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
P224EncryptedKeyExchange(PeerType peer_type,const base::StringPiece & password)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
GetMessage()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
ProcessMessage(const base::StringPiece & message)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
CalculateHash(PeerType peer_type,const std::string & client_masked_dh,const std::string & server_masked_dh,const std::string & k,uint8 * out_digest)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
error() const239 const std::string& P224EncryptedKeyExchange::error() const {
240 return error_;
241 }
242
GetKey()243 const std::string& P224EncryptedKeyExchange::GetKey() {
244 DCHECK_EQ(state_, kStateDone);
245 return key_;
246 }
247
248 } // namespace crypto
249