically dependent
+libraries scanning project source files.
+
+More information about PlatformIO Library Dependency Finder
+- https://docs.platformio.org/page/librarymanager/ldf.html

lib/ed25519/add_scalar.c

@@ -0,0 +1,69 @@
+#include "ed_25519.h"
+#include "ge.h"
+#include "sc.h"
+#include "sha512.h"
+
+
+/* see http://crypto.stackexchange.com/a/6215/4697 */
+void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar) {
+    const unsigned char SC_1[32] = {1}; /* scalar with value 1 */
+    
+    unsigned char n[32]; 
+    ge_p3 nB;
+    ge_p1p1 A_p1p1;
+    ge_p3 A;
+    ge_p3 public_key_unpacked;
+    ge_cached T;
+
+    sha512_context hash;
+    unsigned char hashbuf[64];
+
+    int i;
+
+    /* copy the scalar and clear highest bit */
+    for (i = 0; i < 31; ++i) {
+        n[i] = scalar[i];
+    }
+    n[31] = scalar[31] & 127;
+
+    /* private key: a = n + t */
+    if (private_key) {
+        sc_muladd(private_key, SC_1, n, private_key);
+
+        // https://github.com/orlp/ed25519/issues/3
+        sha512_init(&hash);
+        sha512_update(&hash, private_key + 32, 32);
+        sha512_update(&hash, scalar, 32);
+        sha512_final(&hash, hashbuf);
+        for (i = 0; i < 32; ++i) {
+            private_key[32 + i] = hashbuf[i];
+        }
+    }
+
+    /* public key: A = nB + T */
+    if (public_key) {
+        /* if we know the private key we don't need a point addition, which is faster */
+        /* using a "timing attack" you could find out wether or not we know the private
+           key, but this information seems rather useless - if this is important pass
+           public_key and private_key seperately in 2 function calls */
+        if (private_key) {
+            ge_scalarmult_base(&A, private_key);
+        } else {
+            /* unpack public key into T */
+            ge_frombytes_negate_vartime(&public_key_unpacked, public_key);
+            fe_neg(public_key_unpacked.X, public_key_unpacked.X); /* undo negate */
+            fe_neg(public_key_unpacked.T, public_key_unpacked.T); /* undo negate */
+            ge_p3_to_cached(&T, &public_key_unpacked);
+
+            /* calculate n*B */
+            ge_scalarmult_base(&nB, n);
+
+            /* A = n*B + T */
+            ge_add(&A_p1p1, &nB, &T);
+            ge_p1p1_to_p3(&A, &A_p1p1);
+        }
+            
+        /* pack public key */
+        ge_p3_tobytes(public_key, &A);
+    }
+}

lib/ed25519/ed_25519.h

@@ -0,0 +1,40 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+// Nightcracker's Ed25519 -  https://github.com/orlp/ed25519
+
+#include <stddef.h>
+
+#if defined(_WIN32)
+    #if defined(ED25519_BUILD_DLL)
+        #define ED25519_DECLSPEC __declspec(dllexport)
+    #elif defined(ED25519_DLL)
+        #define ED25519_DECLSPEC __declspec(dllimport)
+    #else
+        #define ED25519_DECLSPEC
+    #endif
+#else
+    #define ED25519_DECLSPEC
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef ED25519_NO_SEED
+int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed);
+#endif
+
+void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed);
+void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key);
+int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key);
+void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar);
+void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

lib/ed25519/fe.c

@@ -0,0 +1,1491 @@
+#include "fixedint.h"
+#include "fe.h"
+
+
+/*
+    helper functions
+*/
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+
+
+/*
+    h = 0
+*/
+
+void fe_0(fe h) {
+    h[0] = 0;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = 1
+*/
+
+void fe_1(fe h) {
+    h[0] = 1;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = f + g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+    Postconditions:
+       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 + g0;
+    int32_t h1 = f1 + g1;
+    int32_t h2 = f2 + g2;
+    int32_t h3 = f3 + g3;
+    int32_t h4 = f4 + g4;
+    int32_t h5 = f5 + g5;
+    int32_t h6 = f6 + g6;
+    int32_t h7 = f7 + g7;
+    int32_t h8 = f8 + g8;
+    int32_t h9 = f9 + g9;
+    
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+    Replace (f,g) with (g,g) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cmov(fe f, const fe g, unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+}
+
+/*
+    Replace (f,g) with (g,f) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+    g[0] = g0 ^ x0;
+    g[1] = g1 ^ x1;
+    g[2] = g2 ^ x2;
+    g[3] = g3 ^ x3;
+    g[4] = g4 ^ x4;
+    g[5] = g5 ^ x5;
+    g[6] = g6 ^ x6;
+    g[7] = g7 ^ x7;
+    g[8] = g8 ^ x8;
+    g[9] = g9 ^ x9;
+}
+
+
+
+/*
+    h = f
+*/
+
+void fe_copy(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    
+    h[0] = f0;
+    h[1] = f1;
+    h[2] = f2;
+    h[3] = f3;
+    h[4] = f4;
+    h[5] = f5;
+    h[6] = f6;
+    h[7] = f7;
+    h[8] = f8;
+    h[9] = f9;
+}
+
+
+
+/*
+    Ignores top bit of h.
+*/
+
+void fe_frombytes(fe h, const unsigned char *s) {
+    int64_t h0 = load_4(s);
+    int64_t h1 = load_3(s + 4) << 6;
+    int64_t h2 = load_3(s + 7) << 5;
+    int64_t h3 = load_3(s + 10) << 3;
+    int64_t h4 = load_3(s + 13) << 2;
+    int64_t h5 = load_4(s + 16);
+    int64_t h6 = load_3(s + 20) << 7;
+    int64_t h7 = load_3(s + 23) << 5;
+    int64_t h8 = load_3(s + 26) << 4;
+    int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+
+void fe_invert(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    fe t3;
+    int i;
+
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t2, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t1, t2);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(out, t1, t0);
+}
+
+
+
+/*
+    return 1 if f is in {1,3,5,...,q-2}
+    return 0 if f is in {0,2,4,...,q-1}
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f) {
+    unsigned char s[32];
+
+    fe_tobytes(s, f);
+    
+    return s[0] & 1;
+}
+
+
+
+/*
+    return 1 if f == 0
+    return 0 if f != 0
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnonzero(const fe f) {
+    unsigned char s[32];
+    unsigned char r;
+
+    fe_tobytes(s, f);
+
+    r = s[0];
+    #define F(i) r |= s[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return r != 0;
+}
+
+
+
+/*
+    h = f * g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+       |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+    Postconditions:
+       |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+    */
+
+    /*
+    Notes on implementation strategy:
+
+    Using schoolbook multiplication.
+    Karatsuba would save a little in some cost models.
+
+    Most multiplications by 2 and 19 are 32-bit precomputations;
+    cheaper than 64-bit postcomputations.
+
+    There is one remaining multiplication by 19 in the carry chain;
+    one *19 precomputation can be merged into this,
+    but the resulting data flow is considerably less clean.
+
+    There are 12 carries below.
+    10 of them are 2-way parallelizable and vectorizable.
+    Can get away with 11 carries, but then data flow is much deeper.
+
+    With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+    int32_t g3_19 = 19 * g3;
+    int32_t g4_19 = 19 * g4;
+    int32_t g5_19 = 19 * g5;
+    int32_t g6_19 = 19 * g6;
+    int32_t g7_19 = 19 * g7;
+    int32_t g8_19 = 19 * g8;
+    int32_t g9_19 = 19 * g9;
+    int32_t f1_2 = 2 * f1;
+    int32_t f3_2 = 2 * f3;
+    int32_t f5_2 = 2 * f5;
+    int32_t f7_2 = 2 * f7;
+    int32_t f9_2 = 2 * f9;
+    int64_t f0g0    = f0   * (int64_t) g0;
+    int64_t f0g1    = f0   * (int64_t) g1;
+    int64_t f0g2    = f0   * (int64_t) g2;
+    int64_t f0g3    = f0   * (int64_t) g3;
+    int64_t f0g4    = f0   * (int64_t) g4;
+    int64_t f0g5    = f0   * (int64_t) g5;
+    int64_t f0g6    = f0   * (int64_t) g6;
+    int64_t f0g7    = f0   * (int64_t) g7;
+    int64_t f0g8    = f0   * (int64_t) g8;
+    int64_t f0g9    = f0   * (int64_t) g9;
+    int64_t f1g0    = f1   * (int64_t) g0;
+    int64_t f1g1_2  = f1_2 * (int64_t) g1;
+    int64_t f1g2    = f1   * (int64_t) g2;
+    int64_t f1g3_2  = f1_2 * (int64_t) g3;
+    int64_t f1g4    = f1   * (int64_t) g4;
+    int64_t f1g5_2  = f1_2 * (int64_t) g5;
+    int64_t f1g6    = f1   * (int64_t) g6;
+    int64_t f1g7_2  = f1_2 * (int64_t) g7;
+    int64_t f1g8    = f1   * (int64_t) g8;
+    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+    int64_t f2g0    = f2   * (int64_t) g0;
+    int64_t f2g1    = f2   * (int64_t) g1;
+    int64_t f2g2    = f2   * (int64_t) g2;
+    int64_t f2g3    = f2   * (int64_t) g3;
+    int64_t f2g4    = f2   * (int64_t) g4;
+    int64_t f2g5    = f2   * (int64_t) g5;
+    int64_t f2g6    = f2   * (int64_t) g6;
+    int64_t f2g7    = f2   * (int64_t) g7;
+    int64_t f2g8_19 = f2   * (int64_t) g8_19;
+    int64_t f2g9_19 = f2   * (int64_t) g9_19;
+    int64_t f3g0    = f3   * (int64_t) g0;
+    int64_t f3g1_2  = f3_2 * (int64_t) g1;
+    int64_t f3g2    = f3   * (int64_t) g2;
+    int64_t f3g3_2  = f3_2 * (int64_t) g3;
+    int64_t f3g4    = f3   * (int64_t) g4;
+    int64_t f3g5_2  = f3_2 * (int64_t) g5;
+    int64_t f3g6    = f3   * (int64_t) g6;
+    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+    int64_t f3g8_19 = f3   * (int64_t) g8_19;
+    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+    int64_t f4g0    = f4   * (int64_t) g0;
+    int64_t f4g1    = f4   * (int64_t) g1;
+    int64_t f4g2    = f4   * (int64_t) g2;
+    int64_t f4g3    = f4   * (int64_t) g3;
+    int64_t f4g4    = f4   * (int64_t) g4;
+    int64_t f4g5    = f4   * (int64_t) g5;
+    int64_t f4g6_19 = f4   * (int64_t) g6_19;
+    int64_t f4g7_19 = f4   * (int64_t) g7_19;
+    int64_t f4g8_19 = f4   * (int64_t) g8_19;
+    int64_t f4g9_19 = f4   * (int64_t) g9_19;
+    int64_t f5g0    = f5   * (int64_t) g0;
+    int64_t f5g1_2  = f5_2 * (int64_t) g1;
+    int64_t f5g2    = f5   * (int64_t) g2;
+    int64_t f5g3_2  = f5_2 * (int64_t) g3;
+    int64_t f5g4    = f5   * (int64_t) g4;
+    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+    int64_t f5g6_19 = f5   * (int64_t) g6_19;
+    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+    int64_t f5g8_19 = f5   * (int64_t) g8_19;
+    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+    int64_t f6g0    = f6   * (int64_t) g0;
+    int64_t f6g1    = f6   * (int64_t) g1;
+    int64_t f6g2    = f6   * (int64_t) g2;
+    int64_t f6g3    = f6   * (int64_t) g3;
+    int64_t f6g4_19 = f6   * (int64_t) g4_19;
+    int64_t f6g5_19 = f6   * (int64_t) g5_19;
+    int64_t f6g6_19 = f6   * (int64_t) g6_19;
+    int64_t f6g7_19 = f6   * (int64_t) g7_19;
+    int64_t f6g8_19 = f6   * (int64_t) g8_19;
+    int64_t f6g9_19 = f6   * (int64_t) g9_19;
+    int64_t f7g0    = f7   * (int64_t) g0;
+    int64_t f7g1_2  = f7_2 * (int64_t) g1;
+    int64_t f7g2    = f7   * (int64_t) g2;
+    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+    int64_t f7g4_19 = f7   * (int64_t) g4_19;
+    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+    int64_t f7g6_19 = f7   * (int64_t) g6_19;
+    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+    int64_t f7g8_19 = f7   * (int64_t) g8_19;
+    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+    int64_t f8g0    = f8   * (int64_t) g0;
+    int64_t f8g1    = f8   * (int64_t) g1;
+    int64_t f8g2_19 = f8   * (int64_t) g2_19;
+    int64_t f8g3_19 = f8   * (int64_t) g3_19;
+    int64_t f8g4_19 = f8   * (int64_t) g4_19;
+    int64_t f8g5_19 = f8   * (int64_t) g5_19;
+    int64_t f8g6_19 = f8   * (int64_t) g6_19;
+    int64_t f8g7_19 = f8   * (int64_t) g7_19;
+    int64_t f8g8_19 = f8   * (int64_t) g8_19;
+    int64_t f8g9_19 = f8   * (int64_t) g9_19;
+    int64_t f9g0    = f9   * (int64_t) g0;
+    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+    int64_t f9g2_19 = f9   * (int64_t) g2_19;
+    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+    int64_t f9g4_19 = f9   * (int64_t) g4_19;
+    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+    int64_t f9g6_19 = f9   * (int64_t) g6_19;
+    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+    int64_t f9g8_19 = f9   * (int64_t) g8_19;
+    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+    int64_t h1 = f0g1 + f1g0   + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+    int64_t h2 = f0g2 + f1g1_2 + f2g0   + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+    int64_t h3 = f0g3 + f1g2   + f2g1   + f3g0   + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+    int64_t h4 = f0g4 + f1g3_2 + f2g2   + f3g1_2 + f4g0   + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+    int64_t h5 = f0g5 + f1g4   + f2g3   + f3g2   + f4g1   + f5g0   + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+    int64_t h6 = f0g6 + f1g5_2 + f2g4   + f3g3_2 + f4g2   + f5g1_2 + f6g0   + f7g9_38 + f8g8_19 + f9g7_38;
+    int64_t h7 = f0g7 + f1g6   + f2g5   + f3g4   + f4g3   + f5g2   + f6g1   + f7g0   + f8g9_19 + f9g8_19;
+    int64_t h8 = f0g8 + f1g7_2 + f2g6   + f3g5_2 + f4g4   + f5g3_2 + f6g2   + f7g1_2 + f8g0   + f9g9_38;
+    int64_t h9 = f0g9 + f1g8   + f2g7   + f3g6   + f4g5   + f5g4   + f6g3   + f7g2   + f8g1   + f9g0   ;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f * 121666
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h, fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int64_t h0 = f0 * (int64_t) 121666;
+    int64_t h1 = f1 * (int64_t) 121666;
+    int64_t h2 = f2 * (int64_t) 121666;
+    int64_t h3 = f3 * (int64_t) 121666;
+    int64_t h4 = f4 * (int64_t) 121666;
+    int64_t h5 = f5 * (int64_t) 121666;
+    int64_t h6 = f6 * (int64_t) 121666;
+    int64_t h7 = f7 * (int64_t) 121666;
+    int64_t h8 = f8 * (int64_t) 121666;
+    int64_t h9 = f9 * (int64_t) 121666;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+    carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_neg(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t h0 = -f0;
+    int32_t h1 = -f1;
+    int32_t h2 = -f2;
+    int32_t h3 = -f3;
+    int32_t h4 = -f4;
+    int32_t h5 = -f5;
+    int32_t h6 = -f6;
+    int32_t h7 = -f7;
+    int32_t h8 = -f8;
+    int32_t h9 = -f9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+void fe_pow22523(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    int i;
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(out, t0, z);
+    return;
+}
+
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq2(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    h0 += h0;
+    h1 += h1;
+    h2 += h2;
+    h3 += h3;
+    h4 += h4;
+    h5 += h5;
+    h6 += h6;
+    h7 += h7;
+    h8 += h8;
+    h9 += h9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 - g0;
+    int32_t h1 = f1 - g1;
+    int32_t h2 = f2 - g2;
+    int32_t h3 = f3 - g3;
+    int32_t h4 = f4 - g4;
+    int32_t h5 = f5 - g5;
+    int32_t h6 = f6 - g6;
+    int32_t h7 = f7 - g7;
+    int32_t h8 = f8 - g8;
+    int32_t h9 = f9 - g9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s, const fe h) {
+    int32_t h0 = h[0];
+    int32_t h1 = h[1];
+    int32_t h2 = h[2];
+    int32_t h3 = h[3];
+    int32_t h4 = h[4];
+    int32_t h5 = h[5];
+    int32_t h6 = h[6];
+    int32_t h7 = h[7];
+    int32_t h8 = h[8];
+    int32_t h9 = h[9];
+    int32_t q;
+    int32_t carry0;
+    int32_t carry1;
+    int32_t carry2;
+    int32_t carry3;
+    int32_t carry4;
+    int32_t carry5;
+    int32_t carry6;
+    int32_t carry7;
+    int32_t carry8;
+    int32_t carry9;
+    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+    q = (h0 + q) >> 26;
+    q = (h1 + q) >> 25;
+    q = (h2 + q) >> 26;
+    q = (h3 + q) >> 25;
+    q = (h4 + q) >> 26;
+    q = (h5 + q) >> 25;
+    q = (h6 + q) >> 26;
+    q = (h7 + q) >> 25;
+    q = (h8 + q) >> 26;
+    q = (h9 + q) >> 25;
+    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+    h0 += 19 * q;
+    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+    carry0 = h0 >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry1 = h1 >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry2 = h2 >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry3 = h3 >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry4 = h4 >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry5 = h5 >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry6 = h6 >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry7 = h7 >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry8 = h8 >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = h9 >> 25;
+    h9 -= carry9 << 25;
+
+    /* h10 = carry9 */
+    /*
+    Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+    Have h0+...+2^230 h9 between 0 and 2^255-1;
+    evidently 2^255 h10-2^255 q = 0.
+    Goal: Output h0+...+2^230 h9.
+    */
+    s[0] = (unsigned char) (h0 >> 0);
+    s[1] = (unsigned char) (h0 >> 8);
+    s[2] = (unsigned char) (h0 >> 16);
+    s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
+    s[4] = (unsigned char) (h1 >> 6);
+    s[5] = (unsigned char) (h1 >> 14);
+    s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
+    s[7] = (unsigned char) (h2 >> 5);
+    s[8] = (unsigned char) (h2 >> 13);
+    s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
+    s[10] = (unsigned char) (h3 >> 3);
+    s[11] = (unsigned char) (h3 >> 11);
+    s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
+    s[13] = (unsigned char) (h4 >> 2);
+    s[14] = (unsigned char) (h4 >> 10);
+    s[15] = (unsigned char) (h4 >> 18);
+    s[16] = (unsigned char) (h5 >> 0);
+    s[17] = (unsigned char) (h5 >> 8);
+    s[18] = (unsigned char) (h5 >> 16);
+    s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
+    s[20] = (unsigned char) (h6 >> 7);
+    s[21] = (unsigned char) (h6 >> 15);
+    s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
+    s[23] = (unsigned char) (h7 >> 5);
+    s[24] = (unsigned char) (h7 >> 13);
+    s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
+    s[26] = (unsigned char) (h8 >> 4);
+    s[27] = (unsigned char) (h8 >> 12);
+    s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
+    s[29] = (unsigned char) (h9 >> 2);
+    s[30] = (unsigned char) (h9 >> 10);
+    s[31] = (unsigned char) (h9 >> 18);
+}

lib/ed25519/fe.h

@@ -0,0 +1,41 @@
+#ifndef FE_H
+#define FE_H
+
+#include "fixedint.h"
+
+
+/*
+    fe means field element.
+    Here the field is \Z/(2^255-19).
+    An element t, entries t[0]...t[9], represents the integer
+    t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
+    Bounds on each t[i] vary depending on context.
+*/
+
+
+typedef int32_t fe[10];
+
+
+void fe_0(fe h);
+void fe_1(fe h);
+
+void fe_frombytes(fe h, const unsigned char *s);
+void fe_tobytes(unsigned char *s, const fe h);
+
+void fe_copy(fe h, const fe f);
+int fe_isnegative(const fe f);
+int fe_isnonzero(const fe f);
+void fe_cmov(fe f, const fe g, unsigned int b);
+void fe_cswap(fe f, fe g, unsigned int b);
+
+void fe_neg(fe h, const fe f);
+void fe_add(fe h, const fe f, const fe g);
+void fe_invert(fe out, const fe z);
+void fe_sq(fe h, const fe f);
+void fe_sq2(fe h, const fe f);
+void fe_mul(fe h, const fe f, const fe g);
+void fe_mul121666(fe h, fe f);
+void fe_pow22523(fe out, const fe z);
+void fe_sub(fe h, const fe f, const fe g);
+
+#endif

lib/ed25519/fixedint.h

@@ -0,0 +1,72 @@
+/*
+    Portable header to provide the 32 and 64 bits type.
+
+    Not a compatible replacement for <stdint.h>, do not blindly use it as such.
+*/
+
+#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED)
+    #include <stdint.h>
+    #define FIXEDINT_H_INCLUDED
+
+    #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C)
+        #include <limits.h>
+        #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX))
+    #endif
+#endif
+
+
+#ifndef FIXEDINT_H_INCLUDED
+    #define FIXEDINT_H_INCLUDED
+    
+    #include <limits.h>
+
+    /* (u)int32_t */
+    #ifndef uint32_t
+        #if (ULONG_MAX == 0xffffffffUL)
+            typedef unsigned long uint32_t;
+        #elif (UINT_MAX == 0xffffffffUL)
+            typedef unsigned int uint32_t;
+        #elif (USHRT_MAX == 0xffffffffUL)
+            typedef unsigned short uint32_t;
+        #endif
+    #endif
+
+
+    #ifndef int32_t
+        #if (LONG_MAX == 0x7fffffffL)
+            typedef signed long int32_t;
+        #elif (INT_MAX == 0x7fffffffL)
+            typedef signed int int32_t;
+        #elif (SHRT_MAX == 0x7fffffffL)
+            typedef signed short int32_t;
+        #endif
+    #endif
+
+
+    /* (u)int64_t */
+    #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__GNUC__)
+        __extension__ typedef long long int64_t;
+        __extension__ typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC)
+        typedef __int64 int64_t;
+        typedef unsigned __int64 uint64_t;
+
+        #define UINT64_C(v) v ##UI64
+        #define INT64_C(v) v ##I64
+    #endif
+#endif

lib/ed25519/ge.c

@@ -0,0 +1,467 @@
+#include "ge.h"
+#include "precomp_data.h"
+
+
+/*
+r = p + q
+*/
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YplusX);
+    fe_mul(r->Y, r->Y, q->YminusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+static void slide(signed char *r, const unsigned char *a) {
+    int i;
+    int b;
+    int k;
+
+    for (i = 0; i < 256; ++i) {
+        r[i] = 1 & (a[i >> 3] >> (i & 7));
+    }
+
+    for (i = 0; i < 256; ++i)
+        if (r[i]) {
+            for (b = 1; b <= 6 && i + b < 256; ++b) {
+                if (r[i + b]) {
+                    if (r[i] + (r[i + b] << b) <= 15) {
+                        r[i] += r[i + b] << b;
+                        r[i + b] = 0;
+                    } else if (r[i] - (r[i + b] << b) >= -15) {
+                        r[i] -= r[i + b] << b;
+
+                        for (k = i + b; k < 256; ++k) {
+                            if (!r[k]) {
+                                r[k] = 1;
+                                break;
+                            }
+
+                            r[k] = 0;
+                        }
+                    } else {
+                        break;
+                    }
+                }
+            }
+        }
+}
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
+    signed char aslide[256];
+    signed char bslide[256];
+    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+    ge_p1p1 t;
+    ge_p3 u;
+    ge_p3 A2;
+    int i;
+    slide(aslide, a);
+    slide(bslide, b);
+    ge_p3_to_cached(&Ai[0], A);
+    ge_p3_dbl(&t, A);
+    ge_p1p1_to_p3(&A2, &t);
+    ge_add(&t, &A2, &Ai[0]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[1], &u);
+    ge_add(&t, &A2, &Ai[1]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[2], &u);
+    ge_add(&t, &A2, &Ai[2]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[3], &u);
+    ge_add(&t, &A2, &Ai[3]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[4], &u);
+    ge_add(&t, &A2, &Ai[4]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[5], &u);
+    ge_add(&t, &A2, &Ai[5]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[6], &u);
+    ge_add(&t, &A2, &Ai[6]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[7], &u);
+    ge_p2_0(r);
+
+    for (i = 255; i >= 0; --i) {
+        if (aslide[i] || bslide[i]) {
+            break;
+        }
+    }
+
+    for (; i >= 0; --i) {
+        ge_p2_dbl(&t, r);
+
+        if (aslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_add(&t, &u, &Ai[aslide[i] / 2]);
+        } else if (aslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+        }
+
+        if (bslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+        } else if (bslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+        }
+
+        ge_p1p1_to_p2(r, &t);
+    }
+}
+
+
+static const fe d = {
+    -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
+};
+
+static const fe sqrtm1 = {
+    -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
+};
+
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) {
+    fe u;
+    fe v;
+    fe v3;
+    fe vxx;
+    fe check;
+    fe_frombytes(h->Y, s);
+    fe_1(h->Z);
+    fe_sq(u, h->Y);
+    fe_mul(v, u, d);
+    fe_sub(u, u, h->Z);     /* u = y^2-1 */
+    fe_add(v, v, h->Z);     /* v = dy^2+1 */
+    fe_sq(v3, v);
+    fe_mul(v3, v3, v);      /* v3 = v^3 */
+    fe_sq(h->X, v3);
+    fe_mul(h->X, h->X, v);
+    fe_mul(h->X, h->X, u);  /* x = uv^7 */
+    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+    fe_mul(h->X, h->X, v3);
+    fe_mul(h->X, h->X, u);  /* x = uv^3(uv^7)^((q-5)/8) */
+    fe_sq(vxx, h->X);
+    fe_mul(vxx, vxx, v);
+    fe_sub(check, vxx, u);  /* vx^2-u */
+
+    if (fe_isnonzero(check)) {
+        fe_add(check, vxx, u); /* vx^2+u */
+
+        if (fe_isnonzero(check)) {
+            return -1;
+        }
+
+        fe_mul(h->X, h->X, sqrtm1);
+    }
+
+    if (fe_isnegative(h->X) == (s[31] >> 7)) {
+        fe_neg(h->X, h->X);
+    }
+
+    fe_mul(h->T, h->X, h->Y);
+    return 0;
+}
+
+
+/*
+r = p + q
+*/
+
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yplusx);
+    fe_mul(r->Y, r->Y, q->yminusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yminusx);
+    fe_mul(r->Y, r->Y, q->yplusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+}
+
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+    fe_mul(r->T, p->X, p->Y);
+}
+
+
+void ge_p2_0(ge_p2 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+}
+
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+    fe t0;
+
+    fe_sq(r->X, p->X);
+    fe_sq(r->Z, p->Y);
+    fe_sq2(r->T, p->Z);
+    fe_add(r->Y, p->X, p->Y);
+    fe_sq(t0, r->Y);
+    fe_add(r->Y, r->Z, r->X);
+    fe_sub(r->Z, r->Z, r->X);
+    fe_sub(r->X, t0, r->Y);
+    fe_sub(r->T, r->T, r->Z);
+}
+
+
+void ge_p3_0(ge_p3 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+    fe_0(h->T);
+}
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+    ge_p2 q;
+    ge_p3_to_p2(&q, p);
+    ge_p2_dbl(r, &q);
+}
+
+
+
+/*
+r = p
+*/
+
+static const fe d2 = {
+    -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
+};
+
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+    fe_add(r->YplusX, p->Y, p->X);
+    fe_sub(r->YminusX, p->Y, p->X);
+    fe_copy(r->Z, p->Z);
+    fe_mul(r->T2d, p->T, d2);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+    fe_copy(r->X, p->X);
+    fe_copy(r->Y, p->Y);
+    fe_copy(r->Z, p->Z);
+}
+
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
+
+
+static unsigned char equal(signed char b, signed char c) {
+    unsigned char ub = b;
+    unsigned char uc = c;
+    unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+    uint64_t y = x; /* 0: yes; 1..255: no */
+    y -= 1; /* large: yes; 0..254: no */
+    y >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) y;
+}
+
+static unsigned char negative(signed char b) {
+    uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+    x >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) x;
+}
+
+static void cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) {
+    fe_cmov(t->yplusx, u->yplusx, b);
+    fe_cmov(t->yminusx, u->yminusx, b);
+    fe_cmov(t->xy2d, u->xy2d, b);
+}
+
+
+static void select(ge_precomp *t, int pos, signed char b) {
+    ge_precomp minust;
+    unsigned char bnegative = negative(b);
+    unsigned char babs = b - (((-bnegative) & b) << 1);
+    fe_1(t->yplusx);
+    fe_1(t->yminusx);
+    fe_0(t->xy2d);
+    cmov(t, &base[pos][0], equal(babs, 1));
+    cmov(t, &base[pos][1], equal(babs, 2));
+    cmov(t, &base[pos][2], equal(babs, 3));
+    cmov(t, &base[pos][3], equal(babs, 4));
+    cmov(t, &base[pos][4], equal(babs, 5));
+    cmov(t, &base[pos][5], equal(babs, 6));
+    cmov(t, &base[pos][6], equal(babs, 7));
+    cmov(t, &base[pos][7], equal(babs, 8));
+    fe_copy(minust.yplusx, t->yminusx);
+    fe_copy(minust.yminusx, t->yplusx);
+    fe_neg(minust.xy2d, t->xy2d);
+    cmov(t, &minust, bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
+    signed char e[64];
+    signed char carry;
+    ge_p1p1 r;
+    ge_p2 s;
+    ge_precomp t;
+    int i;
+
+    for (i = 0; i < 32; ++i) {
+        e[2 * i + 0] = (a[i] >> 0) & 15;
+        e[2 * i + 1] = (a[i] >> 4) & 15;
+    }
+
+    /* each e[i] is between 0 and 15 */
+    /* e[63] is between 0 and 7 */
+    carry = 0;
+
+    for (i = 0; i < 63; ++i) {
+        e[i] += carry;
+        carry = e[i] + 8;
+        carry >>= 4;
+        e[i] -= carry << 4;
+    }
+
+    e[63] += carry;
+    /* each e[i] is between -8 and 8 */
+    ge_p3_0(h);
+
+    for (i = 1; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    ge_p3_dbl(&r, h);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p3(h, &r);
+
+    for (i = 0; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YminusX);
+    fe_mul(r->Y, r->Y, q->YplusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+void ge_tobytes(unsigned char *s, const ge_p2 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}

lib/ed25519/ge.h

@@ -0,0 +1,74 @@
+#ifndef GE_H
+#define GE_H
+
+#include "fe.h"
+
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h);
+void ge_tobytes(unsigned char *s, const ge_p2 *h);
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s);
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b);
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a);
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
+void ge_p2_0(ge_p2 *h);
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p);
+void ge_p3_0(ge_p3 *h);
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p);
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p);
+
+#endif

lib/ed25519/key_exchange.c

@@ -0,0 +1,79 @@
+#include "ed_25519.h"
+#include "fe.h"
+
+void ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key) {
+    unsigned char e[32];
+    unsigned int i;
+    
+    fe x1;
+    fe x2;
+    fe z2;
+    fe x3;
+    fe z3;
+    fe tmp0;
+    fe tmp1;
+
+    int pos;
+    unsigned int swap;
+    unsigned int b;
+
+    /* copy the private key and make sure it's valid */
+    for (i = 0; i < 32; ++i) {
+        e[i] = private_key[i];
+    }
+
+    e[0] &= 248;
+    e[31] &= 63;
+    e[31] |= 64;
+
+    /* unpack the public key and convert edwards to montgomery */
+    /* due to CodesInChaos: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p */
+    fe_frombytes(x1, public_key);
+    fe_1(tmp1);
+    fe_add(tmp0, x1, tmp1);
+    fe_sub(tmp1, tmp1, x1);
+    fe_invert(tmp1, tmp1);
+    fe_mul(x1, tmp0, tmp1);
+
+    fe_1(x2);
+    fe_0(z2);
+    fe_copy(x3, x1);
+    fe_1(z3);
+
+    swap = 0;
+    for (pos = 254; pos >= 0; --pos) {
+        b = e[pos / 8] >> (pos & 7);
+        b &= 1;
+        swap ^= b;
+        fe_cswap(x2, x3, swap);
+        fe_cswap(z2, z3, swap);
+        swap = b;
+
+        /* from montgomery.h */
+        fe_sub(tmp0, x3, z3);
+        fe_sub(tmp1, x2, z2);
+        fe_add(x2, x2, z2);
+        fe_add(z2, x3, z3);
+        fe_mul(z3, tmp0, x2);
+        fe_mul(z2, z2, tmp1);
+        fe_sq(tmp0, tmp1);
+        fe_sq(tmp1, x2);
+        fe_add(x3, z3, z2);
+        fe_sub(z2, z3, z2);
+        fe_mul(x2, tmp1, tmp0);
+        fe_sub(tmp1, tmp1, tmp0);
+        fe_sq(z2, z2);
+        fe_mul121666(z3, tmp1);
+        fe_sq(x3, x3);
+        fe_add(tmp0, tmp0, z3);
+        fe_mul(z3, x1, z2);
+        fe_mul(z2, tmp1, tmp0);
+    }
+
+    fe_cswap(x2, x3, swap);
+    fe_cswap(z2, z3, swap);
+
+    fe_invert(z2, z2);
+    fe_mul(x2, x2, z2);
+    fe_tobytes(shared_secret, x2);
+}

lib/ed25519/keypair.c

@@ -0,0 +1,16 @@
+#include "ed_25519.h"
+#include "sha512.h"
+#include "ge.h"
+
+
+void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed) {
+    ge_p3 A;
+
+    sha512(seed, 32, private_key);
+    private_key[0] &= 248;
+    private_key[31] &= 63;
+    private_key[31] |= 64;
+
+    ge_scalarmult_base(&A, private_key);
+    ge_p3_tobytes(public_key, &A);
+}

lib/ed25519/license.txt

@@ -0,0 +1,16 @@
+Copyright (c) 2015 Orson Peters <orsonpeters@gmail.com>
+
+This software is provided 'as-is', without any express or implied warranty. In no event will the
+authors be held liable for any damages arising from the use of this software.
+
+Permission is granted to anyone to use this software for any purpose, including commercial
+applications, and to alter it and redistribute it freely, subject to the following restrictions:
+
+1. The origin of this software must not be misrepresented; you must not claim that you wrote the
+   original software. If you use this software in a product, an acknowledgment in the product
+   documentation would be appreciated but is not required.
+
+2. Altered source versions must be plainly marked as such, and must not be misrepresented as
+   being the original software.
+
+3. This notice may not be removed or altered from any source distribution.

lib/ed25519/precomp_data.h

@@ -0,0 +1,1391 @@
+static const ge_precomp Bi[8] = {
+    {
+        { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+        { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+        { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+    },
+    {
+        { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+        { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+        { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+    },
+    {
+        { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+        { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+        { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+    },
+    {
+        { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+        { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+        { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+    },
+    {
+        { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
+        { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
+        { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
+    },
+    {
+        { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
+        { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
+        { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
+    },
+    {
+        { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
+        { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
+        { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
+    },
+    {
+        { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
+        { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
+        { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
+    },
+};
+
+
+/* base[i][j] = (j+1)*256^i*B */
+static const ge_precomp base[32][8] = {
+    {
+        {
+            { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+            { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+            { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+        },
+        {
+            { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
+            { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
+            { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
+        },
+        {
+            { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+            { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+            { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+        },
+        {
+            { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
+            { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
+            { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
+        },
+        {
+            { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+            { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+            { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+        },
+        {
+            { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
+            { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
+            { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
+        },
+        {
+            { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+            { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+            { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+        },
+        {
+            { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
+            { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
+            { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
+        },
+    },
+    {
+        {
+            { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
+            { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
+            { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
+        },
+        {
+            { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
+            { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
+            { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
+        },
+        {
+            { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
+            { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
+            { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
+        },
+        {
+            { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
+            { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
+            { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
+        },
+        {
+            { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
+            { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
+            { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
+        },
+        {
+            { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
+            { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
+            { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
+        },
+        {
+            { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
+            { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
+            { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
+        },
+        {
+            { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
+            { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
+            { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
+        },
+    },
+    {
+        {
+            { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
+            { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
+            { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
+        },
+        {
+            { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 },
+            { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 },
+            { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 },
+        },
+        {
+            { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 },
+            { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 },
+            { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 },
+        },
+        {
+            { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 },
+            { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 },
+            { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 },
+        },
+        {
+            { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 },
+            { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 },
+            { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 },
+        },
+        {
+            { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 },
+            { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 },
+            { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 },
+        },
+        {
+            { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 },
+            { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 },
+            { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 },
+        },
+        {
+            { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 },
+            { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 },
+            { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 },
+        },
+    },
+    {
+        {
+            { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 },
+            { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 },
+            { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 },
+        },
+        {
+            { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 },
+            { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 },
+            { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 },
+        },
+        {
+            { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 },
+            { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 },
+            { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 },
+        },
+        {
+            { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 },
+            { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 },
+            { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 },
+        },
+        {
+            { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 },
+            { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 },
+            { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 },
+        },
+        {
+            { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 },
+            { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 },
+            { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 },
+        },
+        {
+            { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 },
+            { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 },
+            { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 },
+        },
+        {
+            { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 },
+            { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 },
+            { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 },
+        },
+    },
+    {
+        {
+            { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 },
+            { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 },
+            { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 },
+        },
+        {
+            { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 },
+            { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 },
+            { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 },
+        },
+        {
+            { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 },
+            { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 },
+            { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 },
+        },
+        {
+            { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 },
+            { -26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727 },
+            { 28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420 },
+        },
+        {
+            { -32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003 },
+            { -1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605 },
+            { -30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384 },
+        },
+        {
+            { -26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701 },
+            { -23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683 },
+            { 29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708 },
+        },
+        {
+            { -3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563 },
+            { -19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260 },
+            { -5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387 },
+        },
+        {
+            { -19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672 },
+            { 23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686 },
+            { -24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665 },
+        },
+    },
+    {
+        {
+            { 11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182 },
+            { -31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277 },
+            { 14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628 },
+        },
+        {
+            { -4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474 },
+            { -26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539 },
+            { -25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822 },
+        },
+        {
+            { -10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970 },
+            { 19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756 },
+            { -24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508 },
+        },
+        {
+            { -26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683 },
+            { -10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655 },
+            { -20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158 },
+        },
+        {
+            { -4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125 },
+            { -15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839 },
+            { -20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664 },
+        },
+        {
+            { 27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294 },
+            { -18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899 },
+            { -11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070 },
+        },
+        {
+            { 3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294 },
+            { -15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949 },
+            { -21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083 },
+        },
+        {
+            { 31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420 },
+            { -5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940 },
+            { 29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396 },
+        },
+    },
+    {
+        {
+            { -12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567 },
+            { 20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127 },
+            { -16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294 },
+        },
+        {
+            { -12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887 },
+            { 22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964 },
+            { 16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195 },
+        },
+        {
+            { 9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244 },
+            { 24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999 },
+            { -1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762 },
+        },
+        {
+            { -18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274 },
+            { -33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236 },
+            { -16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605 },
+        },
+        {
+            { -13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761 },
+            { -22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884 },
+            { -6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482 },
+        },
+        {
+            { -24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638 },
+            { -11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490 },
+            { -32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170 },
+        },
+        {
+            { 5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736 },
+            { 10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124 },
+            { -17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392 },
+        },
+        {
+            { 8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029 },
+            { 6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048 },
+            { 28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958 },
+        },
+    },
+    {
+        {
+            { 24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593 },
+            { 26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071 },
+            { -11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692 },
+        },
+        {
+            { 11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687 },
+            { -160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441 },
+            { -20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001 },
+        },
+        {
+            { -938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460 },
+            { -19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007 },
+            { -21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762 },
+        },
+        {
+            { 15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005 },
+            { -9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674 },
+            { 4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035 },
+        },
+        {
+            { 7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590 },
+            { -2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957 },
+            { -30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812 },
+        },
+        {
+            { 33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740 },
+            { -18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122 },
+            { -27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158 },
+        },
+        {
+            { 8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885 },
+            { 26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140 },
+            { 19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857 },
+        },
+        {
+            { 801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155 },
+            { 19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260 },
+            { 19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483 },
+        },
+    },
+    {
+        {
+            { -3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677 },
+            { 32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815 },
+            { 22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751 },
+        },
+        {
+            { -16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203 },
+            { -11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208 },
+            { 1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230 },
+        },
+        {
+            { 16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850 },
+            { -21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389 },
+            { -9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968 },
+        },
+        {
+            { -11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689 },
+            { 14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880 },
+            { 5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304 },
+        },
+        {
+            { 30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632 },
+            { -3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412 },
+            { 20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566 },
+        },
+        {
+            { -20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038 },
+            { -26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232 },
+            { -1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943 },
+        },
+        {
+            { 17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856 },
+            { 23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738 },
+            { 15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971 },
+        },
+        {
+            { -27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718 },
+            { -13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697 },
+            { -11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883 },
+        },
+    },
+    {
+        {
+            { 5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912 },
+            { -26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358 },
+            { 3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849 },
+        },
+        {
+            { 29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307 },
+            { -14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977 },
+            { -6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335 },
+        },
+        {
+            { -29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644 },
+            { -22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616 },
+            { -27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735 },
+        },
+        {
+            { -21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099 },
+            { 29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341 },
+            { -936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336 },
+        },
+        {
+            { -23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646 },
+            { 31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425 },
+            { -17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388 },
+        },
+        {
+            { -31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743 },
+            { -16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822 },
+            { -8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462 },
+        },
+        {
+            { 18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985 },
+            { 9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702 },
+            { -22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797 },
+        },
+        {
+            { 21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293 },
+            { 27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100 },
+            { 19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688 },
+        },
+    },
+    {
+        {
+            { 12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186 },
+            { 2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610 },
+            { -2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707 },
+        },
+        {
+            { 7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220 },
+            { 915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025 },
+            { 32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044 },
+        },
+        {
+            { 32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992 },
+            { -4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027 },
+            { 21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197 },
+        },
+        {
+            { 8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901 },
+            { 31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952 },
+            { 19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878 },
+        },
+        {
+            { -28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390 },
+            { 32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730 },
+            { 2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730 },
+        },
+        {
+            { -19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180 },
+            { -30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272 },
+            { -15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715 },
+        },
+        {
+            { -22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970 },
+            { -31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772 },
+            { -17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865 },
+        },
+        {
+            { 15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750 },
+            { 20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373 },
+            { 32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348 },
+        },
+    },
+    {
+        {
+            { 9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144 },
+            { -22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195 },
+            { 5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086 },
+        },
+        {
+            { -13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684 },
+            { -8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518 },
+            { -2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233 },
+        },
+        {
+            { -5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793 },
+            { -2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794 },
+            { 580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435 },
+        },
+        {
+            { 23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921 },
+            { 13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518 },
+            { 2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563 },
+        },
+        {
+            { 14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278 },
+            { -27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024 },
+            { 4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030 },
+        },
+        {
+            { 10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783 },
+            { 27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717 },
+            { 6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844 },
+        },
+        {
+            { 14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333 },
+            { 16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048 },
+            { 22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760 },
+        },
+        {
+            { -4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760 },
+            { -15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757 },
+            { -2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112 },
+        },
+    },
+    {
+        {
+            { -19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468 },
+            { 3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184 },
+            { 10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289 },
+        },
+        {
+            { 15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066 },
+            { 24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882 },
+            { 13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226 },
+        },
+        {
+            { 16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101 },
+            { 29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279 },
+            { -6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811 },
+        },
+        {
+            { 27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709 },
+            { 20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714 },
+            { -2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121 },
+        },
+        {
+            { 9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464 },
+            { 12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847 },
+            { 13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400 },
+        },
+        {
+            { 4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414 },
+            { -15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158 },
+            { 17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045 },
+        },
+        {
+            { -461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415 },
+            { -5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459 },
+            { -31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079 },
+        },
+        {
+            { 21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412 },
+            { -20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743 },
+            { -14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836 },
+        },
+    },
+    {
+        {
+            { 12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022 },
+            { 18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429 },
+            { -6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065 },
+        },
+        {
+            { 30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861 },
+            { 10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000 },
+            { -33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101 },
+        },
+        {
+            { 32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815 },
+            { 29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642 },
+            { 10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966 },
+        },
+        {
+            { 25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574 },
+            { -21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742 },
+            { -18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689 },
+        },
+        {
+            { 12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020 },
+            { -10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772 },
+            { 3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982 },
+        },
+        {
+            { -14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953 },
+            { -16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218 },
+            { -17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265 },
+        },
+        {
+            { 29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073 },
+            { -3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325 },
+            { -11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798 },
+        },
+        {
+            { -4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870 },
+            { -7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863 },
+            { -13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927 },
+        },
+    },
+    {
+        {
+            { -2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267 },
+            { -9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663 },
+            { 22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862 },
+        },
+        {
+            { -25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673 },
+            { 15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943 },
+            { 15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020 },
+        },
+        {
+            { -4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238 },
+            { 11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064 },
+            { 14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795 },
+        },
+        {
+            { 15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052 },
+            { -10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904 },
+            { 29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531 },
+        },
+        {
+            { -13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979 },
+            { -5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841 },
+            { 10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431 },
+        },
+        {
+            { 10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324 },
+            { -31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940 },
+            { 10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320 },
+        },
+        {
+            { -15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184 },
+            { 14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114 },
+            { 30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878 },
+        },
+        {
+            { 12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784 },
+            { -2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091 },
+            { -16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585 },
+        },
+    },
+    {
+        {
+            { -8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208 },
+            { 10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864 },
+            { 17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661 },
+        },
+        {
+            { 7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233 },
+            { 26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212 },
+            { -12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525 },
+        },
+        {
+            { -24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068 },
+            { 9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397 },
+            { -8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988 },
+        },
+        {
+            { 5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889 },
+            { 32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038 },
+            { 14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697 },
+        },
+        {
+            { 20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875 },
+            { -25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905 },
+            { -25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656 },
+        },
+        {
+            { 11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818 },
+            { 27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714 },
+            { 10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203 },
+        },
+        {
+            { 20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931 },
+            { -30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024 },
+            { -23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084 },
+        },
+        {
+            { -1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204 },
+            { 20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817 },
+            { 27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667 },
+        },
+    },
+    {
+        {
+            { 11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504 },
+            { -12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768 },
+            { -19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255 },
+        },
+        {
+            { 6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790 },
+            { 1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438 },
+            { -22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333 },
+        },
+        {
+            { 17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971 },
+            { 31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905 },
+            { 29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409 },
+        },
+        {
+            { 12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409 },
+            { 6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499 },
+            { -8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363 },
+        },
+        {
+            { 28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664 },
+            { -11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324 },
+            { -21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940 },
+        },
+        {
+            { 13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990 },
+            { -17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914 },
+            { -25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290 },
+        },
+        {
+            { 24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257 },
+            { -6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433 },
+            { -16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236 },
+        },
+        {
+            { -12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045 },
+            { 11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093 },
+            { -1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347 },
+        },
+    },
+    {
+        {
+            { -28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191 },
+            { -15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507 },
+            { -12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906 },
+        },
+        {
+            { 3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018 },
+            { -16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109 },
+            { -23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926 },
+        },
+        {
+            { -24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528 },
+            { 8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625 },
+            { -32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286 },
+        },
+        {
+            { 2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033 },
+            { 27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866 },
+            { 21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896 },
+        },
+        {
+            { 30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075 },
+            { 26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347 },
+            { -22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437 },
+        },
+        {
+            { -5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165 },
+            { -18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588 },
+            { -32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193 },
+        },
+        {
+            { -19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017 },
+            { -28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883 },
+            { 21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961 },
+        },
+        {
+            { 8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043 },
+            { 29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663 },
+            { -20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362 },
+        },
+    },
+    {
+        {
+            { -33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860 },
+            { 2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466 },
+            { -24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063 },
+        },
+        {
+            { -26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997 },
+            { -1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295 },
+            { -13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369 },
+        },
+        {
+            { 9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385 },
+            { 18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109 },
+            { 2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906 },
+        },
+        {
+            { 4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424 },
+            { -19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185 },
+            { 7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962 },
+        },
+        {
+            { -7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325 },
+            { 10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593 },
+            { 696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404 },
+        },
+        {
+            { -11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644 },
+            { 17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801 },
+            { 26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804 },
+        },
+        {
+            { -31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884 },
+            { -586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577 },
+            { -9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849 },
+        },
+        {
+            { 32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473 },
+            { -8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644 },
+            { -2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319 },
+        },
+    },
+    {
+        {
+            { -11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599 },
+            { -9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768 },
+            { -27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084 },
+        },
+        {
+            { -27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328 },
+            { -15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369 },
+            { 20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920 },
+        },
+        {
+            { 12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815 },
+            { -32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025 },
+            { -21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397 },
+        },
+        {
+            { -20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448 },
+            { 6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981 },
+            { 30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165 },
+        },
+        {
+            { 32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501 },
+            { 17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073 },
+            { -1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861 },
+        },
+        {
+            { 14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845 },
+            { -1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211 },
+            { 18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870 },
+        },
+        {
+            { 10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096 },
+            { 33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803 },
+            { -32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168 },
+        },
+        {
+            { 30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965 },
+            { -14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505 },
+            { 18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598 },
+        },
+    },
+    {
+        {
+            { 5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782 },
+            { 5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900 },
+            { -31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479 },
+        },
+        {
+            { -12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208 },
+            { 8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232 },
+            { 17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719 },
+        },
+        {
+            { 16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271 },
+            { -4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326 },
+            { -8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132 },
+        },
+        {
+            { 14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300 },
+            { 8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570 },
+            { 15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670 },
+        },
+        {
+            { -2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994 },
+            { -12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913 },
+            { 31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317 },
+        },
+        {
+            { -25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730 },
+            { 842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096 },
+            { -4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078 },
+        },
+        {
+            { -15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411 },
+            { -19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905 },
+            { -9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654 },
+        },
+        {
+            { -28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870 },
+            { -23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498 },
+            { 12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579 },
+        },
+    },
+    {
+        {
+            { 14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677 },
+            { 10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647 },
+            { -2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743 },
+        },
+        {
+            { -25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468 },
+            { 21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375 },
+            { -25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155 },
+        },
+        {
+            { 6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725 },
+            { -12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612 },
+            { -10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943 },
+        },
+        {
+            { -30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944 },
+            { 30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928 },
+            { 9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406 },
+        },
+        {
+            { 22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139 },
+            { -8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963 },
+            { -31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693 },
+        },
+        {
+            { 1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734 },
+            { -448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680 },
+            { -24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410 },
+        },
+        {
+            { -9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931 },
+            { -16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654 },
+            { 22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710 },
+        },
+        {
+            { 29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180 },
+            { -26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684 },
+            { -10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895 },
+        },
+    },
+    {
+        {
+            { 22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501 },
+            { -11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413 },
+            { 6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880 },
+        },
+        {
+            { -8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874 },
+            { 22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962 },
+            { -7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899 },
+        },
+        {
+            { 21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152 },
+            { 9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063 },
+            { 7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080 },
+        },
+        {
+            { -9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146 },
+            { -17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183 },
+            { -19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133 },
+        },
+        {
+            { -32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421 },
+            { -3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622 },
+            { -4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197 },
+        },
+        {
+            { 2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663 },
+            { 31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753 },
+            { 4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755 },
+        },
+        {
+            { -9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862 },
+            { -26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118 },
+            { 26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171 },
+        },
+        {
+            { 15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380 },
+            { 16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824 },
+            { 28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270 },
+        },
+    },
+    {
+        {
+            { -817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438 },
+            { -31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584 },
+            { -594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562 },
+        },
+        {
+            { 30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471 },
+            { 18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610 },
+            { 19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269 },
+        },
+        {
+            { -30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650 },
+            { 14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369 },
+            { 19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461 },
+        },
+        {
+            { 30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462 },
+            { -5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793 },
+            { -2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218 },
+        },
+        {
+            { -24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226 },
+            { 18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019 },
+            { -15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037 },
+        },
+        {
+            { 31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171 },
+            { -17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132 },
+            { -28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841 },
+        },
+        {
+            { 21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181 },
+            { -33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210 },
+            { -1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040 },
+        },
+        {
+            { 3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935 },
+            { 24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105 },
+            { -28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814 },
+        },
+    },
+    {
+        {
+            { 793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852 },
+            { 5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581 },
+            { -4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646 },
+        },
+        {
+            { 10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844 },
+            { 10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025 },
+            { 27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453 },
+        },
+        {
+            { -23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068 },
+            { 4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192 },
+            { -17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921 },
+        },
+        {
+            { -9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259 },
+            { -12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426 },
+            { -5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072 },
+        },
+        {
+            { -17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305 },
+            { 13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832 },
+            { 28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943 },
+        },
+        {
+            { -16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011 },
+            { 24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447 },
+            { 17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494 },
+        },
+        {
+            { -28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245 },
+            { -20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859 },
+            { 28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915 },
+        },
+        {
+            { 16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707 },
+            { 10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848 },
+            { -11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224 },
+        },
+    },
+    {
+        {
+            { -25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391 },
+            { 15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215 },
+            { -23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101 },
+        },
+        {
+            { 23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713 },
+            { 21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849 },
+            { -7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930 },
+        },
+        {
+            { -29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940 },
+            { -21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031 },
+            { -17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404 },
+        },
+        {
+            { -25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243 },
+            { -23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116 },
+            { -24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525 },
+        },
+        {
+            { -23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509 },
+            { -10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883 },
+            { 15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865 },
+        },
+        {
+            { -3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660 },
+            { 4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273 },
+            { -28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138 },
+        },
+        {
+            { -25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560 },
+            { -10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135 },
+            { 2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941 },
+        },
+        {
+            { -4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739 },
+            { 18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756 },
+            { -30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819 },
+        },
+    },
+    {
+        {
+            { -6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347 },
+            { -27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028 },
+            { 21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075 },
+        },
+        {
+            { 16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799 },
+            { -2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609 },
+            { -25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817 },
+        },
+        {
+            { -23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989 },
+            { -30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523 },
+            { 4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278 },
+        },
+        {
+            { 31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045 },
+            { 19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377 },
+            { 24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480 },
+        },
+        {
+            { 17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016 },
+            { 510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426 },
+            { 18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525 },
+        },
+        {
+            { 13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396 },
+            { 9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080 },
+            { 12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892 },
+        },
+        {
+            { 15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275 },
+            { 11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074 },
+            { 20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140 },
+        },
+        {
+            { -16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717 },
+            { -1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101 },
+            { 24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127 },
+        },
+    },
+    {
+        {
+            { -12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632 },
+            { -26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415 },
+            { -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160 },
+        },
+        {
+            { 31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876 },
+            { 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625 },
+            { -15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478 },
+        },
+        {
+            { 27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164 },
+            { 26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595 },
+            { -7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248 },
+        },
+        {
+            { -16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858 },
+            { 15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193 },
+            { 8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184 },
+        },
+        {
+            { -18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942 },
+            { -1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635 },
+            { 21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948 },
+        },
+        {
+            { 11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935 },
+            { -25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415 },
+            { -15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416 },
+        },
+        {
+            { -7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018 },
+            { 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778 },
+            { 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659 },
+        },
+        {
+            { -24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385 },
+            { 18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503 },
+            { 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329 },
+        },
+    },
+    {
+        {
+            { 20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056 },
+            { -13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838 },
+            { 24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948 },
+        },
+        {
+            { -3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691 },
+            { -15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118 },
+            { -23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517 },
+        },
+        {
+            { -20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269 },
+            { -6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904 },
+            { -23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589 },
+        },
+        {
+            { -28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193 },
+            { -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910 },
+            { -30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930 },
+        },
+        {
+            { -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667 },
+            { 25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481 },
+            { -9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876 },
+        },
+        {
+            { 22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640 },
+            { -8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278 },
+            { -21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112 },
+        },
+        {
+            { 26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272 },
+            { 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012 },
+            { -10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221 },
+        },
+        {
+            { 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046 },
+            { 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 },
+            { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
+        },
+    },
+    {
+        {
+            { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
+            { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
+            { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
+        },
+        {
+            { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
+            { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
+            { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
+        },
+        {
+            { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
+            { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
+            { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
+        },
+        {
+            { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
+            { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
+            { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
+        },
+        {
+            { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
+            { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
+            { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
+        },
+        {
+            { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
+            { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
+            { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
+        },
+        {
+            { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
+            { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
+            { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
+        },
+        {
+            { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
+            { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
+            { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
+        },
+    },
+    {
+        {
+            { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
+            { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
+            { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
+        },
+        {
+            { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
+            { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
+            { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
+        },
+        {
+            { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
+            { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
+            { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
+        },
+        {
+            { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
+            { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
+            { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
+        },
+        {
+            { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
+            { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
+            { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
+        },
+        {
+            { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
+            { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
+            { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
+        },
+        {
+            { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
+            { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
+            { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
+        },
+        {
+            { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
+            { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
+            { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
+        },
+    },
+    {
+        {
+            { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
+            { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
+            { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
+        },
+        {
+            { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
+            { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
+            { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
+        },
+        {
+            { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
+            { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
+            { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
+        },
+        {
+            { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
+            { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
+            { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
+        },
+        {
+            { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
+            { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
+            { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
+        },
+        {
+            { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
+            { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
+            { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
+        },
+        {
+            { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
+            { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
+            { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
+        },
+        {
+            { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
+            { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
+            { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
+        },
+    },
+};

lib/ed25519/sc.c

@@ -0,0 +1,809 @@
+#include "fixedint.h"
+#include "sc.h"
+
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s) {
+    int64_t s0 = 2097151 & load_3(s);
+    int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+    int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+    int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+    int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+    int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+    int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+    int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+    int64_t s8 = 2097151 & load_3(s + 21);
+    int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+    int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+    int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+    int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+    int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+    int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+    int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+    int64_t s16 = 2097151 & load_3(s + 42);
+    int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+    int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+    int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+    int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+    int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+    int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+    int64_t s23 = (load_4(s + 60) >> 3);
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
+
+
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+    int64_t a0 = 2097151 & load_3(a);
+    int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+    int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+    int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+    int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+    int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+    int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+    int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+    int64_t a8 = 2097151 & load_3(a + 21);
+    int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+    int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+    int64_t a11 = (load_4(a + 28) >> 7);
+    int64_t b0 = 2097151 & load_3(b);
+    int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+    int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+    int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+    int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+    int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+    int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+    int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+    int64_t b8 = 2097151 & load_3(b + 21);
+    int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+    int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+    int64_t b11 = (load_4(b + 28) >> 7);
+    int64_t c0 = 2097151 & load_3(c);
+    int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+    int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+    int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+    int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+    int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+    int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+    int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+    int64_t c8 = 2097151 & load_3(c + 21);
+    int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+    int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+    int64_t c11 = (load_4(c + 28) >> 7);
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0 = c0 + a0 * b0;
+    s1 = c1 + a0 * b1 + a1 * b0;
+    s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+    s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+    s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+    s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+    s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+    s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+    s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+    s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+    s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+    s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+    s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+    s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+    s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+    s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+    s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+    s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+    s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+    s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+    s20 = a9 * b11 + a10 * b10 + a11 * b9;
+    s21 = a10 * b11 + a11 * b10;
+    s22 = a11 * b11;
+    s23 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry18 = (s18 + (1 << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 << 21;
+    carry20 = (s20 + (1 << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 << 21;
+    carry22 = (s22 + (1 << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    carry17 = (s17 + (1 << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 << 21;
+    carry19 = (s19 + (1 << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 << 21;
+    carry21 = (s21 + (1 << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 << 21;
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}

lib/ed25519/sc.h

@@ -0,0 +1,12 @@
+#ifndef SC_H
+#define SC_H
+
+/*
+The set of scalars is \Z/l
+where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_reduce(unsigned char *s);
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c);
+
+#endif

lib/ed25519/seed.c

@@ -0,0 +1,40 @@
+#include "ed_25519.h"
+
+#ifndef ED25519_NO_SEED
+
+#ifdef _WIN32
+#include <windows.h>
+#include <wincrypt.h>
+#else
+#include <stdio.h>
+#endif
+
+int ed25519_create_seed(unsigned char *seed) {
+#ifdef _WIN32
+    HCRYPTPROV prov;
+
+    if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT))  {
+        return 1;
+    }
+
+    if (!CryptGenRandom(prov, 32, seed))  {
+        CryptReleaseContext(prov, 0);
+        return 1;
+    }
+
+    CryptReleaseContext(prov, 0);
+#else
+    FILE *f = fopen("/dev/urandom", "rb");
+
+    if (f == NULL) {
+        return 1;
+    }
+
+    fread(seed, 1, 32, f);
+    fclose(f);
+#endif
+
+    return 0;
+}
+
+#endif

lib/ed25519/sha512.c

@@ -0,0 +1,275 @@
+/* LibTomCrypt, modular cryptographic library -- Tom St Denis
+ *
+ * LibTomCrypt is a library that provides various cryptographic
+ * algorithms in a highly modular and flexible manner.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+#include "fixedint.h"
+#include "sha512.h"
+
+/* the K array */
+static const uint64_t K[80] = {
+    UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd), 
+    UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc),
+    UINT64_C(0x3956c25bf348b538), UINT64_C(0x59f111f1b605d019), 
+    UINT64_C(0x923f82a4af194f9b), UINT64_C(0xab1c5ed5da6d8118),
+    UINT64_C(0xd807aa98a3030242), UINT64_C(0x12835b0145706fbe), 
+    UINT64_C(0x243185be4ee4b28c), UINT64_C(0x550c7dc3d5ffb4e2),
+    UINT64_C(0x72be5d74f27b896f), UINT64_C(0x80deb1fe3b1696b1), 
+    UINT64_C(0x9bdc06a725c71235), UINT64_C(0xc19bf174cf692694),
+    UINT64_C(0xe49b69c19ef14ad2), UINT64_C(0xefbe4786384f25e3), 
+    UINT64_C(0x0fc19dc68b8cd5b5), UINT64_C(0x240ca1cc77ac9c65),
+    UINT64_C(0x2de92c6f592b0275), UINT64_C(0x4a7484aa6ea6e483), 
+    UINT64_C(0x5cb0a9dcbd41fbd4), UINT64_C(0x76f988da831153b5),
+    UINT64_C(0x983e5152ee66dfab), UINT64_C(0xa831c66d2db43210), 
+    UINT64_C(0xb00327c898fb213f), UINT64_C(0xbf597fc7beef0ee4),
+    UINT64_C(0xc6e00bf33da88fc2), UINT64_C(0xd5a79147930aa725), 
+    UINT64_C(0x06ca6351e003826f), UINT64_C(0x142929670a0e6e70),
+    UINT64_C(0x27b70a8546d22ffc), UINT64_C(0x2e1b21385c26c926), 
+    UINT64_C(0x4d2c6dfc5ac42aed), UINT64_C(0x53380d139d95b3df),
+    UINT64_C(0x650a73548baf63de), UINT64_C(0x766a0abb3c77b2a8), 
+    UINT64_C(0x81c2c92e47edaee6), UINT64_C(0x92722c851482353b),
+    UINT64_C(0xa2bfe8a14cf10364), UINT64_C(0xa81a664bbc423001),
+    UINT64_C(0xc24b8b70d0f89791), UINT64_C(0xc76c51a30654be30),
+    UINT64_C(0xd192e819d6ef5218), UINT64_C(0xd69906245565a910), 
+    UINT64_C(0xf40e35855771202a), UINT64_C(0x106aa07032bbd1b8),
+    UINT64_C(0x19a4c116b8d2d0c8), UINT64_C(0x1e376c085141ab53), 
+    UINT64_C(0x2748774cdf8eeb99), UINT64_C(0x34b0bcb5e19b48a8),
+    UINT64_C(0x391c0cb3c5c95a63), UINT64_C(0x4ed8aa4ae3418acb), 
+    UINT64_C(0x5b9cca4f7763e373), UINT64_C(0x682e6ff3d6b2b8a3),
+    UINT64_C(0x748f82ee5defb2fc), UINT64_C(0x78a5636f43172f60), 
+    UINT64_C(0x84c87814a1f0ab72), UINT64_C(0x8cc702081a6439ec),
+    UINT64_C(0x90befffa23631e28), UINT64_C(0xa4506cebde82bde9), 
+    UINT64_C(0xbef9a3f7b2c67915), UINT64_C(0xc67178f2e372532b),
+    UINT64_C(0xca273eceea26619c), UINT64_C(0xd186b8c721c0c207), 
+    UINT64_C(0xeada7dd6cde0eb1e), UINT64_C(0xf57d4f7fee6ed178),
+    UINT64_C(0x06f067aa72176fba), UINT64_C(0x0a637dc5a2c898a6), 
+    UINT64_C(0x113f9804bef90dae), UINT64_C(0x1b710b35131c471b),
+    UINT64_C(0x28db77f523047d84), UINT64_C(0x32caab7b40c72493), 
+    UINT64_C(0x3c9ebe0a15c9bebc), UINT64_C(0x431d67c49c100d4c),
+    UINT64_C(0x4cc5d4becb3e42b6), UINT64_C(0x597f299cfc657e2a), 
+    UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817)
+};
+
+/* Various logical functions */
+
+#define ROR64c(x, y) \
+    ( ((((x)&UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)(y)&UINT64_C(63))) | \
+      ((x)<<((uint64_t)(64-((y)&UINT64_C(63)))))) & UINT64_C(0xFFFFFFFFFFFFFFFF))
+
+#define STORE64H(x, y)                                                                     \
+   { (y)[0] = (unsigned char)(((x)>>56)&255); (y)[1] = (unsigned char)(((x)>>48)&255);     \
+     (y)[2] = (unsigned char)(((x)>>40)&255); (y)[3] = (unsigned char)(((x)>>32)&255);     \
+     (y)[4] = (unsigned char)(((x)>>24)&255); (y)[5] = (unsigned char)(((x)>>16)&255);     \
+     (y)[6] = (unsigned char)(((x)>>8)&255); (y)[7] = (unsigned char)((x)&255); }
+
+#define LOAD64H(x, y)                                                      \
+   { x = (((uint64_t)((y)[0] & 255))<<56)|(((uint64_t)((y)[1] & 255))<<48) | \
+         (((uint64_t)((y)[2] & 255))<<40)|(((uint64_t)((y)[3] & 255))<<32) | \
+         (((uint64_t)((y)[4] & 255))<<24)|(((uint64_t)((y)[5] & 255))<<16) | \
+         (((uint64_t)((y)[6] & 255))<<8)|(((uint64_t)((y)[7] & 255))); }
+
+
+#define Ch(x,y,z)       (z ^ (x & (y ^ z)))
+#define Maj(x,y,z)      (((x | y) & z) | (x & y)) 
+#define S(x, n)         ROR64c(x, n)
+#define R(x, n)         (((x) &UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)n))
+#define Sigma0(x)       (S(x, 28) ^ S(x, 34) ^ S(x, 39))
+#define Sigma1(x)       (S(x, 14) ^ S(x, 18) ^ S(x, 41))
+#define Gamma0(x)       (S(x, 1) ^ S(x, 8) ^ R(x, 7))
+#define Gamma1(x)       (S(x, 19) ^ S(x, 61) ^ R(x, 6))
+#ifndef MIN
+   #define MIN(x, y) ( ((x)<(y))?(x):(y) )
+#endif
+
+/* compress 1024-bits */
+static int sha512_compress(sha512_context *md, unsigned char *buf)
+{
+    uint64_t S[8], W[80], t0, t1;
+    int i;
+
+    /* copy state into S */
+    for (i = 0; i < 8; i++) {
+        S[i] = md->state[i];
+    }
+
+    /* copy the state into 1024-bits into W[0..15] */
+    for (i = 0; i < 16; i++) {
+        LOAD64H(W[i], buf + (8*i));
+    }
+
+    /* fill W[16..79] */
+    for (i = 16; i < 80; i++) {
+        W[i] = Gamma1(W[i - 2]) + W[i - 7] + Gamma0(W[i - 15]) + W[i - 16];
+    }        
+
+/* Compress */
+    #define RND(a,b,c,d,e,f,g,h,i) \
+    t0 = h + Sigma1(e) + Ch(e, f, g) + K[i] + W[i]; \
+    t1 = Sigma0(a) + Maj(a, b, c);\
+    d += t0; \
+    h  = t0 + t1;
+
+    for (i = 0; i < 80; i += 8) {
+       RND(S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],i+0);
+       RND(S[7],S[0],S[1],S[2],S[3],S[4],S[5],S[6],i+1);
+       RND(S[6],S[7],S[0],S[1],S[2],S[3],S[4],S[5],i+2);
+       RND(S[5],S[6],S[7],S[0],S[1],S[2],S[3],S[4],i+3);
+       RND(S[4],S[5],S[6],S[7],S[0],S[1],S[2],S[3],i+4);
+       RND(S[3],S[4],S[5],S[6],S[7],S[0],S[1],S[2],i+5);
+       RND(S[2],S[3],S[4],S[5],S[6],S[7],S[0],S[1],i+6);
+       RND(S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[0],i+7);
+   }
+
+   #undef RND
+
+
+
+    /* feedback */
+   for (i = 0; i < 8; i++) {
+        md->state[i] = md->state[i] + S[i];
+    }
+
+    return 0;
+}
+
+
+/**
+   Initialize the hash state
+   @param md   The hash state you wish to initialize
+   @return 0 if successful
+*/
+int sha512_init(sha512_context * md) {
+    if (md == NULL) return 1;
+
+    md->curlen = 0;
+    md->length = 0;
+    md->state[0] = UINT64_C(0x6a09e667f3bcc908);
+    md->state[1] = UINT64_C(0xbb67ae8584caa73b);
+    md->state[2] = UINT64_C(0x3c6ef372fe94f82b);
+    md->state[3] = UINT64_C(0xa54ff53a5f1d36f1);
+    md->state[4] = UINT64_C(0x510e527fade682d1);
+    md->state[5] = UINT64_C(0x9b05688c2b3e6c1f);
+    md->state[6] = UINT64_C(0x1f83d9abfb41bd6b);
+    md->state[7] = UINT64_C(0x5be0cd19137e2179);
+
+    return 0;
+}
+
+/**
+   Process a block of memory though the hash
+   @param md     The hash state
+   @param in     The data to hash
+   @param inlen  The length of the data (octets)
+   @return 0 if successful
+*/
+int sha512_update (sha512_context * md, const unsigned char *in, size_t inlen)               
+{                                                                                           
+    size_t n;
+    size_t i;                                                                        
+    int           err;     
+    if (md == NULL) return 1;  
+    if (in == NULL) return 1;                                                              
+    if (md->curlen > sizeof(md->buf)) {                             
+       return 1;                                                            
+    }                                                                                       
+    while (inlen > 0) {                                                                     
+        if (md->curlen == 0 && inlen >= 128) {                           
+           if ((err = sha512_compress (md, (unsigned char *)in)) != 0) {               
+              return err;                                                                   
+           }                                                                                
+           md->length += 128 * 8;                                        
+           in             += 128;                                                    
+           inlen          -= 128;                                                    
+        } else {                                                                            
+           n = MIN(inlen, (128 - md->curlen));
+
+           for (i = 0; i < n; i++) {
+            md->buf[i + md->curlen] = in[i];
+           }
+
+
+           md->curlen += n;                                                     
+           in             += n;                                                             
+           inlen          -= n;                                                             
+           if (md->curlen == 128) {                                      
+              if ((err = sha512_compress (md, md->buf)) != 0) {            
+                 return err;                                                                
+              }                                                                             
+              md->length += 8*128;                                       
+              md->curlen = 0;                                                   
+           }                                                                                
+       }                                                                                    
+    }                                                                                       
+    return 0;                                                                        
+}
+
+/**
+   Terminate the hash to get the digest
+   @param md  The hash state
+   @param out [out] The destination of the hash (64 bytes)
+   @return 0 if successful
+*/
+   int sha512_final(sha512_context * md, unsigned char *out)
+   {
+    int i;
+
+    if (md == NULL) return 1;
+    if (out == NULL) return 1;
+
+    if (md->curlen >= sizeof(md->buf)) {
+     return 1;
+ }
+
+    /* increase the length of the message */
+ md->length += md->curlen * UINT64_C(8);
+
+    /* append the '1' bit */
+ md->buf[md->curlen++] = (unsigned char)0x80;
+
+    /* if the length is currently above 112 bytes we append zeros
+     * then compress.  Then we can fall back to padding zeros and length
+     * encoding like normal.
+     */
+     if (md->curlen > 112) {
+        while (md->curlen < 128) {
+            md->buf[md->curlen++] = (unsigned char)0;
+        }
+        sha512_compress(md, md->buf);
+        md->curlen = 0;
+    }
+
+    /* pad upto 120 bytes of zeroes 
+     * note: that from 112 to 120 is the 64 MSB of the length.  We assume that you won't hash
+     * > 2^64 bits of data... :-)
+     */
+while (md->curlen < 120) {
+    md->buf[md->curlen++] = (unsigned char)0;
+}
+
+    /* store length */
+STORE64H(md->length, md->buf+120);
+sha512_compress(md, md->buf);
+
+    /* copy output */
+for (i = 0; i < 8; i++) {
+    STORE64H(md->state[i], out+(8*i));
+}
+
+return 0;
+}
+
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out)
+{
+    sha512_context ctx;
+    int ret;
+    if ((ret = sha512_init(&ctx))) return ret;
+    if ((ret = sha512_update(&ctx, message, message_len))) return ret;
+    if ((ret = sha512_final(&ctx, out))) return ret;
+    return 0;
+}

lib/ed25519/sha512.h

@@ -0,0 +1,21 @@
+#ifndef SHA512_H
+#define SHA512_H
+
+#include <stddef.h>
+
+#include "fixedint.h"
+
+/* state */
+typedef struct sha512_context_ {
+    uint64_t  length, state[8];
+    size_t curlen;
+    unsigned char buf[128];
+} sha512_context;
+
+
+int sha512_init(sha512_context * md);
+int sha512_final(sha512_context * md, unsigned char *out);
+int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen);
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out);
+
+#endif

lib/ed25519/sign.c

@@ -0,0 +1,31 @@
+#include "ed_25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+
+void ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key) {
+    sha512_context hash;
+    unsigned char hram[64];
+    unsigned char r[64];
+    ge_p3 R;
+
+
+    sha512_init(&hash);
+    sha512_update(&hash, private_key + 32, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, r);
+
+    sc_reduce(r);
+    ge_scalarmult_base(&R, r);
+    ge_p3_tobytes(signature, &R);
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, hram);
+
+    sc_reduce(hram);
+    sc_muladd(signature + 32, hram, private_key, r);
+}

lib/ed25519/verify.c

@@ -0,0 +1,77 @@
+#include "ed_25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+static int consttime_equal(const unsigned char *x, const unsigned char *y) {
+    unsigned char r = 0;
+
+    r = x[0] ^ y[0];
+    #define F(i) r |= x[i] ^ y[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return !r;
+}
+
+int ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key) {
+    unsigned char h[64];
+    unsigned char checker[32];
+    sha512_context hash;
+    ge_p3 A;
+    ge_p2 R;
+
+    if (signature[63] & 224) {
+        return 0;
+    }
+
+    if (ge_frombytes_negate_vartime(&A, public_key) != 0) {
+        return 0;
+    }
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, h);
+    
+    sc_reduce(h);
+    ge_double_scalarmult_vartime(&R, h, &A, signature + 32);
+    ge_tobytes(checker, &R);
+
+    if (!consttime_equal(checker, signature)) {
+        return 0;
+    }
+
+    return 1;
+}

license.txt

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2025 Scott Powell
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

platformio.ini

@@ -0,0 +1,94 @@
+; PlatformIO Project Configuration File
+;
+;   Build options: build flags, source filter
+;   Upload options: custom upload port, speed and extra flags
+;   Library options: dependencies, extra library storages
+;   Advanced options: extra scripting
+;
+; Please visit documentation for the other options and examples
+; https://docs.platformio.org/page/projectconf.html
+
+[arduino_base]
+framework = arduino
+monitor_speed = 115200
+lib_deps = 
+  SPI
+  Wire
+  jgromes/RadioLib @ ^6.3.0
+  rweather/Crypto @ ^0.4.0
+build_flags = -w -DNDEBUG -DRADIOLIB_STATIC_ONLY=1
+build_src_filter = +<*.cpp> +<helpers/*.cpp>
+
+[esp32_base]
+extends = arduino_base
+platform = espressif32
+monitor_filters = esp32_exception_decoder
+build_src_filter = ${arduino_base.build_src_filter}
+
+[esp32_S3]
+extends = esp32_base
+platform = espressif32
+board = esp32-s3-devkitc-1
+build_src_filter = ${esp32_base.build_src_filter}
+build_flags =
+  ${esp32_base.build_flags}
+lib_deps =
+  ${esp32_base.lib_deps}
+
+[Heltec_stick_lite]
+extends = esp32_base
+board = heltec_wireless_stick_lite
+
+[Heltec_lora32_v2]
+extends = esp32_base
+board = heltec_wifi_lora_32_V2
+
+; ================
+[Heltec_lora32_v3]
+extends = esp32_base
+board = esp32-s3-devkitc-1
+build_flags =
+  ${esp32_base.build_flags} 
+  -D HELTEC_LORA_V3
+build_src_filter = ${esp32_base.build_src_filter}
+
+[env:Heltec_v3_ping_server]
+extends = Heltec_lora32_v3
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/ping_server/main.cpp>
+
+[env:Heltec_v3_ping_client]
+extends = Heltec_lora32_v3
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/ping_client/main.cpp>
+
+[env:Heltec_v3_repeater]
+extends = Heltec_lora32_v3
+build_flags =
+  ${Heltec_lora32_v3.build_flags} 
+; -D NODE_ID=2
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/simple_repeater/main.cpp>
+
+[env:Heltec_v3_chat_alice]
+extends = Heltec_lora32_v3
+build_flags =
+  ${Heltec_lora32_v3.build_flags} 
+  -D RUN_AS_ALICE=true
+; -D NODE_ID=1
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/simple_secure_chat/main.cpp>
+
+[env:Heltec_v3_chat_bob]
+extends = Heltec_lora32_v3
+build_flags =
+  ${Heltec_lora32_v3.build_flags} 
+  -D RUN_AS_ALICE=false
+; -D NODE_ID=3
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/simple_secure_chat/main.cpp>
+
+[env:Heltec_v3_test_admin]
+extends = Heltec_lora32_v3
+build_flags =
+  ${Heltec_lora32_v3.build_flags} 
+; -D NODE_ID=1
+build_src_filter = ${Heltec_lora32_v3.build_src_filter} +<../examples/test_admin/main.cpp>
+
+; =============
+

src/Destination.cpp

@@ -0,0 +1,29 @@
+#include "Destination.h"
+#include "Utils.h"
+#include <string.h>
+
+namespace mesh {
+
+Destination::Destination(const Identity& identity, const char* name) {
+  uint8_t name_hash[MAX_HASH_SIZE];
+  Utils::sha256(name_hash, MAX_HASH_SIZE, (const uint8_t *)name, strlen(name));
+
+  Utils::sha256(hash, MAX_HASH_SIZE, name_hash, MAX_HASH_SIZE, identity.pub_key, PUB_KEY_SIZE);
+}
+
+Destination::Destination(const char* name) {
+  uint8_t name_hash[MAX_HASH_SIZE];
+  Utils::sha256(name_hash, MAX_HASH_SIZE, (const uint8_t *)name, strlen(name));
+
+  Utils::sha256(hash, MAX_HASH_SIZE, name_hash, MAX_HASH_SIZE);
+}
+
+Destination::Destination() {
+  memset(hash, 0, MAX_HASH_SIZE);
+}
+
+bool Destination::matches(const uint8_t* other_hash) {
+  return memcmp(hash, other_hash, MAX_HASH_SIZE) == 0;
+}
+
+}

src/Destination.h

@@ -0,0 +1,25 @@
+#pragma once
+
+#include <MeshCore.h>
+#include <Identity.h>
+
+namespace mesh {
+
+/**
+ * \brief  Represents an end-point in the mesh, identified by a truncated SHA256 hash. (of DEST_HASH_SIZE)
+ *      The hash is either from just a 'name' (C-string), and these can be thought of as 'broadcast' addresses,
+ *      or can be the hash of name + Identity.public_key
+*/
+class Destination {
+public:
+  uint8_t hash[MAX_HASH_SIZE];
+
+  Destination(const Identity& identity, const char* name);
+  Destination(const char* name);
+  Destination(const uint8_t desthash[]) { memcpy(hash, desthash, MAX_HASH_SIZE); }
+  Destination();
+
+  bool matches(const uint8_t* other_hash);
+};
+
+}

src/Dispatcher.cpp

@@ -0,0 +1,161 @@
+#include "Dispatcher.h"
+
+namespace mesh {
+
+void Dispatcher::begin() {
+  _radio->begin();
+}
+
+float Dispatcher::getAirtimeBudgetFactor() const {
+  return 5.0;   // default, 16.6%  (1/6th)
+}
+
+void Dispatcher::loop() {
+  if (outbound) {  // waiting for outbound send to be completed
+    if (_radio->isSendComplete()) {
+      long t = _ms->getMillis() - outbound_start;
+      total_air_time += t;  // keep track of how much air time we are using
+      //Serial.print("  airtime="); Serial.println(t);
+
+      // will need radio silence up to next_tx_time
+      next_tx_time = futureMillis(t * getAirtimeBudgetFactor());
+
+      _radio->onSendFinished();
+      onPacketSent(outbound);
+      outbound = NULL;
+    } else if (millisHasNowPassed(outbound_expiry)) {
+      MESH_DEBUG_PRINTLN("Dispatcher::loop(): WARNING: outbound packed send timed out!");
+      //Serial.println("  timed out");
+
+      _radio->onSendFinished();
+      releasePacket(outbound);  // return to pool
+      outbound = NULL;
+    } else {
+      return;  // can't do any more radio activity until send is complete or timed out
+    }
+  }
+
+  checkRecv();
+  checkSend();
+}
+
+void Dispatcher::onPacketSent(Packet* packet) {
+  releasePacket(packet);  // default behaviour, return packet to pool
+}
+
+void Dispatcher::checkRecv() {
+  Packet* pkt;
+  {
+    uint8_t raw[MAX_TRANS_UNIT];
+    int len = _radio->recvRaw(raw, MAX_TRANS_UNIT);
+    if (len > 0) {
+      pkt = _mgr->allocNew();
+      if (pkt == NULL) {
+        MESH_DEBUG_PRINTLN("Dispatcher::checkRecv(): WARNING: received data, no unused packets available!");
+      } else {
+        int i = 0;
+#ifdef NODE_ID
+        uint8_t sender_id = raw[i++];
+        if (sender_id == NODE_ID - 1 || sender_id == NODE_ID + 1) {  // simulate that NODE_ID can only hear NODE_ID-1 or NODE_ID+1, eg. 3 can't hear 1
+        } else {
+          _mgr->free(pkt);  // put back into pool
+          return;
+        }
+#endif
+        //Serial.print("LoRa recv: len="); Serial.println(len);
+
+        pkt->header = raw[i++];
+        pkt->path_len = raw[i++];
+
+        if (pkt->path_len > MAX_PATH_SIZE || i + pkt->path_len > len) {
+          MESH_DEBUG_PRINTLN("Dispatcher::checkRecv(): partial or corrupt packet received, len=%d", len);
+          _mgr->free(pkt);  // put back into pool
+          pkt = NULL;
+        } else {
+          memcpy(pkt->path, &raw[i], pkt->path_len); i += pkt->path_len;
+
+          pkt->payload_len = len - i;  // payload is remainder
+          memcpy(pkt->payload, &raw[i], pkt->payload_len);
+        }
+      }
+    } else {
+      pkt = NULL;
+    }
+  }
+  if (pkt) {
+    DispatcherAction action = onRecvPacket(pkt);
+    if (action == ACTION_RELEASE) {
+      _mgr->free(pkt);
+    } else if (action == ACTION_MANUAL_HOLD) {
+      // sub-class is wanting to manually hold Packet instance, and call releasePacket() at appropriate time
+    } else {   // ACTION_RETRANSMIT*
+      uint8_t priority = (action >> 24) - 1;
+      uint32_t _delay = action & 0xFFFFFF;
+
+      _mgr->queueOutbound(pkt, priority, futureMillis(_delay));
+    }
+  }
+}
+
+void Dispatcher::checkSend() {
+  if (_mgr->getOutboundCount() == 0) return;  // nothing waiting to send
+  if (!millisHasNowPassed(next_tx_time)) return;   // still in 'radio silence' phase (from airtime budget setting)
+  if (_radio->isReceiving()) return;  // check if radio is currently mid-receive
+
+  outbound = _mgr->getNextOutbound(_ms->getMillis());
+  if (outbound) {
+    int len = 0;
+    uint8_t raw[MAX_TRANS_UNIT];
+
+#ifdef NODE_ID
+    raw[len++] = NODE_ID;
+#endif
+    raw[len++] = outbound->header;
+    raw[len++] = outbound->path_len;
+    memcpy(&raw[len], outbound->path, outbound->path_len); len += outbound->path_len;
+
+    if (len + outbound->payload_len > MAX_TRANS_UNIT) {
+      MESH_DEBUG_PRINTLN("Dispatcher::checkSend(): FATAL: Invalid packet queued... too long, len=%d", len + outbound->payload_len);
+      _mgr->free(outbound);
+      outbound = NULL;
+    } else {
+      memcpy(&raw[len], outbound->payload, outbound->payload_len); len += outbound->payload_len;
+
+      uint32_t max_airtime = _radio->getEstAirtimeFor(len)*3/2;
+      outbound_start = _ms->getMillis();
+      _radio->startSendRaw(raw, len);
+      outbound_expiry = futureMillis(max_airtime);
+
+      //Serial.print("LoRa send: len="); Serial.print(len);
+    }
+  }
+}
+
+Packet* Dispatcher::obtainNewPacket() {
+  return _mgr->allocNew();  // TODO: zero out all fields
+}
+
+void Dispatcher::releasePacket(Packet* packet) {
+  _mgr->free(packet);
+}
+
+void Dispatcher::sendPacket(Packet* packet, uint8_t priority, uint32_t delay_millis) {
+  if (packet->path_len > MAX_PATH_SIZE || packet->payload_len > MAX_PACKET_PAYLOAD) {
+    MESH_DEBUG_PRINTLN("Dispatcher::sendPacket(): ERROR: invalid packet... path_len=%d, payload_len=%d", (uint32_t) packet->path_len, (uint32_t) packet->payload_len);
+    _mgr->free(packet);
+  } else {
+    _mgr->queueOutbound(packet, priority, futureMillis(delay_millis));
+  }
+}
+
+// Utility function -- handles the case where millis() wraps around back to zero
+//   2's complement arithmetic will handle any unsigned subtraction up to HALF the word size (32-bits in this case)
+bool Dispatcher::millisHasNowPassed(unsigned long timestamp) const {
+  return (long)(_ms->getMillis() - timestamp) > 0;
+}
+
+unsigned long Dispatcher::futureMillis(int millis_from_now) const {
+  return _ms->getMillis() + millis_from_now;
+}
+
+}

src/Dispatcher.h

@@ -0,0 +1,129 @@
+#pragma once
+
+#include <MeshCore.h>
+#include <Identity.h>
+#include <Packet.h>
+#include <Utils.h>
+#include <string.h>
+
+namespace mesh {
+
+/**
+ * \brief  Abstraction of local/volatile clock with Millisecond granularity.
+*/
+class MillisecondClock {
+public:
+  virtual unsigned long getMillis() = 0;
+};
+
+/**
+ * \brief  Abstraction of this device's packet radio.
+*/
+class Radio {
+public:
+  virtual void begin() { }
+
+  /**
+   * \brief  polls for incoming raw packet.
+   * \param  bytes  destination to store incoming raw packet.
+   * \param  sz   maximum packet size allowed.
+   * \returns 0 if no incoming data, otherwise length of complete packet received.
+  */
+  virtual int recvRaw(uint8_t* bytes, int sz) = 0;
+
+  /**
+   * \returns  estimated transmit air-time needed for packet of 'len_bytes', in milliseconds.
+  */
+  virtual uint32_t getEstAirtimeFor(int len_bytes) = 0;
+
+  /**
+   * \brief  starts the raw packet send. (no wait)
+   * \param  bytes   the raw packet data
+   * \param  len  the length in bytes
+  */
+  virtual void startSendRaw(const uint8_t* bytes, int len) = 0;
+
+  /**
+   * \returns true if the previous 'startSendRaw()' completed successfully.
+  */
+  virtual bool isSendComplete() = 0;
+
+  /**
+   * \brief  a hook for doing any necessary clean up after transmit.
+  */
+  virtual void onSendFinished() = 0;
+
+  /**
+   * \returns  true if the radio is currently mid-receive of a packet.
+  */
+  virtual bool isReceiving() { return false; }
+};
+
+/**
+ * \brief  An abstraction for managing instances of Packets (eg. in a static pool),
+ *        and for managing the outbound packet queue.
+*/
+class PacketManager {
+public:
+  virtual Packet* allocNew() = 0;
+  virtual void free(Packet* packet) = 0;
+
+  virtual void queueOutbound(Packet* packet, uint8_t priority, uint32_t scheduled_for) = 0;
+  virtual Packet* getNextOutbound(uint32_t now) = 0;    // by priority
+  virtual int getOutboundCount() const = 0;
+  virtual int getFreeCount() const = 0;
+  virtual Packet* getOutboundByIdx(int i) = 0;
+  virtual Packet* removeOutboundByIdx(int i) = 0;
+};
+
+typedef uint32_t  DispatcherAction;
+
+#define ACTION_RELEASE           (0)
+#define ACTION_MANUAL_HOLD       (1)
+#define ACTION_RETRANSMIT(pri)   (((uint32_t)1 + (pri))<<24)
+#define ACTION_RETRANSMIT_DELAYED(pri, _delay)  ((((uint32_t)1 + (pri))<<24) | (_delay))
+
+/**
+ * \brief  The low-level task that manages detecting incoming Packets, and the queueing
+ *      and scheduling of outbound Packets.
+*/
+class Dispatcher {
+  Packet* outbound;  // current outbound packet
+  unsigned long outbound_expiry, outbound_start, total_air_time;
+  unsigned long next_tx_time;
+
+protected:
+  PacketManager* _mgr;
+  Radio* _radio;
+  MillisecondClock* _ms;
+
+  Dispatcher(Radio& radio, MillisecondClock& ms, PacketManager& mgr)
+    : _radio(&radio), _ms(&ms), _mgr(&mgr)
+  {
+    outbound = NULL; total_air_time = 0; next_tx_time = 0;
+  }
+
+  virtual DispatcherAction onRecvPacket(Packet* pkt) = 0;
+  virtual void onPacketSent(Packet* packet);
+  virtual float getAirtimeBudgetFactor() const;
+
+public:
+  void begin();
+  void loop();
+
+  Packet* obtainNewPacket();
+  void releasePacket(Packet* packet);
+  void sendPacket(Packet* packet, uint8_t priority, uint32_t delay_millis=0);
+
+  unsigned long getTotalAirTime() const { return total_air_time; }  // in milliseconds
+
+  // helper methods
+  bool millisHasNowPassed(unsigned long timestamp) const;
+  unsigned long futureMillis(int millis_from_now) const;
+
+private:
+  void checkRecv();
+  void checkSend();
+};
+
+}

src/Identity.cpp

@@ -0,0 +1,70 @@
+#include "Identity.h"
+#include <string.h>
+#define ED25519_NO_SEED  1
+#include <ed_25519.h>
+
+namespace mesh {
+
+Identity::Identity() {
+  memset(pub_key, 0, sizeof(pub_key));
+}
+
+Identity::Identity(const char* pub_hex) {
+  Utils::fromHex(pub_key, PUB_KEY_SIZE, pub_hex);
+}
+
+bool Identity::verify(const uint8_t* sig, const uint8_t* message, int msg_len) const {
+  return ed25519_verify(sig, message, msg_len, pub_key);
+}
+
+bool Identity::readFrom(Stream& s) {
+  return (s.readBytes(pub_key, PUB_KEY_SIZE) == PUB_KEY_SIZE);
+}
+
+bool Identity::writeTo(Stream& s) const {
+  return (s.write(pub_key, PUB_KEY_SIZE) == PUB_KEY_SIZE);
+}
+
+void Identity::printTo(Stream& s) const {
+  Utils::printHex(s, pub_key, PUB_KEY_SIZE);
+}
+
+LocalIdentity::LocalIdentity() {
+  memset(prv_key, 0, sizeof(prv_key));
+}
+LocalIdentity::LocalIdentity(const char* prv_hex, const char* pub_hex) : Identity(pub_hex) {
+  Utils::fromHex(prv_key, PRV_KEY_SIZE, prv_hex);
+}
+
+LocalIdentity::LocalIdentity(RNG* rng) {
+  uint8_t seed[SEED_SIZE];
+  rng->random(seed, SEED_SIZE);
+  ed25519_create_keypair(pub_key, prv_key, seed);
+}
+
+bool LocalIdentity::readFrom(Stream& s) {
+  bool success = (s.readBytes(pub_key, PUB_KEY_SIZE) == PUB_KEY_SIZE);
+  success = success && (s.readBytes(prv_key, PRV_KEY_SIZE) == PRV_KEY_SIZE);
+  return success;
+}
+
+bool LocalIdentity::writeTo(Stream& s) const {
+  bool success = (s.write(pub_key, PUB_KEY_SIZE) == PUB_KEY_SIZE);
+  success = success && (s.write(prv_key, PRV_KEY_SIZE) == PRV_KEY_SIZE);
+  return success;
+}
+
+void LocalIdentity::printTo(Stream& s) const {
+  s.print("pub_key: "); Utils::printHex(s, pub_key, PUB_KEY_SIZE); s.println();
+  s.print("prv_key: "); Utils::printHex(s, prv_key, PRV_KEY_SIZE); s.println();
+}
+
+void LocalIdentity::sign(uint8_t* sig, const uint8_t* message, int msg_len) const {
+  ed25519_sign(sig, message, msg_len, pub_key, prv_key);
+}
+
+void LocalIdentity::calcSharedSecret(uint8_t* secret, const Identity& other) {
+  ed25519_key_exchange(secret, other.pub_key, prv_key);
+}
+
+}

src/Identity.h

@@ -0,0 +1,75 @@
+#pragma once
+
+#include <Utils.h>
+#include <Stream.h>
+
+namespace mesh {
+
+/**
+ * \brief  An identity in the mesh, with given Ed25519 public key, ie. a party whose signatures can be VERIFIED.
+*/
+class Identity {
+public:
+  uint8_t pub_key[PUB_KEY_SIZE];
+
+  Identity();
+  Identity(const char* pub_hex);
+  Identity(const uint8_t* _pub) { memcpy(pub_key, _pub, PUB_KEY_SIZE); }
+
+  int copyHashTo(uint8_t* dest) const { 
+    memcpy(dest, pub_key, PATH_HASH_SIZE);    // hash is just prefix of pub_key
+    return PATH_HASH_SIZE;
+  }
+  bool isHashMatch(const uint8_t* hash) const {
+    return memcmp(hash, pub_key, PATH_HASH_SIZE) == 0;
+  }
+
+  /**
+   * \brief  Performs Ed25519 signature verification.
+   * \param sig IN - must be SIGNATURE_SIZE buffer.
+   * \param message IN - the original message which was signed.
+   * \param msg_len IN - the length in bytes of message.
+   * \returns true, if signature is valid.
+  */
+  bool verify(const uint8_t* sig, const uint8_t* message, int msg_len) const;
+
+  bool matches(const Identity& other) const { return memcmp(pub_key, other.pub_key, PUB_KEY_SIZE) == 0; }
+  bool matches(const uint8_t* other_pubkey) const { return memcmp(pub_key, other_pubkey, PUB_KEY_SIZE) == 0; }
+
+  bool readFrom(Stream& s);
+  bool writeTo(Stream& s) const;
+  void printTo(Stream& s) const;
+};
+
+/**
+ * \brief  An Identity generated on THIS device, ie. with public/private Ed25519 key pair being on this device.
+*/
+class LocalIdentity : public Identity {
+  uint8_t prv_key[PRV_KEY_SIZE];
+public:
+  LocalIdentity();
+  LocalIdentity(const char* prv_hex, const char* pub_hex);
+  LocalIdentity(RNG* rng);   // create new random
+
+  /**
+   * \brief  Ed25519 digital signature.
+   * \param sig OUT - must be SIGNATURE_SIZE buffer.
+   * \param message IN - the raw message bytes to sign.
+   * \param msg_len IN - the length in bytes of message.
+  */
+  void sign(uint8_t* sig, const uint8_t* message, int msg_len) const;
+
+  /**
+   * \brief  the ECDH key exhange, with Ed25519 public key transposed to Ex25519.
+   * \param  secret OUT - the 'shared secret' (must be PUB_KEY_SIZE bytes)
+   * \param  other IN - the second party in the exchange.
+  */
+  void calcSharedSecret(uint8_t* secret, const Identity& other);
+
+  bool readFrom(Stream& s);
+  bool writeTo(Stream& s) const;
+  void printTo(Stream& s) const;
+};
+
+}
+

src/Mesh.cpp

@@ -0,0 +1,392 @@
+#include "Mesh.h"
+//#include <Arduino.h>
+
+namespace mesh {
+
+void Mesh::begin() {
+  Dispatcher::begin();
+}
+
+void Mesh::loop() {
+  Dispatcher::loop();
+}
+
+bool Mesh::allowPacketForward(mesh::Packet* packet) { 
+  return false;  // by default, Transport NOT enabled
+}
+
+int Mesh::searchPeersByHash(const uint8_t* hash) {
+  return 0;  // not found
+}
+
+int Mesh::searchChannelsByHash(const uint8_t* hash, GroupChannel channels[], int max_matches) {
+  return 0;  // not found
+}
+
+DispatcherAction Mesh::onRecvPacket(Packet* pkt) {
+  if (pkt->getPayloadVer() > PAYLOAD_VER_1) {  // not supported in this firmware version
+    MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): unsupported packet version");
+    return ACTION_RELEASE;
+  }
+
+  if (pkt->isRouteDirect() && pkt->path_len >= PATH_HASH_SIZE) {
+    if (self_id.isHashMatch(pkt->path) && allowPacketForward(pkt)) {
+      // remove our hash from 'path', then re-broadcast
+      pkt->path_len -= PATH_HASH_SIZE;
+      memcpy(pkt->path, &pkt->path[PATH_HASH_SIZE], pkt->path_len);
+      return ACTION_RETRANSMIT(0);   // Routed traffic is HIGHEST priority
+    }
+    return ACTION_RELEASE;   // this node is NOT the next hop (OR this packet has already been forwarded), so discard.
+  }
+
+  DispatcherAction action = ACTION_RELEASE;
+
+  switch (pkt->getPayloadType()) {
+    case PAYLOAD_TYPE_ACK: {
+      int i = 0;
+      uint32_t ack_crc;
+      memcpy(&ack_crc, &pkt->payload[i], 4); i += 4;
+      if (i > pkt->payload_len) {
+        MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): incomplete ACK packet");
+      } else {
+        onAckRecv(pkt, ack_crc);
+        action = routeRecvPacket(pkt);
+      }
+      break;
+    }
+    case PAYLOAD_TYPE_PATH:
+    case PAYLOAD_TYPE_REQ:
+    case PAYLOAD_TYPE_RESPONSE:
+    case PAYLOAD_TYPE_TXT_MSG: {
+      int i = 0;
+      uint8_t dest_hash = pkt->payload[i++];
+      uint8_t src_hash = pkt->payload[i++];
+
+      uint8_t* macAndData = &pkt->payload[i];   // MAC + encrypted data 
+      if (i + 2 >= pkt->payload_len) {
+        MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): incomplete data packet");
+      } else {
+        if (self_id.isHashMatch(&dest_hash)) {
+          // scan contacts DB, for all matching hashes of 'src_hash' (max 4 matches supported ATM)
+          int num = searchPeersByHash(&src_hash);
+          // for each matching contact, try to decrypt data
+          for (int j = 0; j < num; j++) {
+            uint8_t secret[PUB_KEY_SIZE];
+            getPeerSharedSecret(secret, j);
+
+            // decrypt, checking MAC is valid
+            uint8_t data[MAX_PACKET_PAYLOAD];
+            int len = Utils::MACThenDecrypt(secret, data, macAndData, pkt->payload_len - i);
+            if (len > 0) {  // success!
+              if (pkt->getPayloadType() == PAYLOAD_TYPE_PATH) {
+                int k = 0;
+                uint8_t path_len = data[k++];
+                uint8_t* path = &data[k]; k += path_len;
+                uint8_t extra_type = data[k++];
+                uint8_t* extra = &data[k];
+                uint8_t extra_len = len - k;   // remainder of packet (may be padded with zeroes!)
+                onPeerPathRecv(pkt, j, path, path_len, extra_type, extra, extra_len);
+              } else {
+                onPeerDataRecv(pkt, pkt->getPayloadType(), j, data, len);
+              }
+              break;
+            }
+          }
+        }
+        action = routeRecvPacket(pkt);
+      }
+      break;
+    }
+    case PAYLOAD_TYPE_ANON_REQ: {
+      int i = 0;
+      uint8_t dest_hash = pkt->payload[i++];
+      uint8_t* sender_pub_key = &pkt->payload[i]; i += PUB_KEY_SIZE;
+
+      uint8_t* macAndData = &pkt->payload[i];   // MAC + encrypted data 
+      if (i + 2 >= pkt->payload_len) {
+        MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): incomplete data packet");
+      } else {
+        if (self_id.isHashMatch(&dest_hash)) {
+          Identity sender(sender_pub_key);
+
+          uint8_t secret[PUB_KEY_SIZE];
+          self_id.calcSharedSecret(secret, sender);
+
+          // decrypt, checking MAC is valid
+          uint8_t data[MAX_PACKET_PAYLOAD];
+          int len = Utils::MACThenDecrypt(secret, data, macAndData, pkt->payload_len - i);
+          if (len > 0) {  // success!
+            onAnonDataRecv(pkt, pkt->getPayloadType(), sender, data, len);
+          }
+        }
+        action = routeRecvPacket(pkt);
+      }
+      break;
+    }
+    case PAYLOAD_TYPE_GRP_DATA: 
+    case PAYLOAD_TYPE_GRP_TXT: {
+      int i = 0;
+      uint8_t channel_hash = pkt->payload[i++];
+
+      uint8_t* macAndData = &pkt->payload[i];   // MAC + encrypted data 
+      if (i + 2 >= pkt->payload_len) {
+        MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): incomplete data packet");
+      } else {
+        // scan channels DB, for all matching hashes of 'channel_hash' (max 2 matches supported ATM)
+        GroupChannel channels[2];
+        int num = searchChannelsByHash(&channel_hash, channels, 2);
+        // for each matching channel, try to decrypt data
+        for (int j = 0; j < num; j++) {
+          // decrypt, checking MAC is valid
+          uint8_t data[MAX_PACKET_PAYLOAD];
+          int len = Utils::MACThenDecrypt(channels[j].secret, data, macAndData, pkt->payload_len - i);
+          if (len > 0) {  // success!
+            onGroupDataRecv(pkt, pkt->getPayloadType(), channels[j], data, len);
+            break;
+          }
+        }
+        action = routeRecvPacket(pkt);
+      }
+      break;
+    }
+    case PAYLOAD_TYPE_ADVERT: {
+      int i = 0;
+      Identity id;
+      memcpy(id.pub_key, &pkt->payload[i], PUB_KEY_SIZE); i += PUB_KEY_SIZE;
+
+      uint32_t timestamp;
+      memcpy(&timestamp, &pkt->payload[i], 4); i += 4;
+      uint8_t* signature = &pkt->payload[i]; i += SIGNATURE_SIZE;
+
+      if (i > pkt->payload_len) {
+        MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): incomplete advertisement packet");
+      } else {
+        uint8_t* app_data = &pkt->payload[i];
+        int app_data_len = pkt->payload_len - i;
+        if (app_data_len > MAX_ADVERT_DATA_SIZE) { app_data_len = MAX_ADVERT_DATA_SIZE; }
+
+        // check that signature is valid
+        bool is_ok;
+        {
+          uint8_t message[PUB_KEY_SIZE + 4 + MAX_ADVERT_DATA_SIZE];
+          int msg_len = 0;
+          memcpy(&message[msg_len], id.pub_key, PUB_KEY_SIZE); msg_len += PUB_KEY_SIZE;
+          memcpy(&message[msg_len], &timestamp, 4); msg_len += 4;
+          memcpy(&message[msg_len], app_data, app_data_len); msg_len += app_data_len;
+
+          is_ok = id.verify(signature, message, msg_len);
+        }
+        if (is_ok) {
+          MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): valid advertisement received!");
+          onAdvertRecv(pkt, id, timestamp, app_data, app_data_len);
+          action = routeRecvPacket(pkt);
+        } else {
+          MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): received advertisement with forged signature!");
+        }
+      }
+      break;
+    }
+    default:
+      MESH_DEBUG_PRINTLN("Mesh::onRecvPacket(): unknown payload type, header: %d", (int) pkt->header);
+      action = routeRecvPacket(pkt);
+      break;
+  }
+  return action;
+}
+
+DispatcherAction Mesh::routeRecvPacket(Packet* packet) {
+  if (packet->isRouteFlood() && packet->path_len + PATH_HASH_SIZE <= MAX_PATH_SIZE && allowPacketForward(packet)) {
+    // append this node's hash to 'path'
+    packet->path_len += self_id.copyHashTo(&packet->path[packet->path_len]);
+
+    // as this propagates outwards, give it lower and lower priority
+    return ACTION_RETRANSMIT(packet->path_len);   // give priority to closer sources, than ones further away
+  }
+  return ACTION_RELEASE;
+}
+
+Packet* Mesh::createAdvert(const LocalIdentity& id, const uint8_t* app_data, size_t app_data_len) {
+  if (app_data_len > MAX_ADVERT_DATA_SIZE) return NULL;
+
+  Packet* packet = obtainNewPacket();
+  if (packet == NULL) {
+    MESH_DEBUG_PRINTLN("Mesh::createAdvert(): error, packet pool empty");
+    return NULL;
+  }
+
+  packet->header = (PAYLOAD_TYPE_ADVERT << PH_TYPE_SHIFT);  // ROUTE_TYPE_* is set later
+  packet->path_len = 0;
+
+  int len = 0;
+  memcpy(&packet->payload[len], id.pub_key, PUB_KEY_SIZE); len += PUB_KEY_SIZE;
+
+  uint32_t emitted_timestamp = _rtc->getCurrentTime();
+  memcpy(&packet->payload[len], &emitted_timestamp, 4); len += 4;
+
+  uint8_t* signature = &packet->payload[len]; len += SIGNATURE_SIZE;  // will fill this in later
+
+  memcpy(&packet->payload[len], app_data, app_data_len); len += app_data_len;
+
+  packet->payload_len = len;
+
+  {
+    uint8_t message[PUB_KEY_SIZE + 4 + MAX_ADVERT_DATA_SIZE];
+    int msg_len = 0;
+    memcpy(&message[msg_len], id.pub_key, PUB_KEY_SIZE); msg_len += PUB_KEY_SIZE;
+    memcpy(&message[msg_len], &emitted_timestamp, 4); msg_len += 4;
+    memcpy(&message[msg_len], app_data, app_data_len); msg_len += app_data_len;
+
+    id.sign(signature, message, msg_len);
+  }
+
+  return packet;
+}
+
+#define MAX_COMBINED_PATH  (MAX_PACKET_PAYLOAD - 2 - CIPHER_BLOCK_SIZE)
+
+Packet* Mesh::createPathReturn(const Identity& dest, const uint8_t* secret, const uint8_t* path, uint8_t path_len, uint8_t extra_type, const uint8_t*extra, size_t extra_len) {
+  if (path_len + extra_len + 5 > MAX_COMBINED_PATH) return NULL;  // too long!!
+
+  Packet* packet = obtainNewPacket();
+  if (packet == NULL) {
+    MESH_DEBUG_PRINTLN("Mesh::createPathReturn(): error, packet pool empty");
+    return NULL;
+  }
+  packet->header = (PAYLOAD_TYPE_PATH << PH_TYPE_SHIFT);  // ROUTE_TYPE_* set later
+  packet->path_len = 0;
+
+  int len = 0;
+  len += dest.copyHashTo(&packet->payload[len]);  // dest hash
+  len += self_id.copyHashTo(&packet->payload[len]);  // src hash
+
+  {
+    int data_len = 0;
+    uint8_t data[MAX_PACKET_PAYLOAD];
+
+    data[data_len++] = path_len;
+    memcpy(&data[data_len], path, path_len); data_len += path_len;
+    if (extra_len > 0) {
+      data[data_len++] = extra_type;
+      memcpy(&data[data_len], extra, extra_len); data_len += extra_len;
+    } else {
+      // append a timestamp, or random blob (to make packet_hash unique)
+      data[data_len++] = 0xFF;  // dummy payload type
+      getRNG()->random(&data[data_len], 4); data_len += 4;
+    }
+
+    len += Utils::encryptThenMAC(secret, &packet->payload[len], data, data_len);
+  }
+
+  packet->payload_len = len;
+
+  return packet;
+}
+
+Packet* Mesh::createDatagram(uint8_t type, const Identity& dest, const uint8_t* secret, const uint8_t* data, size_t data_len) {
+  if (type == PAYLOAD_TYPE_ANON_REQ) {
+    if (data_len + 1 + PUB_KEY_SIZE + CIPHER_BLOCK_SIZE-1 > MAX_PACKET_PAYLOAD) return NULL;
+  } else if (type == PAYLOAD_TYPE_TXT_MSG || type == PAYLOAD_TYPE_REQ || type == PAYLOAD_TYPE_RESPONSE) {
+    if (data_len + 2 + CIPHER_BLOCK_SIZE-1 > MAX_PACKET_PAYLOAD) return NULL;
+  } else {
+    return NULL;  // invalid type
+  }
+
+  Packet* packet = obtainNewPacket();
+  if (packet == NULL) {
+    MESH_DEBUG_PRINTLN("Mesh::createDatagram(): error, packet pool empty");
+    return NULL;
+  }
+  packet->header = (type << PH_TYPE_SHIFT);  // ROUTE_TYPE_* set later
+  packet->path_len = 0;
+
+  int len = 0;
+  if (type == PAYLOAD_TYPE_ANON_REQ) {
+    len += dest.copyHashTo(&packet->payload[len]);  // dest hash
+    memcpy(&packet->payload[len], self_id.pub_key, PUB_KEY_SIZE); len += PUB_KEY_SIZE;  // sender pub_key
+  } else {
+    len += dest.copyHashTo(&packet->payload[len]);  // dest hash
+    len += self_id.copyHashTo(&packet->payload[len]);  // src hash
+  }
+  len += Utils::encryptThenMAC(secret, &packet->payload[len], data, data_len);
+
+  packet->payload_len = len;
+
+  return packet;
+}
+
+Packet* Mesh::createGroupDatagram(uint8_t type, const GroupChannel& channel, const uint8_t* data, size_t data_len) {
+  if (!(type == PAYLOAD_TYPE_GRP_TXT || type == PAYLOAD_TYPE_GRP_DATA)) return NULL;   // invalid type
+  if (data_len + 1 + CIPHER_BLOCK_SIZE-1 > MAX_PACKET_PAYLOAD) return NULL; // too long
+
+  Packet* packet = obtainNewPacket();
+  if (packet == NULL) {
+    MESH_DEBUG_PRINTLN("Mesh::createGroupDatagram(): error, packet pool empty");
+    return NULL;
+  }
+  packet->header = (type << PH_TYPE_SHIFT);  // ROUTE_TYPE_* set later
+  packet->path_len = 0;
+
+  int len = 0;
+  memcpy(&packet->payload[len], channel.hash, PATH_HASH_SIZE); len += PATH_HASH_SIZE;
+  len += Utils::encryptThenMAC(channel.secret, &packet->payload[len], data, data_len);
+
+  packet->payload_len = len;
+
+  return packet;
+}
+
+Packet* Mesh::createAck(uint32_t ack_crc) {
+  Packet* packet = obtainNewPacket();
+  if (packet == NULL) {
+    MESH_DEBUG_PRINTLN("Mesh::createAck(): error, packet pool empty");
+    return NULL;
+  }
+  packet->header = (PAYLOAD_TYPE_ACK << PH_TYPE_SHIFT);  // ROUTE_TYPE_* set later
+  packet->path_len = 0;
+
+  memcpy(packet->payload, &ack_crc, 4);
+  packet->payload_len = 4;
+
+  return packet;
+}
+
+void Mesh::sendFlood(Packet* packet, uint32_t delay_millis) {
+  packet->header &= ~PH_ROUTE_MASK;
+  packet->header |= ROUTE_TYPE_FLOOD;
+
+  allowPacketForward(packet);  // mark this packet as already sent in case it is rebroadcast back to us
+
+  uint8_t pri;
+  if (packet->getPayloadType() == PAYLOAD_TYPE_PATH) {
+    pri = 2;
+  } else if (packet->getPayloadType() == PAYLOAD_TYPE_ADVERT) {
+    pri = 3;   // de-prioritie these
+  } else {
+    pri = 1;
+  }
+  sendPacket(packet, pri, delay_millis);
+}
+
+void Mesh::sendDirect(Packet* packet, const uint8_t* path, uint8_t path_len, uint32_t delay_millis) {
+  packet->header &= ~PH_ROUTE_MASK;
+  packet->header |= ROUTE_TYPE_DIRECT;
+
+  memcpy(packet->path, path, packet->path_len = path_len);
+
+  allowPacketForward(packet);  // mark this packet as already sent in case it is rebroadcast back to us
+
+  sendPacket(packet, 0, delay_millis);
+}
+
+void Mesh::sendZeroHop(Packet* packet, uint32_t delay_millis) {
+  packet->header &= ~PH_ROUTE_MASK;
+  packet->header |= ROUTE_TYPE_DIRECT;
+
+  packet->path_len = 0;  // path_len of zero means Zero Hop
+
+  allowPacketForward(packet);  // mark this packet as already sent in case it is rebroadcast back to us
+
+  sendPacket(packet, 0, delay_millis);
+}
+
+}

src/Mesh.h

@@ -0,0 +1,151 @@
+#pragma once
+
+#include <Dispatcher.h>
+
+namespace mesh {
+
+/**
+ * An abstraction of the device's Realtime Clock.
+*/
+class RTCClock {
+public:
+  /**
+   * \returns  the current time. in UNIX epoch seconds.
+  */
+  virtual uint32_t getCurrentTime() = 0;
+
+  /**
+   * \param time  current time in UNIX epoch seconds.
+  */
+  virtual void setCurrentTime(uint32_t time) = 0;
+};
+
+class GroupChannel {
+public:
+  uint8_t hash[PATH_HASH_SIZE];
+  uint8_t secret[PUB_KEY_SIZE];
+};
+
+/**
+ * \brief  The next layer in the basic Dispatcher task, Mesh recognises the particular Payload TYPES,
+ *     and provides virtual methods for sub-classes on handling incoming, and also preparing outbound Packets.
+*/
+class Mesh : public Dispatcher {
+  RTCClock* _rtc;
+  RNG* _rng;
+
+protected:
+  DispatcherAction onRecvPacket(Packet* pkt) override;
+
+  /**
+   * \brief  Decide what to do with received packet, ie. discard, forward, or hold
+   */
+  DispatcherAction routeRecvPacket(Packet* packet);
+
+  /**
+   * \brief  Check whether this packet should be forwarded (re-transmitted) or not.
+   *     Is sub-classes responsibility to make sure given packet is only transmitted ONCE (by this node)
+   */
+  virtual bool allowPacketForward(Packet* packet);
+
+  /**
+   * \brief  Perform search of local DB of peers/contacts.
+   * \returns  Number of peers with matching hash
+   */
+  virtual int searchPeersByHash(const uint8_t* hash);
+
+  /**
+   * \brief  lookup the ECDH shared-secret between this node and peer by idx (calculate if necessary)
+   * \param  dest_secret  destination array to copy the secret (must be PUB_KEY_SIZE bytes)
+   * \param  peer_idx  index of peer, [0..n) where n is what searchPeersByHash() returned
+   */
+  virtual void getPeerSharedSecret(uint8_t* dest_secret, int peer_idx) { }
+
+  /**
+   * \brief  A (now decrypted) data packet has been received (by a known peer).
+   *         NOTE: these can be received multiple times (per sender/msg-id), via different routes
+   * \param  type  one of: PAYLOAD_TYPE_TXT_MSG, PAYLOAD_TYPE_REQ, PAYLOAD_TYPE_RESPONSE
+   * \param  sender_idx  index of peer, [0..n) where n is what searchPeersByHash() returned
+  */
+  virtual void onPeerDataRecv(Packet* packet, uint8_t type, int sender_idx, uint8_t* data, size_t len) { }
+
+  /**
+   * \brief  A path TO peer (sender_idx) has been received. (also with optional 'extra' data encoded)
+   *         NOTE: these can be received multiple times (per sender), via differen routes
+   * \param  sender_idx  index of peer, [0..n) where n is what searchPeersByHash() returned
+  */
+  virtual void onPeerPathRecv(Packet* packet, int sender_idx, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) { }
+
+  virtual int searchChannelsByHash(const uint8_t* hash, GroupChannel channels[], int max_matches);
+
+  /**
+   * \brief  A new incoming Advertisement has been received.
+   *         NOTE: these can be received multiple times (per id/timestamp), via different routes
+  */
+  virtual void onAdvertRecv(Packet* packet, const Identity& id, uint32_t timestamp, const uint8_t* app_data, size_t app_data_len) { }
+
+  /**
+   * \brief  A (now decrypted) data packet has been received.
+   *         NOTE: these can be received multiple times (per sender/contents), via different routes
+   * \param  type  one of: PAYLOAD_TYPE_ANON_REQ
+   * \param  sender  public key provided by sender
+  */
+  virtual void onAnonDataRecv(Packet* packet, uint8_t type, const Identity& sender, uint8_t* data, size_t len) { }
+
+  /**
+   * \brief  A path TO 'sender' has been received. (also with optional 'extra' data encoded)
+   *         NOTE: these can be received multiple times (per sender), via differen routes
+  */
+  virtual void onPathRecv(Packet* packet, Identity& sender, uint8_t* path, uint8_t path_len, uint8_t extra_type, uint8_t* extra, uint8_t extra_len) { }
+
+  /**
+   * \brief  An encrypted group data packet has been received.
+   *         NOTE: the same payload can be received multiple times, via different routes
+   * \param  type  one of: PAYLOAD_TYPE_GRP_TXT, PAYLOAD_TYPE_GRP_DATA
+   * \param  channel  the matching GroupChannel
+  */
+  virtual void onGroupDataRecv(Packet* packet, uint8_t type, const GroupChannel& channel, uint8_t* data, size_t len) { }
+
+  /**
+   * \brief  A simple ACK packet has been received.
+   *         NOTE: same ACK can be received multiple times, via different routes
+  */
+  virtual void onAckRecv(Packet* packet, uint32_t ack_crc) { }
+
+  Mesh(Radio& radio, MillisecondClock& ms, RNG& rng, RTCClock& rtc, PacketManager& mgr)
+    : Dispatcher(radio, ms, mgr), _rng(&rng), _rtc(&rtc)
+  {
+  }
+
+public:
+  void begin();
+  void loop();
+
+  LocalIdentity self_id;
+
+  RNG* getRNG() const { return _rng; }
+  RTCClock* getRTCClock() const { return _rtc; }
+
+  Packet* createAdvert(const LocalIdentity& id, const uint8_t* app_data=NULL, size_t app_data_len=0);
+  Packet* createDatagram(uint8_t type, const Identity& dest, const uint8_t* secret, const uint8_t* data, size_t len);
+  Packet* createGroupDatagram(uint8_t type, const GroupChannel& channel, const uint8_t* data, size_t data_len);
+  Packet* createAck(uint32_t ack_crc);
+  Packet* createPathReturn(const Identity& dest, const uint8_t* secret, const uint8_t* path, uint8_t path_len, uint8_t extra_type, const uint8_t*extra, size_t extra_len);
+
+  /**
+   * \brief  send a locally-generated Packet with flood routing
+  */
+  void sendFlood(Packet* packet, uint32_t delay_millis=0);
+
+  /**
+   * \brief  send a locally-generated Packet with Direct routing
+  */
+  void sendDirect(Packet* packet, const uint8_t* path, uint8_t path_len, uint32_t delay_millis=0);
+
+  /**
+   * \brief  send a locally-generated Packet to just neigbor nodes (zero hops)
+  */
+  void sendZeroHop(Packet* packet, uint32_t delay_millis=0);
+};
+
+}

src/MeshCore.h

@@ -0,0 +1,46 @@
+#pragma once
+
+#include <stdint.h>
+
+#define MAX_HASH_SIZE        8
+#define PUB_KEY_SIZE        32
+#define PRV_KEY_SIZE        64
+#define SEED_SIZE           32
+#define SIGNATURE_SIZE      64
+#define MAX_ADVERT_DATA_SIZE  32
+#define CIPHER_KEY_SIZE     16
+#define CIPHER_BLOCK_SIZE   16
+
+// V1
+#define CIPHER_MAC_SIZE      2
+#define PATH_HASH_SIZE       1
+
+#define MAX_PACKET_PAYLOAD  184
+#define MAX_PATH_SIZE        64
+#define MAX_TRANS_UNIT      255
+
+#if MESH_DEBUG && ARDUINO
+  #include <Arduino.h>
+  #define MESH_DEBUG_PRINT(...) Serial.printf(__VA_ARGS__)
+  #define MESH_DEBUG_PRINTLN(F, ...) Serial.printf(F "\n", ##__VA_ARGS__)
+#else
+  #define MESH_DEBUG_PRINT(...) {}
+  #define MESH_DEBUG_PRINTLN(...) {}
+#endif
+
+namespace mesh {
+
+#define  BD_STARTUP_NORMAL     0  // getStartupReason() codes
+#define  BD_STARTUP_RX_PACKET  1
+
+class MainBoard {
+public:
+  virtual uint16_t getBattMilliVolts() = 0;
+  virtual const char* getManufacturerName() const = 0;
+  virtual void onBeforeTransmit() { }
+  virtual void onAfterTransmit() { }
+  virtual void reboot() = 0;
+  virtual uint8_t getStartupReason() const = 0;
+};
+
+}

src/MeshTables.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include <Mesh.h>
+
+namespace mesh {
+
+/**
+ * An abstraction of the data tables needed to be maintained, for the routing engine.
+*/
+class MeshTables {
+public:
+  virtual bool hasForwarded(const uint8_t* packet_hash) const = 0;
+  virtual void setHasForwarded(const uint8_t* packet_hash) = 0;
+};
+
+}

src/Packet.cpp

@@ -0,0 +1,23 @@
+#include "Packet.h"
+#include <string.h>
+#include <SHA256.h>
+
+namespace mesh {
+
+Packet::Packet() {
+  header = 0;
+  path_len = 0;
+  payload_len = 0;
+}
+
+
+void Packet::calculatePacketHash(uint8_t* hash) const {
+  SHA256 sha;
+  uint8_t t = getPayloadType();
+  sha.update(&t, 1);
+  sha.update(payload, payload_len);
+  sha.finalize(hash, MAX_HASH_SIZE);
+}
+
+
+}

src/Packet.h

@@ -0,0 +1,73 @@
+#pragma once
+
+#include <MeshCore.h>
+
+namespace mesh {
+
+// Packet::header values
+#define PH_ROUTE_MASK     0x03   // 2-bits
+#define PH_TYPE_SHIFT        2
+#define PH_TYPE_MASK      0x0F   // 4-bits
+#define PH_VER_SHIFT         6
+#define PH_VER_MASK       0x03   // 2-bits
+
+#define ROUTE_TYPE_RESERVED1     0x00    // FUTURE
+#define ROUTE_TYPE_FLOOD         0x01    // flood mode, needs 'path' to be built up (max 64 bytes)
+#define ROUTE_TYPE_DIRECT        0x02    // direct route, 'path' is supplied
+#define ROUTE_TYPE_RESERVED2     0x03    // FUTURE
+
+#define PAYLOAD_TYPE_REQ         0x00    // request (prefixed with dest/src hashes, MAC) (enc data: timestamp, blob)
+#define PAYLOAD_TYPE_RESPONSE    0x01    // response to REQ or ANON_REQ (prefixed with dest/src hashes, MAC) (enc data: timestamp, blob)
+#define PAYLOAD_TYPE_TXT_MSG     0x02    // a plain text message (prefixed with dest/src hashes, MAC) (enc data: timestamp, text)
+#define PAYLOAD_TYPE_ACK         0x03    // a simple ack
+#define PAYLOAD_TYPE_ADVERT      0x04    // a node advertising its Identity
+#define PAYLOAD_TYPE_GRP_TXT     0x05    // an (unverified) group text message (prefixed with channel hash, MAC) (enc data: timestamp, "name: msg")
+#define PAYLOAD_TYPE_GRP_DATA    0x06    // an (unverified) group datagram (prefixed with channel hash, MAC) (enc data: timestamp, blob)
+#define PAYLOAD_TYPE_ANON_REQ    0x07    // generic request (prefixed with dest_hash, ephemeral pub_key, MAC) (enc data: ...)
+#define PAYLOAD_TYPE_PATH        0x08    // returned path (prefixed with dest/src hashes, MAC) (enc data: path, extra)
+//...
+#define PAYLOAD_TYPE_RESERVEDM   0x0F    // FUTURE
+
+#define PAYLOAD_VER_1       0x00   // 1-byte src/dest hashes, 2-byte MAC
+#define PAYLOAD_VER_2       0x01   // FUTURE (eg. 2-byte hashes, 4-byte MAC ??)
+#define PAYLOAD_VER_3       0x02   // FUTURE
+#define PAYLOAD_VER_4       0x03   // FUTURE
+
+/**
+ * \brief  The fundamental transmission unit.
+*/
+class Packet {
+public:
+  Packet();
+
+  uint8_t header;
+  uint16_t payload_len, path_len;
+  uint8_t path[MAX_PATH_SIZE];
+  uint8_t payload[MAX_PACKET_PAYLOAD];
+
+  /**
+   * \brief calculate the hash of payload + type
+   * \param  dest_hash   destination to store the hash (must be MAX_HASH_SIZE bytes)
+   */
+  void calculatePacketHash(uint8_t* dest_hash) const;
+
+  /**
+   * \returns  one of ROUTE_ values
+   */
+  uint8_t getRouteType() const { return header & PH_ROUTE_MASK; }
+
+  bool isRouteFlood() const { return getRouteType() == ROUTE_TYPE_FLOOD; }
+  bool isRouteDirect() const { return getRouteType() == ROUTE_TYPE_DIRECT; }
+
+  /**
+   * \returns  one of PAYLOAD_TYPE_ values
+   */
+  uint8_t getPayloadType() const { return (header >> PH_TYPE_SHIFT) & PH_TYPE_MASK; }
+
+  /**
+   * \returns  one of PAYLOAD_VER_ values
+   */
+  uint8_t getPayloadVer() const { return (header >> PH_VER_SHIFT) & PH_VER_MASK; }
+};
+
+}

src/Utils.cpp

@@ -0,0 +1,149 @@
+#include "Utils.h"
+#include <AES.h>
+#include <SHA256.h>
+
+#ifdef ARDUINO
+  #include <Arduino.h>
+#endif
+
+namespace mesh {
+
+uint32_t RNG::nextInt(uint32_t _min, uint32_t _max) {
+  uint32_t num;
+  random((uint8_t *) &num, sizeof(num));
+  return (num % (_max - _min)) + _min;
+}
+
+void Utils::sha256(uint8_t *hash, size_t hash_len, const uint8_t* msg, int msg_len) {
+  SHA256 sha;
+  sha.update(msg, msg_len);
+  sha.finalize(hash, hash_len);
+}
+
+void Utils::sha256(uint8_t *hash, size_t hash_len, const uint8_t* frag1, int frag1_len, const uint8_t* frag2, int frag2_len) {
+  SHA256 sha;
+  sha.update(frag1, frag1_len);
+  sha.update(frag2, frag2_len);
+  sha.finalize(hash, hash_len);
+}
+
+int Utils::decrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len) {
+  AES128 aes;
+  uint8_t* dp = dest;
+  const uint8_t* sp = src;
+
+  aes.setKey(shared_secret, CIPHER_KEY_SIZE);
+  while (sp - src < src_len) {
+    aes.decryptBlock(dp, sp);
+    dp += 16; sp += 16;
+  }
+
+  return sp - src;  // will always be multiple of 16
+}
+
+int Utils::encrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len) {
+  AES128 aes;
+  uint8_t* dp = dest;
+
+  aes.setKey(shared_secret, CIPHER_KEY_SIZE);
+  while (src_len >= 16) {
+    aes.encryptBlock(dp, src);
+    dp += 16; src += 16; src_len -= 16;
+  }
+  if (src_len > 0) {  // remaining partial block
+    uint8_t tmp[16];
+    memset(tmp, 0, 16);
+    memcpy(tmp, src, src_len);
+    aes.encryptBlock(dp, tmp);
+    dp += 16;
+  }
+  return dp - dest;  // will always be multiple of 16
+}
+
+int Utils::encryptThenMAC(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len) {
+  int enc_len = encrypt(shared_secret, dest + CIPHER_MAC_SIZE, src, src_len);
+
+  SHA256 sha;
+  sha.resetHMAC(shared_secret, PUB_KEY_SIZE);
+  sha.update(dest + CIPHER_MAC_SIZE, enc_len);
+  sha.finalizeHMAC(shared_secret, PUB_KEY_SIZE, dest, CIPHER_MAC_SIZE);
+
+  return CIPHER_MAC_SIZE + enc_len;
+}
+
+int Utils::MACThenDecrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len) {
+  if (src_len <= CIPHER_MAC_SIZE) return 0;  // invalid src bytes
+
+  uint8_t hmac[CIPHER_MAC_SIZE];
+  {
+    SHA256 sha;
+    sha.resetHMAC(shared_secret, PUB_KEY_SIZE);
+    sha.update(src + CIPHER_MAC_SIZE, src_len - CIPHER_MAC_SIZE);
+    sha.finalizeHMAC(shared_secret, PUB_KEY_SIZE, hmac, CIPHER_MAC_SIZE);
+  }
+  if (memcmp(hmac, src, CIPHER_MAC_SIZE) == 0) {
+    return decrypt(shared_secret, dest, src + CIPHER_MAC_SIZE, src_len - CIPHER_MAC_SIZE);
+  }
+  return 0; // invalid HMAC
+}
+
+static const char hex_chars[] = "0123456789ABCDEF";
+
+void Utils::toHex(char* dest, const uint8_t* src, size_t len) {
+  while (len > 0) {
+    uint8_t b = *src++;
+    *dest++ = hex_chars[b >> 4];
+    *dest++ = hex_chars[b & 0x0F];
+    len--;
+  }
+  *dest = 0;
+}
+
+void Utils::printHex(Stream& s, const uint8_t* src, size_t len) {
+  while (len > 0) {
+    uint8_t b = *src++;
+    s.print(hex_chars[b >> 4]);
+    s.print(hex_chars[b & 0x0F]);
+    len--;
+  }
+}
+
+static uint8_t hexVal(char c) {
+  if (c >= 'A' && c <= 'F') return c - 'A' + 10;
+  if (c >= 'a' && c <= 'f') return c - 'a' + 10;
+  if (c >= '0' && c <= '9') return c - '0';
+  return 0;
+}
+
+bool Utils::fromHex(uint8_t* dest, int dest_size, const char *src_hex) {
+  int len = strlen(src_hex);
+  if (len != dest_size*2) return false;  // incorrect length
+
+  uint8_t* dp = dest;
+  while (dp - dest < dest_size) {
+    char ch = *src_hex++;
+    char cl = *src_hex++;
+    *dp++ = (hexVal(ch) << 4) | hexVal(cl);
+  }
+  return true;
+}
+
+int Utils::parseTextParts(char* text, const char* parts[], int max_num, char separator) {
+  int num = 0;
+  char* sp = text;
+  while (*sp && num < max_num) {
+    parts[num++] = sp;
+    while (*sp && *sp != separator) sp++;
+    if (*sp) {
+       *sp++ = 0;  // replace the seperator with a null, and skip past it
+    }
+  }
+  // if we hit the maximum parts, make sure LAST entry does NOT have separator 
+  while (*sp && *sp != separator) sp++;
+  if (*sp) {
+    *sp = 0;  // replace the separator with null
+  }
+  return num;
+}
+
+}

src/Utils.h

@@ -0,0 +1,81 @@
+#pragma once
+
+#include <MeshCore.h>
+#include <Stream.h>
+#include <string.h>
+
+namespace mesh {
+
+class RNG {
+public:
+  virtual void random(uint8_t* dest, size_t sz) = 0;
+  uint32_t nextInt(uint32_t _min, uint32_t _max);
+};
+
+class Utils {
+public:
+  /**
+   * \brief  calculates the SHA256 hash of 'msg', storing in 'hash' and truncating the hash to 'hash_len' bytes.
+  */
+  static void sha256(uint8_t *hash, size_t hash_len, const uint8_t* msg, int msg_len);
+
+  /**
+   * \brief  calculates the SHA256 hash of two fragments, 'frag1' and 'frag2' (in that order), storing in 'hash' and truncating.
+  */
+  static void sha256(uint8_t *hash, size_t hash_len, const uint8_t* frag1, int frag1_len, const uint8_t* frag2, int frag2_len);
+
+  /**
+   * \brief  Encrypts the 'src' bytes using AES128 cipher, using 'shared_secret' as key, with key length fixed at CIPHER_KEY_SIZE.
+   *         Final block is padded with zero bytes before encrypt. Result stored in 'dest'.
+   * \returns  The length in bytes put into 'dest'. (rounded up to block size)
+  */
+  static int encrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len);
+
+  /**
+   * \brief  Decrypt the 'src' bytes using AES128 cipher, using 'shared_secret' as key, with key length fixed at CIPHER_KEY_SIZE.
+   *         'src_len' should be multiple of block size, as returned by 'encrypt()'.
+   * \returns  The length in bytes put into 'dest'. (dest may contain trailing zero bytes in final block)
+  */
+  static int decrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len);
+
+  /**
+   * \brief  encrypts bytes in src, then calculates MAC on ciphertext, inserting into leading bytes of 'dest'.
+   * \returns  total length of bytes in 'dest' (MAC + ciphertext)
+  */
+  static int encryptThenMAC(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len);
+
+  /**
+   * \brief  checks the MAC (in leading bytes of 'src'), then if valid, decrypts remaining bytes in src.
+   * \returns  zero if MAC is invalid, otherwise the length of decrypted bytes in 'dest'
+  */
+  static int MACThenDecrypt(const uint8_t* shared_secret, uint8_t* dest, const uint8_t* src, int src_len);
+
+  /**
+   * \brief  converts 'src' bytes with given length to Hex representation, and null terminates.
+  */
+  static void toHex(char* dest, const uint8_t* src, size_t len);
+
+  /**
+   * \brief  converts 'src_hex' hexadecimal string (should be null term) back to raw bytes, storing in 'dest'.
+   * \param dest_size   must be exactly the expected size in bytes.
+   * \returns  true if successful
+  */
+  static bool fromHex(uint8_t* dest, int dest_size, const char *src_hex);
+
+  /**
+   * \brief  Prints the hexadecimal representation of 'src' bytes of given length, to Stream 's'.
+  */
+  static void printHex(Stream& s, const uint8_t* src, size_t len);
+
+  /**
+   * \brief  parse 'text' into parts separated by 'separator' char.
+   * \param  text  the text to parse (note is MODIFIED!)
+   * \param  parts  destination array to store pointers to starts of parse parts
+   * \param  max_num  max elements to store in 'parts' array
+   * \param  separator  the separator character
+   * \returns  the number of parts parsed (in 'parts')
+   */
+  static int parseTextParts(char* text, const char* parts[], int max_num, char separator=',');
+};
+
+}

src/helpers/ArduinoHelpers.h

@@ -0,0 +1,27 @@
+#pragma once
+
+#include <Mesh.h>
+#include <Arduino.h>
+
+class VolatileRTCClock : public mesh::RTCClock {
+  long millis_offset;
+public:
+  VolatileRTCClock() { millis_offset = 1715770351; } // 15 May 2024, 8:50pm
+  uint32_t getCurrentTime() override { return (millis()/1000 + millis_offset); }
+  void setCurrentTime(uint32_t time) override { millis_offset = time - millis()/1000; }
+};
+
+class ArduinoMillis : public mesh::MillisecondClock {
+public:
+  unsigned long getMillis() override { return millis(); }
+};
+
+class StdRNG : public mesh::RNG {
+public:
+  void begin(long seed) { randomSeed(seed); }
+  void random(uint8_t* dest, size_t sz) override {
+    for (int i = 0; i < sz; i++) {
+      dest[i] = (::random(0, 256) & 0xFF);
+    }
+  }
+};

src/helpers/CustomSX1262.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include <RadioLib.h>
+
+#define SX126X_IRQ_HEADER_VALID                     0b0000010000  //  4     4     valid LoRa header received
+
+class CustomSX1262 : public SX1262 {
+  public:
+    CustomSX1262(Module *mod) : SX1262(mod) { }
+
+    bool isReceiving() {
+      uint16_t irq = getIrqStatus();
+      bool hasPreamble = (irq & SX126X_IRQ_HEADER_VALID);
+      return hasPreamble;
+    }
+};

src/helpers/CustomSX1262Wrapper.h

@@ -0,0 +1,12 @@
+#pragma once
+
+#include "CustomSX1262.h"
+#include "RadioLibWrappers.h"
+
+class CustomSX1262Wrapper : public RadioLibWrapper {
+public:
+  CustomSX1262Wrapper(CustomSX1262& radio, mesh::MainBoard& board) : RadioLibWrapper(radio, board) { }
+  bool isReceiving() override { return ((CustomSX1262 *)_radio)->isReceiving(); }
+  float getLastRSSI() const override { return ((CustomSX1262 *)_radio)->getRSSI(); }
+  float getLastSNR() const override { return ((CustomSX1262 *)_radio)->getSNR(); }
+};

src/helpers/CustomSX1268.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include <RadioLib.h>
+
+#define SX126X_IRQ_HEADER_VALID                     0b0000010000  //  4     4     valid LoRa header received
+
+class CustomSX1268 : public SX1268 {
+  public:
+    CustomSX1268(Module *mod) : SX1268(mod) { }
+
+    bool isReceiving() {
+      uint16_t irq = getIrqStatus();
+      bool hasPreamble = (irq & SX126X_IRQ_HEADER_VALID);
+      return hasPreamble;
+    }
+};

src/helpers/CustomSX1268Wrapper.h

@@ -0,0 +1,12 @@
+#pragma once
+
+#include "CustomSX1268.h"
+#include "RadioLibWrappers.h"
+
+class CustomSX1268Wrapper : public RadioLibWrapper {
+public:
+  CustomSX1268Wrapper(CustomSX1268& radio, mesh::MainBoard& board) : RadioLibWrapper(radio, board) { }
+  bool isReceiving() override { return ((CustomSX1268 *)_radio)->isReceiving(); }
+  float getLastRSSI() const override { return ((CustomSX1268 *)_radio)->getRSSI(); }
+  float getLastSNR() const override { return ((CustomSX1268 *)_radio)->getSNR(); }
+};

src/helpers/ESP32Board.h

@@ -0,0 +1,48 @@
+#pragma once
+
+#include <MeshCore.h>
+#include <Arduino.h>
+
+#if defined(ESP_PLATFORM)
+
+#include <rom/rtc.h>
+#include <sys/time.h>
+
+class ESP32Board : public mesh::MainBoard {  // abstract class
+public:
+  void begin() {
+    // for future use, sub-classes SHOULD call this from their begin()
+  }
+
+  void reboot() override {
+    esp_restart();
+  }
+};
+
+class ESP32RTCClock : public mesh::RTCClock {
+public:
+  ESP32RTCClock() { }
+  void begin() {
+    esp_reset_reason_t reason = esp_reset_reason();
+    if (reason == ESP_RST_POWERON) {
+      // start with some date/time in the recent past
+      struct timeval tv;
+      tv.tv_sec = 1715770351;  // 15 May 2024, 8:50pm
+      tv.tv_usec = 0;
+      settimeofday(&tv, NULL);
+    }
+  }
+  uint32_t getCurrentTime() override {
+    time_t _now;
+    time(&_now);
+    return _now;
+  }
+  void setCurrentTime(uint32_t time) override { 
+    struct timeval tv;
+    tv.tv_sec = time;
+    tv.tv_usec = 0;
+    settimeofday(&tv, NULL);
+  }
+};
+
+#endif

src/helpers/HeltecV3Board.h

@@ -0,0 +1,91 @@
+#pragma once
+
+#include "ESP32Board.h"
+#include <Arduino.h>
+
+// LoRa radio module pins for Heltec V3
+#define  P_LORA_DIO_1   14
+#define  P_LORA_NSS      8
+#define  P_LORA_RESET   RADIOLIB_NC
+#define  P_LORA_BUSY    13
+#define  P_LORA_SCLK     9
+#define  P_LORA_MISO    11
+#define  P_LORA_MOSI    10
+
+// built-ins
+#define  PIN_VBAT_READ    1
+#define  PIN_ADC_CTRL    37
+#define  PIN_ADC_CTRL_ACTIVE    LOW
+#define  PIN_ADC_CTRL_INACTIVE  HIGH
+#define  PIN_LED_BUILTIN 35
+
+#include <driver/rtc_io.h>
+
+class HeltecV3Board : public ESP32Board {
+  uint8_t startup_reason;
+public:
+  void begin() {
+    startup_reason = BD_STARTUP_NORMAL;
+    ESP32Board::begin();
+
+    esp_reset_reason_t reason = esp_reset_reason();
+    if (reason == ESP_RST_DEEPSLEEP) {
+      long wakeup_source = esp_sleep_get_ext1_wakeup_status();
+      if (wakeup_source & (1 << P_LORA_DIO_1)) {  // received a LoRa packet (while in deep sleep)
+        startup_reason = BD_STARTUP_RX_PACKET;
+      }
+
+      rtc_gpio_hold_dis((gpio_num_t)P_LORA_NSS);
+      rtc_gpio_deinit((gpio_num_t)P_LORA_DIO_1);
+    }
+
+    // battery read support
+    pinMode(PIN_VBAT_READ, INPUT);
+    adcAttachPin(PIN_VBAT_READ);
+    analogReadResolution(10);
+    pinMode(PIN_ADC_CTRL, OUTPUT);
+  }
+
+  uint8_t getStartupReason() const { return startup_reason; }
+
+  void enterDeepSleep(uint32_t secs, int pin_wake_btn = -1) {
+    esp_sleep_pd_config(ESP_PD_DOMAIN_RTC_PERIPH, ESP_PD_OPTION_ON);
+
+    // Make sure the DIO1 and NSS GPIOs are hold on required levels during deep sleep 
+    rtc_gpio_set_direction((gpio_num_t)P_LORA_DIO_1, RTC_GPIO_MODE_INPUT_ONLY);
+    rtc_gpio_pulldown_en((gpio_num_t)P_LORA_DIO_1);
+
+    rtc_gpio_hold_en((gpio_num_t)P_LORA_NSS);
+
+    if (pin_wake_btn < 0) {
+      esp_sleep_enable_ext1_wakeup( (1L << P_LORA_DIO_1), ESP_EXT1_WAKEUP_ANY_HIGH);  // wake up on: recv LoRa packet
+    } else {
+      esp_sleep_enable_ext1_wakeup( (1L << P_LORA_DIO_1) | (1L << pin_wake_btn), ESP_EXT1_WAKEUP_ANY_HIGH);  // wake up on: recv LoRa packet OR wake btn
+    }
+
+    if (secs > 0) {
+      esp_sleep_enable_timer_wakeup(secs * 1000000);
+    }
+
+    // Finally set ESP32 into sleep
+    esp_deep_sleep_start();   // CPU halts here and never returns!
+  }
+
+  uint16_t getBattMilliVolts() override {
+    digitalWrite(PIN_ADC_CTRL, PIN_ADC_CTRL_ACTIVE);
+
+    uint32_t raw = 0;
+    for (int i = 0; i < 8; i++) {
+      raw += analogRead(PIN_VBAT_READ);
+    }
+    raw = raw / 8;
+
+    digitalWrite(PIN_ADC_CTRL, PIN_ADC_CTRL_INACTIVE);
+
+    return (5.2 * (3.3 / 1024.0) * raw) * 1000;
+  }
+
+  const char* getManufacturerName() const override {
+    return "Heltec V3";
+  }
+};

src/helpers/IdentityStore.cpp

@@ -0,0 +1,27 @@
+#include "IdentityStore.h"
+
+bool IdentityStore::load(const char *name, mesh::LocalIdentity& id) {
+  bool loaded = false;
+  char filename[40];
+  sprintf(filename, "%s/%s.id", _dir, name);
+  if (_fs->exists(filename)) {
+    File file = _fs->open(filename);
+    if (file) {
+      loaded = id.readFrom(file);
+      file.close();
+    }
+  }
+  return loaded;
+}
+
+bool IdentityStore::save(const char *name, const mesh::LocalIdentity& id) {
+  char filename[40];
+  sprintf(filename, "%s/%s.id", _dir, name);
+  File file = _fs->open(filename, "w", true);
+  if (file) {
+    id.writeTo(file);
+    file.close();
+    return true;
+  }
+  return false;
+}

src/helpers/IdentityStore.h

@@ -0,0 +1,15 @@
+#pragma once
+
+#include <FS.h>
+#include <Identity.h>
+
+class IdentityStore {
+  fs::FS* _fs;
+  const char* _dir;
+public:
+  IdentityStore(fs::FS& fs, const char* dir): _fs(&fs), _dir(dir) { }
+
+  void begin() { _fs->mkdir(_dir); }
+  bool load(const char *name, mesh::LocalIdentity& id);
+  bool save(const char *name, const mesh::LocalIdentity& id);
+};

src/helpers/RadioLibWrappers.cpp

@@ -0,0 +1,93 @@
+
+#define RADIOLIB_STATIC_ONLY 1
+#include "RadioLibWrappers.h"
+
+#define STATE_IDLE       0
+#define STATE_RX         1
+#define STATE_TX_WAIT    3
+#define STATE_TX_DONE    4
+#define STATE_INT_READY 16
+
+static volatile uint8_t state = STATE_IDLE;
+
+// this function is called when a complete packet
+// is transmitted by the module
+static 
+#if defined(ESP8266) || defined(ESP32)
+  ICACHE_RAM_ATTR
+#endif
+void setFlag(void) {
+  // we sent a packet, set the flag
+  state |= STATE_INT_READY;
+}
+
+void RadioLibWrapper::begin() {
+  _radio->setPacketReceivedAction(setFlag);  // this is also SentComplete interrupt
+  state = STATE_IDLE;
+
+  if (_board->getStartupReason() == BD_STARTUP_RX_PACKET) {  // received a LoRa packet (while in deep sleep)
+    setFlag(); // LoRa packet is already received
+  }
+}
+
+int RadioLibWrapper::recvRaw(uint8_t* bytes, int sz) {
+  if (state & STATE_INT_READY) {
+    int len = _radio->getPacketLength();
+    if (len > 0) {
+      if (len > sz) { len = sz; }
+      int err = _radio->readData(bytes, len);
+      if (err != RADIOLIB_ERR_NONE) {
+        MESH_DEBUG_PRINTLN("RadioLibWrapper: error: readData()");
+      } else {
+      //  Serial.print("  readData() -> "); Serial.println(len);
+      }
+      n_recv++;
+    }
+    state = STATE_IDLE;   // need another startReceive()
+    return len;
+  }
+
+  if (state != STATE_RX) {
+    int err = _radio->startReceive();
+    if (err != RADIOLIB_ERR_NONE) {
+      MESH_DEBUG_PRINTLN("RadioLibWrapper: error: startReceive()");
+    }
+    state = STATE_RX;
+  }
+  return 0;
+}
+
+uint32_t RadioLibWrapper::getEstAirtimeFor(int len_bytes) {
+  return _radio->getTimeOnAir(len_bytes) / 1000;
+}
+
+void RadioLibWrapper::startSendRaw(const uint8_t* bytes, int len) {
+  state = STATE_TX_WAIT;
+  _board->onBeforeTransmit();
+  int err = _radio->startTransmit((uint8_t *) bytes, len);
+  if (err != RADIOLIB_ERR_NONE) {
+    MESH_DEBUG_PRINTLN("RadioLibWrapper: error: startTransmit()");
+  }
+}
+
+bool RadioLibWrapper::isSendComplete() {
+  if (state & STATE_INT_READY) {
+    state = STATE_IDLE;
+    n_sent++;
+    return true;
+  }
+  return false;
+}
+
+void RadioLibWrapper::onSendFinished() {
+  _radio->finishTransmit();
+  _board->onAfterTransmit();
+  state = STATE_IDLE;
+}
+
+float RadioLibWrapper::getLastRSSI() const {
+  return _radio->getRSSI();
+}
+float RadioLibWrapper::getLastSNR() const {
+  return _radio->getSNR();
+}

src/helpers/RadioLibWrappers.h

@@ -0,0 +1,42 @@
+#pragma once
+
+#include <Mesh.h>
+#include <RadioLib.h>
+
+class RadioLibWrapper : public mesh::Radio {
+protected:
+  PhysicalLayer* _radio;
+  mesh::MainBoard* _board;
+  uint32_t n_recv, n_sent;
+
+public:
+  RadioLibWrapper(PhysicalLayer& radio, mesh::MainBoard& board) : _radio(&radio), _board(&board) { n_recv = n_sent = 0; }
+
+  void begin() override;
+  int recvRaw(uint8_t* bytes, int sz) override;
+  uint32_t getEstAirtimeFor(int len_bytes) override;
+  void startSendRaw(const uint8_t* bytes, int len) override;
+  bool isSendComplete() override;
+  void onSendFinished() override;
+
+  uint32_t getPacketsRecv() const { return n_recv; }
+  uint32_t getPacketsSent() const { return n_sent; }
+  virtual float getLastRSSI() const;
+  virtual float getLastSNR() const;
+};
+
+/**
+ * \brief  an RNG impl using the noise from the LoRa radio as entropy.
+ *         NOTE: this is VERY SLOW!  Use only for things like creating new LocalIdentity
+*/
+class RadioNoiseListener : public mesh::RNG {
+  PhysicalLayer* _radio;
+public:
+  RadioNoiseListener(PhysicalLayer& radio): _radio(&radio) { }
+
+  void random(uint8_t* dest, size_t sz) override {
+    for (int i = 0; i < sz; i++) {
+      dest[i] = _radio->randomByte() ^ (::random(0, 256) & 0xFF);
+    }
+  }
+};

src/helpers/SimpleMeshTables.h

@@ -0,0 +1,56 @@
+#pragma once
+
+#include <MeshTables.h>
+
+#ifdef ESP32
+  #include <FS.h>
+#endif
+
+#define MAX_PACKET_HASHES  64
+
+class SimpleMeshTables : public mesh::MeshTables {
+  uint8_t _fwd_hashes[MAX_PACKET_HASHES*MAX_HASH_SIZE];
+  int _next_fwd_idx;
+
+  int lookupHashIndex(const uint8_t* hash) const {
+    const uint8_t* sp = _fwd_hashes;
+    for (int i = 0; i < MAX_PACKET_HASHES; i++, sp += MAX_HASH_SIZE) {
+      if (memcmp(hash, sp, MAX_HASH_SIZE) == 0) return i;
+    }
+    return -1;
+  }
+
+public:
+  SimpleMeshTables() { 
+    memset(_fwd_hashes, 0, sizeof(_fwd_hashes));
+    _next_fwd_idx = 0;
+  }
+
+#ifdef ESP32
+  void restoreFrom(File f) {
+    f.read(_fwd_hashes, sizeof(_fwd_hashes));
+    f.read((uint8_t *) &_next_fwd_idx, sizeof(_next_fwd_idx));
+  }
+  void saveTo(File f) {
+    f.write(_fwd_hashes, sizeof(_fwd_hashes));
+    f.write((const uint8_t *) &_next_fwd_idx, sizeof(_next_fwd_idx));
+  }
+#endif
+
+  bool hasForwarded(const uint8_t* packet_hash) const override {
+    int i = lookupHashIndex(packet_hash);
+    return i >= 0;
+  }
+
+  void setHasForwarded(const uint8_t* packet_hash) override {
+    int i = lookupHashIndex(packet_hash);
+    if (i >= 0) {
+      // already in table
+    } else {
+      memcpy(&_fwd_hashes[_next_fwd_idx*MAX_HASH_SIZE], packet_hash, MAX_HASH_SIZE);
+
+      _next_fwd_idx = (_next_fwd_idx + 1) % MAX_PACKET_HASHES;  // cyclic table
+    }
+  }
+
+};

src/helpers/SimpleSeenTable.h

@@ -0,0 +1,33 @@
+#pragma once
+
+#include <Packet.h>
+#include <string.h>
+
+#define MAX_PACKET_HASHES  64
+
+class SimpleSeenTable {
+  uint8_t _hashes[MAX_PACKET_HASHES*MAX_HASH_SIZE];
+  int _next_idx;
+
+public:
+  SimpleSeenTable() { 
+    memset(_hashes, 0, sizeof(_hashes));
+    _next_idx = 0;
+  }
+
+  bool hasSeenPacket(const mesh::Packet* packet) {
+    uint8_t hash[MAX_HASH_SIZE];
+    packet->calculatePacketHash(hash);
+
+    const uint8_t* sp = _hashes;
+    for (int i = 0; i < MAX_PACKET_HASHES; i++, sp += MAX_HASH_SIZE) {
+      if (memcmp(hash, sp, MAX_HASH_SIZE) == 0) return true;
+    }
+
+    memcpy(&_hashes[_next_idx*MAX_HASH_SIZE], hash, MAX_HASH_SIZE);
+    _next_idx = (_next_idx + 1) % MAX_PACKET_HASHES;  // cyclic table
+
+    return false;
+  }
+
+};

src/helpers/StaticPoolPacketManager.cpp

@@ -0,0 +1,97 @@
+#include "StaticPoolPacketManager.h"
+
+PacketQueue::PacketQueue(int max_entries) {
+  _table = new mesh::Packet*[max_entries];
+  _pri_table = new uint8_t[max_entries];
+  _schedule_table = new uint32_t[max_entries];
+  _size = max_entries;
+  _num = 0;
+}
+
+mesh::Packet* PacketQueue::get(uint32_t now) {
+  uint8_t min_pri = 0xFF;
+  int best_idx = -1;
+  for (int j = 0; j < _num; j++) {
+    if (_schedule_table[j] > now) continue;   // scheduled for future... ignore for now
+    if (_pri_table[j] < min_pri) {  // select most important priority amongst non-future entries
+      min_pri = _pri_table[j];
+      best_idx = j;
+    }
+  }
+  if (best_idx < 0) return NULL;   // empty, or all items are still in the future
+
+  mesh::Packet* top = _table[best_idx];
+  int i = best_idx;
+  _num--;
+  while (i < _num) {
+    _table[i] = _table[i+1];
+    _pri_table[i] = _pri_table[i+1];
+    _schedule_table[i] = _schedule_table[i+1];
+    i++;
+  }
+  return top;
+}
+
+mesh::Packet* PacketQueue::removeByIdx(int i) {
+  if (i >= _num) return NULL;  // invalid index
+
+  mesh::Packet* item = _table[i];
+  _num--;
+  while (i < _num) {
+    _table[i] = _table[i+1];
+    _pri_table[i] = _pri_table[i+1];
+    _schedule_table[i] = _schedule_table[i+1];
+    i++;
+  }
+  return item;
+}
+
+void PacketQueue::add(mesh::Packet* packet, uint8_t priority, uint32_t scheduled_for) {
+  if (_num == _size) {
+    // TODO: log "FATAL: queue is full!"
+    return;
+  }
+  _table[_num] = packet;
+  _pri_table[_num] = priority;
+  _schedule_table[_num] = scheduled_for;
+  _num++;
+}
+
+StaticPoolPacketManager::StaticPoolPacketManager(int pool_size): unused(pool_size), send_queue(pool_size) {
+  // load up our unusued Packet pool
+  for (int i = 0; i < pool_size; i++) {
+    unused.add(new mesh::Packet(), 0, 0);
+  }
+}
+
+mesh::Packet* StaticPoolPacketManager::allocNew() {
+  return unused.removeByIdx(0);  // just get first one (returns NULL if empty)
+}
+
+void StaticPoolPacketManager::free(mesh::Packet* packet) {
+  unused.add(packet, 0, 0);
+}
+
+void StaticPoolPacketManager::queueOutbound(mesh::Packet* packet, uint8_t priority, uint32_t scheduled_for) {
+  send_queue.add(packet, priority, scheduled_for);
+}
+
+mesh::Packet* StaticPoolPacketManager::getNextOutbound(uint32_t now) {
+  //send_queue.sort();   // sort by scheduled_for/priority first
+  return send_queue.get(now);
+}
+
+int  StaticPoolPacketManager::getOutboundCount() const {
+  return send_queue.count();
+}
+
+int StaticPoolPacketManager::getFreeCount() const {
+  return unused.count();
+}
+
+mesh::Packet* StaticPoolPacketManager::getOutboundByIdx(int i) {
+  return send_queue.itemAt(i);
+}
+mesh::Packet* StaticPoolPacketManager::removeOutboundByIdx(int i) {
+  return send_queue.removeByIdx(i);
+}

src/helpers/StaticPoolPacketManager.h

@@ -0,0 +1,34 @@
+#pragma once
+
+#include <Dispatcher.h>
+
+class PacketQueue {
+  mesh::Packet** _table;
+  uint8_t* _pri_table;
+  uint32_t* _schedule_table;
+  int _size, _num;
+
+public:
+  PacketQueue(int max_entries);
+  mesh::Packet* get(uint32_t now);
+  void add(mesh::Packet* packet, uint8_t priority, uint32_t scheduled_for);
+  int count() const { return _num; }
+  mesh::Packet* itemAt(int i) const { return _table[i]; }
+  mesh::Packet* removeByIdx(int i);
+};
+
+class StaticPoolPacketManager : public mesh::PacketManager {
+  PacketQueue unused, send_queue;
+
+public:
+  StaticPoolPacketManager(int pool_size);
+
+  mesh::Packet* allocNew() override;
+  void free(mesh::Packet* packet) override;
+  void queueOutbound(mesh::Packet* packet, uint8_t priority, uint32_t scheduled_for) override;
+  mesh::Packet* getNextOutbound(uint32_t now) override;
+  int getOutboundCount() const override;
+  int getFreeCount() const override;
+  mesh::Packet* getOutboundByIdx(int i) override;
+  mesh::Packet* removeOutboundByIdx(int i) override;
+};