net: add low-entropy, shared secret authentication protocol.

crypto/p224_spake.cc

+// Copyright (c) 2011 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// This code implements SPAKE2, a varient of EKE:
+//  http://www.di.ens.fr/~pointche/pub.php?reference=AbPo04
+
+#include <crypto/p224_spake.h>
+
+#include <base/logging.h>
+#include <base/rand_util.h>
+#include <crypto/p224.h>
+#include <crypto/secure_util.h>
+
+namespace {
+
+// The following two points (M and N in the protocol) are verifiable random
+// points on the curve and can be generated with the following code:
+
+// #include <stdint.h>
+// #include <stdio.h>
+// #include <string.h>
+//
+// #include <openssl/ec.h>
+// #include <openssl/obj_mac.h>
+// #include <openssl/sha.h>
+//
+// static const char kSeed1[] = "P224 point generation seed (M)";
+// static const char kSeed2[] = "P224 point generation seed (N)";
+//
+// void find_seed(const char* seed) {
+//   SHA256_CTX sha256;
+//   uint8_t digest[SHA256_DIGEST_LENGTH];
+//
+//   SHA256_Init(&sha256);
+//   SHA256_Update(&sha256, seed, strlen(seed));
+//   SHA256_Final(digest, &sha256);
+//
+//   BIGNUM x, y;
+//   EC_GROUP* p224 = EC_GROUP_new_by_curve_name(NID_secp224r1);
+//   EC_POINT* p = EC_POINT_new(p224);
+//
+//   for (unsigned i = 0;; i++) {
+//     BN_init(&x);
+//     BN_bin2bn(digest, 28, &x);
+//
+//     if (EC_POINT_set_compressed_coordinates_GFp(
+//             p224, p, &x, digest[28] & 1, NULL)) {
+//       BN_init(&y);
+//       EC_POINT_get_affine_coordinates_GFp(p224, p, &x, &y, NULL);
+//       char* x_str = BN_bn2hex(&x);
+//       char* y_str = BN_bn2hex(&y);
+//       printf("Found after %u iterations:\n%s\n%s\n", i, x_str, y_str);
+//       OPENSSL_free(x_str);
+//       OPENSSL_free(y_str);
+//       BN_free(&x);
+//       BN_free(&y);
+//       break;
+//     }
+//
+//     SHA256_Init(&sha256);
+//     SHA256_Update(&sha256, digest, sizeof(digest));
+//     SHA256_Final(digest, &sha256);
+//
+//     BN_free(&x);
+//   }
+//
+//   EC_POINT_free(p);
+//   EC_GROUP_free(p224);
+// }
+//
+// int main() {
+//   find_seed(kSeed1);
+//   find_seed(kSeed2);
+//   return 0;
+// }
+
+const crypto::p224::Point kM = {
+  {174237515, 77186811, 235213682, 33849492,
+   33188520, 48266885, 177021753, 81038478},
+  {104523827, 245682244, 266509668, 236196369,
+   28372046, 145351378, 198520366, 113345994},
+  {1, 0, 0, 0, 0, 0, 0},
+};
+
+const crypto::p224::Point kN = {
+  {136176322, 263523628, 251628795, 229292285,
+   5034302, 185981975, 171998428, 11653062},
+  {197567436, 51226044, 60372156, 175772188,
+   42075930, 8083165, 160827401, 65097570},
+  {1, 0, 0, 0, 0, 0, 0},
+};
+
+}  // anonymous namespace
+
+namespace crypto {
+
+P224EncryptedKeyExchange::P224EncryptedKeyExchange(
+    PeerType peer_type,
+    const base::StringPiece& password,
+    const base::StringPiece& session)
+    : state_(kStateInitial),
+      is_server_(peer_type == kPeerTypeServer) {
+  // x_ is a random scalar.
+  base::RandBytes(x_, sizeof(x_));
+
+  // X = g**x_
+  p224::Point X;
+  p224::ScalarBaseMult(x_, &X);
+
+  // The "password" in the SPAKE2 protocol is
+  // SHA256(P(password) + P(session)) where P is function that prepends a
+  // uint32, big-endian length prefix.
+  uint8 password_length[4], session_length[4];
+  password_length[0] = password.size() >> 24;
+  password_length[1] = password.size() >> 16;
+  password_length[2] = password.size() >> 8;
+  password_length[3] = password.size();
+  session_length[0] = session.size() >> 24;
+  session_length[1] = session.size() >> 16;
+  session_length[2] = session.size() >> 8;
+  session_length[3] = session.size();
+  SHA256HashString(std::string(reinterpret_cast<const char *>(password_length),
+                               sizeof(password_length)) +
+                   password.as_string() +
+                   std::string(reinterpret_cast<const char *>(session_length),
+                               sizeof(session_length)) +
+                   session.as_string(),
+                   pw_,
+                   sizeof(pw_));
+
+  // The client masks the Diffie-Hellman value, X, by adding M**pw and the
+  // server uses N**pw.
+  p224::Point MNpw;
+  p224::ScalarMult(is_server_ ? kN : kM, pw_, &MNpw);
+
+  // X* = X + (N|M)**pw
+  p224::Point Xstar;
+  p224::Add(X, MNpw, &Xstar);
+
+  next_message_ = Xstar.ToString();
+}
+
+const std::string& P224EncryptedKeyExchange::GetMessage() {
+  if (state_ == kStateInitial) {
+    state_ = kStateRecvDH;
+    return next_message_;
+  } else if (state_ == kStateSendHash) {
+    state_ = kStateRecvHash;
+    return next_message_;
+  }
+
+  LOG(FATAL) << "P224EncryptedKeyExchange::GetMessage called in"
+                " bad state " << state_;
+  next_message_ = "";
+  return next_message_;
+}
+
+P224EncryptedKeyExchange::Result P224EncryptedKeyExchange::ProcessMessage(
+    const base::StringPiece& message) {
+  if (state_ == kStateRecvHash) {
+    // This is the final state of the protocol: we are reading the peer's
+    // authentication hash and checking that it matches the one that we expect.
+    if (message.size() != sizeof(expected_authenticator_)) {
+      error_ = "peer's hash had an incorrect size";
+      return kResultFailed;
+    }
+    if (!SecureMemEqual(message.data(), expected_authenticator_,
+                        message.size())) {
+      error_ = "peer's hash had incorrect value";
+      return kResultFailed;
+    }
+    state_ = kStateDone;
+    return kResultSuccess;
+  }
+
+  if (state_ != kStateRecvDH) {
+    LOG(FATAL) << "P224EncryptedKeyExchange::ProcessMessage called in"
+                  " bad state " << state_;
+    error_ = "internal error";
+    return kResultFailed;
+  }
+
+  // Y* is the other party's masked, Diffie-Hellman value.
+  p224::Point Ystar;
+  if (!Ystar.SetFromString(message)) {
+    error_ = "failed to parse peer's masked Diffie-Hellman value";
+    return kResultFailed;
+  }
+
+  // We calculate the mask value: (N|M)**pw
+  p224::Point MNpw, minus_MNpw, Y, k;
+  p224::ScalarMult(is_server_ ? kM : kN, pw_, &MNpw);
+  p224::Negate(MNpw, &minus_MNpw);
+
+  // Y = Y* - (N|M)**pw
+  p224::Add(Ystar, minus_MNpw, &Y);
+
+  // K = Y**x_
+  p224::ScalarMult(Y, x_, &k);
+
+  // If everything worked out, then K is the same for both parties.
+  std::string k_str = k.ToString();
+
+  std::string client_masked_dh, server_masked_dh;
+  if (is_server_) {
+    client_masked_dh = message.as_string();
+    server_masked_dh = next_message_;
+  } else {
+    client_masked_dh = next_message_;
+    server_masked_dh = message.as_string();
+  }
+
+  // Now we calculate the hashes that each side will use to prove to the other
+  // that they derived the correct value for K.
+  uint8 client_hash[kSHA256Length], server_hash[kSHA256Length];
+  CalculateHash(kPeerTypeClient, client_masked_dh, server_masked_dh, k_str,
+                client_hash);
+  CalculateHash(kPeerTypeServer, client_masked_dh, server_masked_dh, k_str,
+                server_hash);
+
+  const uint8* my_hash = is_server_ ? server_hash : client_hash;
+  const uint8* their_hash = is_server_ ? client_hash : server_hash;
+
+  next_message_ =
+      std::string(reinterpret_cast<const char*>(my_hash), kSHA256Length);
+  memcpy(expected_authenticator_, their_hash, kSHA256Length);
+  state_ = kStateSendHash;
+  return kResultPending;
+}
+
+void P224EncryptedKeyExchange::CalculateHash(
+    PeerType peer_type,
+    const std::string& client_masked_dh,
+    const std::string& server_masked_dh,
+    const std::string& k,
+    uint8* out_digest) {
+  std::string hash_contents;
+
+  if (peer_type == kPeerTypeServer) {
+    hash_contents = "server";
+  } else {
+    hash_contents = "client";
+  }
+
+  hash_contents += client_masked_dh;
+  hash_contents += server_masked_dh;
+  hash_contents +=
+      std::string(reinterpret_cast<const char *>(pw_), sizeof(pw_));
+  hash_contents += k;
+
+  SHA256HashString(hash_contents, out_digest, kSHA256Length);
+}
+
+const std::string& P224EncryptedKeyExchange::error() const {
+  return error_;
+}
+
+}  // namespace crypto