crypto/p224_spake.cc

   1 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style license that can be
   3 // found in the LICENSE file.
   4
   5 // This code implements SPAKE2, a variant of EKE:
   6 //  http://www.di.ens.fr/~pointche/pub.php?reference=AbPo04
   7
   8 #include <crypto/p224_spake.h>
   9
  10 #include <base/logging.h>
  11 #include <crypto/p224.h>
  12 #include <crypto/random.h>
  13 #include <crypto/secure_util.h>
  14
  15 namespace {
  16
  17 // The following two points (M and N in the protocol) are verifiable random
  18 // points on the curve and can be generated with the following code:
  19
  20 // #include <stdint.h>
  21 // #include <stdio.h>
  22 // #include <string.h>
  23 //
  24 // #include <openssl/ec.h>
  25 // #include <openssl/obj_mac.h>
  26 // #include <openssl/sha.h>
  27 //
  28 // static const char kSeed1[] = "P224 point generation seed (M)";
  29 // static const char kSeed2[] = "P224 point generation seed (N)";
  30 //
  31 // void find_seed(const char* seed) {
  32 //   SHA256_CTX sha256;
  33 //   uint8_t digest[SHA256_DIGEST_LENGTH];
  34 //
  35 //   SHA256_Init(&sha256);
  36 //   SHA256_Update(&sha256, seed, strlen(seed));
  37 //   SHA256_Final(digest, &sha256);
  38 //
  39 //   BIGNUM x, y;
  40 //   EC_GROUP* p224 = EC_GROUP_new_by_curve_name(NID_secp224r1);
  41 //   EC_POINT* p = EC_POINT_new(p224);
  42 //
  43 //   for (unsigned i = 0;; i++) {
  44 //     BN_init(&x);
  45 //     BN_bin2bn(digest, 28, &x);
  46 //
  47 //     if (EC_POINT_set_compressed_coordinates_GFp(
  48 //             p224, p, &x, digest[28] & 1, NULL)) {
  49 //       BN_init(&y);
  50 //       EC_POINT_get_affine_coordinates_GFp(p224, p, &x, &y, NULL);
  51 //       char* x_str = BN_bn2hex(&x);
  52 //       char* y_str = BN_bn2hex(&y);
  53 //       printf("Found after %u iterations:\n%s\n%s\n", i, x_str, y_str);
  54 //       OPENSSL_free(x_str);
  55 //       OPENSSL_free(y_str);
  56 //       BN_free(&x);
  57 //       BN_free(&y);
  58 //       break;
  59 //     }
  60 //
  61 //     SHA256_Init(&sha256);
  62 //     SHA256_Update(&sha256, digest, sizeof(digest));
  63 //     SHA256_Final(digest, &sha256);
  64 //
  65 //     BN_free(&x);
  66 //   }
  67 //
  68 //   EC_POINT_free(p);
  69 //   EC_GROUP_free(p224);
  70 // }
  71 //
  72 // int main() {
  73 //   find_seed(kSeed1);
  74 //   find_seed(kSeed2);
  75 //   return 0;
  76 // }
  77
  78 const crypto::p224::Point kM = {
  79   {174237515, 77186811, 235213682, 33849492,
  80    33188520, 48266885, 177021753, 81038478},
  81   {104523827, 245682244, 266509668, 236196369,
  82    28372046, 145351378, 198520366, 113345994},
  83   {1, 0, 0, 0, 0, 0, 0},
  84 };
  85
  86 const crypto::p224::Point kN = {
  87   {136176322, 263523628, 251628795, 229292285,
  88    5034302, 185981975, 171998428, 11653062},
  89   {197567436, 51226044, 60372156, 175772188,
  90    42075930, 8083165, 160827401, 65097570},
  91   {1, 0, 0, 0, 0, 0, 0},
  92 };
  93
  94 }  // anonymous namespace
  95
  96 namespace crypto {
  97
  98 P224EncryptedKeyExchange::P224EncryptedKeyExchange(
  99     PeerType peer_type, const base::StringPiece& password)
 100     : state_(kStateInitial),
 101       is_server_(peer_type == kPeerTypeServer) {
 102   memset(&x_, 0, sizeof(x_));
 103   memset(&expected_authenticator_, 0, sizeof(expected_authenticator_));
 104
 105   // x_ is a random scalar.
 106   RandBytes(x_, sizeof(x_));
 107
 108   // X = g**x_
 109   p224::Point X;
 110   p224::ScalarBaseMult(x_, &X);
 111
 112   // Calculate |password| hash to get SPAKE password value.
 113   SHA256HashString(std::string(password.data(), password.length()),
 114                    pw_, sizeof(pw_));
 115
 116   // The client masks the Diffie-Hellman value, X, by adding M**pw and the
 117   // server uses N**pw.
 118   p224::Point MNpw;
 119   p224::ScalarMult(is_server_ ? kN : kM, pw_, &MNpw);
 120
 121   // X* = X + (N|M)**pw
 122   p224::Point Xstar;
 123   p224::Add(X, MNpw, &Xstar);
 124
 125   next_message_ = Xstar.ToString();
 126 }
 127
 128 const std::string& P224EncryptedKeyExchange::GetMessage() {
 129   if (state_ == kStateInitial) {
 130     state_ = kStateRecvDH;
 131     return next_message_;
 132   } else if (state_ == kStateSendHash) {
 133     state_ = kStateRecvHash;
 134     return next_message_;
 135   }
 136
 137   LOG(FATAL) << "P224EncryptedKeyExchange::GetMessage called in"
 138                 " bad state " << state_;
 139   next_message_ = "";
 140   return next_message_;
 141 }
 142
 143 P224EncryptedKeyExchange::Result P224EncryptedKeyExchange::ProcessMessage(
 144     const base::StringPiece& message) {
 145   if (state_ == kStateRecvHash) {
 146     // This is the final state of the protocol: we are reading the peer's
 147     // authentication hash and checking that it matches the one that we expect.
 148     if (message.size() != sizeof(expected_authenticator_)) {
 149       error_ = "peer's hash had an incorrect size";
 150       return kResultFailed;
 151     }
 152     if (!SecureMemEqual(message.data(), expected_authenticator_,
 153                         message.size())) {
 154       error_ = "peer's hash had incorrect value";
 155       return kResultFailed;
 156     }
 157     state_ = kStateDone;
 158     return kResultSuccess;
 159   }
 160
 161   if (state_ != kStateRecvDH) {
 162     LOG(FATAL) << "P224EncryptedKeyExchange::ProcessMessage called in"
 163                   " bad state " << state_;
 164     error_ = "internal error";
 165     return kResultFailed;
 166   }
 167
 168   // Y* is the other party's masked, Diffie-Hellman value.
 169   p224::Point Ystar;
 170   if (!Ystar.SetFromString(message)) {
 171     error_ = "failed to parse peer's masked Diffie-Hellman value";
 172     return kResultFailed;
 173   }
 174
 175   // We calculate the mask value: (N|M)**pw
 176   p224::Point MNpw, minus_MNpw, Y, k;
 177   p224::ScalarMult(is_server_ ? kM : kN, pw_, &MNpw);
 178   p224::Negate(MNpw, &minus_MNpw);
 179
 180   // Y = Y* - (N|M)**pw
 181   p224::Add(Ystar, minus_MNpw, &Y);
 182
 183   // K = Y**x_
 184   p224::ScalarMult(Y, x_, &k);
 185
 186   // If everything worked out, then K is the same for both parties.
 187   key_ = k.ToString();
 188
 189   std::string client_masked_dh, server_masked_dh;
 190   if (is_server_) {
 191     client_masked_dh = message.as_string();
 192     server_masked_dh = next_message_;
 193   } else {
 194     client_masked_dh = next_message_;
 195     server_masked_dh = message.as_string();
 196   }
 197
 198   // Now we calculate the hashes that each side will use to prove to the other
 199   // that they derived the correct value for K.
 200   uint8 client_hash[kSHA256Length], server_hash[kSHA256Length];
 201   CalculateHash(kPeerTypeClient, client_masked_dh, server_masked_dh, key_,
 202                 client_hash);
 203   CalculateHash(kPeerTypeServer, client_masked_dh, server_masked_dh, key_,
 204                 server_hash);
 205
 206   const uint8* my_hash = is_server_ ? server_hash : client_hash;
 207   const uint8* their_hash = is_server_ ? client_hash : server_hash;
 208
 209   next_message_ =
 210       std::string(reinterpret_cast<const char*>(my_hash), kSHA256Length);
 211   memcpy(expected_authenticator_, their_hash, kSHA256Length);
 212   state_ = kStateSendHash;
 213   return kResultPending;
 214 }
 215
 216 void P224EncryptedKeyExchange::CalculateHash(
 217     PeerType peer_type,
 218     const std::string& client_masked_dh,
 219     const std::string& server_masked_dh,
 220     const std::string& k,
 221     uint8* out_digest) {
 222   std::string hash_contents;
 223
 224   if (peer_type == kPeerTypeServer) {
 225     hash_contents = "server";
 226   } else {
 227     hash_contents = "client";
 228   }
 229
 230   hash_contents += client_masked_dh;
 231   hash_contents += server_masked_dh;
 232   hash_contents +=
 233       std::string(reinterpret_cast<const char *>(pw_), sizeof(pw_));
 234   hash_contents += k;
 235
 236   SHA256HashString(hash_contents, out_digest, kSHA256Length);
 237 }
 238
 239 const std::string& P224EncryptedKeyExchange::error() const {
 240   return error_;
 241 }
 242
 243 const std::string& P224EncryptedKeyExchange::GetKey() {
 244   DCHECK_EQ(state_, kStateDone);
 245   return key_;
 246 }
 247
 248 }  // namespace crypto