1 /* Copyright (c) 2016, Google Inc.
2 *
3 * Permission to use, copy, modify, and/or distribute this software for any
4 * purpose with or without fee is hereby granted, provided that the above
5 * copyright notice and this permission notice appear in all copies.
6 *
7 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
10 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
12 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
13 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
14
15 #include <openssl/curve25519.h>
16
17 #include <string.h>
18
19 #include <openssl/bytestring.h>
20 #include <openssl/mem.h>
21 #include <openssl/rand.h>
22 #include <openssl/sha.h>
23
24 #include "internal.h"
25 #include "../internal.h"
26
27
28 /* The following precomputation tables are for the following
29 * points used in the SPAKE2 protocol.
30 *
31 * N:
32 * x: 49918732221787544735331783592030787422991506689877079631459872391322455579424
33 * y: 54629554431565467720832445949441049581317094546788069926228343916274969994000
34 * encoded: 10e3df0ae37d8e7a99b5fe74b44672103dbddcbd06af680d71329a11693bc778
35 *
36 * M:
37 * x: 31406539342727633121250288103050113562375374900226415211311216773867585644232
38 * y: 21177308356423958466833845032658859666296341766942662650232962324899758529114
39 * encoded: 5ada7e4bf6ddd9adb6626d32131c6b5c51a1e347a3478f53cfcf441b88eed12e
40 *
41 * These points and their precomputation tables are generated with the
42 * following Python code. For a description of the precomputation table,
43 * see curve25519.c in this directory.
44 *
45 * Exact copies of the source code are kept in bug 27296743.
46 *
47 * import hashlib
48 * import ed25519 as E # http://ed25519.cr.yp.to/python/ed25519.py
49 *
50 * SEED_N = 'edwards25519 point generation seed (N)'
51 * SEED_M = 'edwards25519 point generation seed (M)'
52 *
53 * def genpoint(seed):
54 * v = hashlib.sha256(seed).digest()
55 * it = 1
56 * while True:
57 * try:
58 * x,y = E.decodepoint(v)
59 * except Exception, e:
60 * print e
61 * it += 1
62 * v = hashlib.sha256(v).digest()
63 * continue
64 * print "Found in %d iterations:" % it
65 * print " x = %d" % x
66 * print " y = %d" % y
67 * print " Encoded (hex)"
68 * print E.encodepoint((x,y)).encode('hex')
69 * return (x,y)
70 *
71 * def gentable(P):
72 * t = []
73 * for i in range(1,16):
74 * k = (i >> 3 & 1) * (1 << 192) + \
75 * (i >> 2 & 1) * (1 << 128) + \
76 * (i >> 1 & 1) * (1 << 64) + \
77 * (i & 1)
78 * t.append(E.scalarmult(P, k))
79 * return ''.join(E.encodeint(x) + E.encodeint(y) for (x,y) in t)
80 *
81 * def printtable(table, name):
82 * print "static const uint8_t %s[15 * 2 * 32] = {" % name,
83 * for i in range(15 * 2 * 32):
84 * if i % 12 == 0:
85 * print "\n ",
86 * print " 0x%02x," % ord(table[i]),
87 * print "\n};"
88 *
89 * if __name__ == "__main__":
90 * print "Searching for N"
91 * N = genpoint(SEED_N)
92 * print "Generating precomputation table for N"
93 * Ntable = gentable(N)
94 * printtable(Ntable, "kSpakeNSmallPrecomp")
95 *
96 * print "Searching for M"
97 * M = genpoint(SEED_M)
98 * print "Generating precomputation table for M"
99 * Mtable = gentable(M)
100 * printtable(Mtable, "kSpakeMSmallPrecomp")
101 */
102 static const uint8_t kSpakeNSmallPrecomp[15 * 2 * 32] = {
103 0x20, 0x1b, 0xc5, 0xb3, 0x43, 0x17, 0x71, 0x10, 0x44, 0x1e, 0x73, 0xb3,
104 0xae, 0x3f, 0xbf, 0x9f, 0xf5, 0x44, 0xc8, 0x13, 0x8f, 0xd1, 0x01, 0xc2,
105 0x8a, 0x1a, 0x6d, 0xea, 0x4d, 0x00, 0x5d, 0x6e, 0x10, 0xe3, 0xdf, 0x0a,
106 0xe3, 0x7d, 0x8e, 0x7a, 0x99, 0xb5, 0xfe, 0x74, 0xb4, 0x46, 0x72, 0x10,
107 0x3d, 0xbd, 0xdc, 0xbd, 0x06, 0xaf, 0x68, 0x0d, 0x71, 0x32, 0x9a, 0x11,
108 0x69, 0x3b, 0xc7, 0x78, 0x93, 0xf1, 0x57, 0x97, 0x6e, 0xf0, 0x6e, 0x45,
109 0x37, 0x4a, 0xf4, 0x0b, 0x18, 0x51, 0xf5, 0x4f, 0x67, 0x3c, 0xdc, 0xec,
110 0x84, 0xed, 0xd0, 0xeb, 0xca, 0xfb, 0xdb, 0xff, 0x7f, 0xeb, 0xa8, 0x23,
111 0x68, 0x87, 0x13, 0x64, 0x6a, 0x10, 0xf7, 0x45, 0xe0, 0x0f, 0x32, 0x21,
112 0x59, 0x7c, 0x0e, 0x50, 0xad, 0x56, 0xd7, 0x12, 0x69, 0x7b, 0x58, 0xf8,
113 0xb9, 0x3b, 0xa5, 0xbb, 0x4d, 0x1b, 0x87, 0x1c, 0x46, 0xa7, 0x17, 0x9d,
114 0x6d, 0x84, 0x45, 0xbe, 0x7f, 0x95, 0xd2, 0x34, 0xcd, 0x89, 0x95, 0xc0,
115 0xf0, 0xd3, 0xdf, 0x6e, 0x10, 0x4a, 0xe3, 0x7b, 0xce, 0x7f, 0x40, 0x27,
116 0xc7, 0x2b, 0xab, 0x66, 0x03, 0x59, 0xb4, 0x7b, 0xc7, 0xc7, 0xf0, 0x39,
117 0x9a, 0x33, 0x35, 0xbf, 0xcc, 0x2f, 0xf3, 0x2e, 0x68, 0x9d, 0x53, 0x5c,
118 0x88, 0x52, 0xe3, 0x77, 0x90, 0xa1, 0x27, 0x85, 0xc5, 0x74, 0x7f, 0x23,
119 0x0e, 0x93, 0x01, 0x3e, 0xe7, 0x2e, 0x2e, 0x95, 0xf3, 0x0d, 0xc2, 0x25,
120 0x25, 0x39, 0x39, 0x3d, 0x6e, 0x8e, 0x89, 0xbd, 0xe8, 0xbb, 0x67, 0x5e,
121 0x8c, 0x66, 0x8b, 0x63, 0x28, 0x1e, 0x4e, 0x74, 0x85, 0xa8, 0xaf, 0x0f,
122 0x12, 0x5d, 0xb6, 0x8a, 0x83, 0x1a, 0x77, 0x76, 0x5e, 0x62, 0x8a, 0xa7,
123 0x3c, 0xb8, 0x05, 0x57, 0x2b, 0xaf, 0x36, 0x2e, 0x10, 0x90, 0xb2, 0x39,
124 0xb4, 0x3e, 0x75, 0x6d, 0x3a, 0xa8, 0x31, 0x35, 0xc2, 0x1e, 0x8f, 0xc2,
125 0x79, 0x89, 0x35, 0x16, 0x26, 0xd1, 0xc7, 0x0b, 0x04, 0x1f, 0x1d, 0xf9,
126 0x9c, 0x05, 0xa6, 0x6b, 0xb5, 0x19, 0x5a, 0x24, 0x6d, 0x91, 0xc5, 0x31,
127 0xfd, 0xc5, 0xfa, 0xe7, 0xa6, 0xcb, 0x0e, 0x4b, 0x18, 0x0d, 0x94, 0xc7,
128 0xee, 0x1d, 0x46, 0x1f, 0x92, 0xb1, 0xb2, 0x4a, 0x2b, 0x43, 0x37, 0xfe,
129 0xc2, 0x15, 0x11, 0x89, 0xef, 0x59, 0x73, 0x3c, 0x06, 0x76, 0x78, 0xcb,
130 0xa6, 0x0d, 0x79, 0x5f, 0x28, 0x0b, 0x5b, 0x8c, 0x9e, 0xe4, 0xaa, 0x51,
131 0x9a, 0x42, 0x6f, 0x11, 0x50, 0x3d, 0x01, 0xd6, 0x21, 0xc0, 0x99, 0x5e,
132 0x1a, 0xe8, 0x81, 0x25, 0x80, 0xeb, 0xed, 0x5d, 0x37, 0x47, 0x30, 0x70,
133 0xa0, 0x4e, 0x0b, 0x43, 0x17, 0xbe, 0xb6, 0x47, 0xe7, 0x2a, 0x62, 0x9d,
134 0x5d, 0xa6, 0xc5, 0x33, 0x62, 0x9d, 0x56, 0x24, 0x9d, 0x1d, 0xb2, 0x13,
135 0xbc, 0x17, 0x66, 0x43, 0xd1, 0x68, 0xd5, 0x3b, 0x17, 0x69, 0x17, 0xa6,
136 0x06, 0x9e, 0x12, 0xb8, 0x7c, 0xd5, 0xaf, 0x3e, 0x21, 0x1b, 0x31, 0xeb,
137 0x0b, 0xa4, 0x98, 0x1c, 0xf2, 0x6a, 0x5e, 0x7c, 0x9b, 0x45, 0x8f, 0xb2,
138 0x12, 0x06, 0xd5, 0x8c, 0x1d, 0xb2, 0xa7, 0x57, 0x5f, 0x2f, 0x4f, 0xdb,
139 0x52, 0x99, 0x7c, 0x58, 0x01, 0x5f, 0xf2, 0xa5, 0xf6, 0x51, 0x86, 0x21,
140 0x2f, 0x5b, 0x8d, 0x6a, 0xae, 0x83, 0x34, 0x6d, 0x58, 0x4b, 0xef, 0xfe,
141 0xbf, 0x73, 0x5d, 0xdb, 0xc4, 0x97, 0x2a, 0x85, 0xf3, 0x6c, 0x46, 0x42,
142 0xb3, 0x90, 0xc1, 0x57, 0x97, 0x50, 0x35, 0xb1, 0x9d, 0xb7, 0xc7, 0x3c,
143 0x85, 0x6d, 0x6c, 0xfd, 0xce, 0xb0, 0xc9, 0xa2, 0x77, 0xee, 0xc3, 0x6b,
144 0x0c, 0x37, 0xfa, 0x30, 0x91, 0xd1, 0x2c, 0xb8, 0x5e, 0x7f, 0x81, 0x5f,
145 0x87, 0xfd, 0x18, 0x02, 0x5a, 0x30, 0x4e, 0x62, 0xbc, 0x65, 0xc6, 0xce,
146 0x1a, 0xcf, 0x2b, 0xaa, 0x56, 0x3e, 0x4d, 0xcf, 0xba, 0x62, 0x5f, 0x9a,
147 0xd0, 0x72, 0xff, 0xef, 0x28, 0xbd, 0xbe, 0xd8, 0x57, 0x3d, 0xf5, 0x57,
148 0x7d, 0xe9, 0x71, 0x31, 0xec, 0x98, 0x90, 0x94, 0xd9, 0x54, 0xbf, 0x84,
149 0x0b, 0xe3, 0x06, 0x47, 0x19, 0x9a, 0x13, 0x1d, 0xef, 0x9d, 0x13, 0xf3,
150 0xdb, 0xc3, 0x5c, 0x72, 0x9e, 0xed, 0x24, 0xaa, 0x64, 0xed, 0xe7, 0x0d,
151 0xa0, 0x7c, 0x73, 0xba, 0x9b, 0x86, 0xa7, 0x3b, 0x55, 0xab, 0x58, 0x30,
152 0xf1, 0x15, 0x81, 0x83, 0x2f, 0xf9, 0x62, 0x84, 0x98, 0x66, 0xf6, 0x55,
153 0x21, 0xd8, 0xf2, 0x25, 0x64, 0x71, 0x4b, 0x12, 0x76, 0x59, 0xc5, 0xaa,
154 0x93, 0x67, 0xc3, 0x86, 0x25, 0xab, 0x4e, 0x4b, 0xf6, 0xd8, 0x3f, 0x44,
155 0x2e, 0x11, 0xe0, 0xbd, 0x6a, 0xf2, 0x5d, 0xf5, 0xf9, 0x53, 0xea, 0xa4,
156 0xc8, 0xd9, 0x50, 0x33, 0x81, 0xd9, 0xa8, 0x2d, 0x91, 0x7d, 0x13, 0x2a,
157 0x11, 0xcf, 0xde, 0x3f, 0x0a, 0xd2, 0xbc, 0x33, 0xb2, 0x62, 0x53, 0xea,
158 0x77, 0x88, 0x43, 0x66, 0x27, 0x43, 0x85, 0xe9, 0x5f, 0x55, 0xf5, 0x2a,
159 0x8a, 0xac, 0xdf, 0xff, 0x9b, 0x4c, 0x96, 0x9c, 0xa5, 0x7a, 0xce, 0xd5,
160 0x79, 0x18, 0xf1, 0x0b, 0x58, 0x95, 0x7a, 0xe7, 0xd3, 0x74, 0x65, 0x0b,
161 0xa4, 0x64, 0x30, 0xe8, 0x5c, 0xfc, 0x55, 0x56, 0xee, 0x14, 0x14, 0xd3,
162 0x45, 0x3b, 0xf8, 0xde, 0x05, 0x3e, 0xb9, 0x3c, 0xd7, 0x6a, 0x52, 0x72,
163 0x5b, 0x39, 0x09, 0xbe, 0x82, 0x23, 0x10, 0x4a, 0xb7, 0xc3, 0xdc, 0x4c,
164 0x5d, 0xc9, 0xf1, 0x14, 0x83, 0xf9, 0x0b, 0x9b, 0xe9, 0x23, 0x84, 0x6a,
165 0xc4, 0x08, 0x3d, 0xda, 0x3d, 0x12, 0x95, 0x87, 0x18, 0xa4, 0x7d, 0x3f,
166 0x23, 0xde, 0xd4, 0x1e, 0xa8, 0x47, 0xc3, 0x71, 0xdb, 0xf5, 0x03, 0x6c,
167 0x57, 0xe7, 0xa4, 0x43, 0x82, 0x33, 0x7b, 0x62, 0x46, 0x7d, 0xf7, 0x10,
168 0x69, 0x18, 0x38, 0x27, 0x9a, 0x6f, 0x38, 0xac, 0xfa, 0x92, 0xc5, 0xae,
169 0x66, 0xa6, 0x73, 0x95, 0x15, 0x0e, 0x4c, 0x04, 0xb6, 0xfc, 0xf5, 0xc7,
170 0x21, 0x3a, 0x99, 0xdb, 0x0e, 0x36, 0xf0, 0x56, 0xbc, 0x75, 0xf9, 0x87,
171 0x9b, 0x11, 0x18, 0x92, 0x64, 0x1a, 0xe7, 0xc7, 0xab, 0x5a, 0xc7, 0x26,
172 0x7f, 0x13, 0x98, 0x42, 0x52, 0x43, 0xdb, 0xc8, 0x6d, 0x0b, 0xb7, 0x31,
173 0x93, 0x24, 0xd6, 0xe8, 0x24, 0x1f, 0x6f, 0x21, 0xa7, 0x8c, 0xeb, 0xdb,
174 0x83, 0xb8, 0x89, 0xe3, 0xc1, 0xd7, 0x69, 0x3b, 0x02, 0x6b, 0x54, 0x0f,
175 0x84, 0x2f, 0xb5, 0x5c, 0x17, 0x77, 0xbe, 0xe5, 0x61, 0x0d, 0xc5, 0xdf,
176 0x3b, 0xcf, 0x3e, 0x93, 0x4f, 0xf5, 0x89, 0xb9, 0x5a, 0xc5, 0x29, 0x31,
177 0xc0, 0xc2, 0xff, 0xe5, 0x3f, 0xa6, 0xac, 0x03, 0xca, 0xf5, 0xff, 0xe0,
178 0x36, 0xce, 0xf3, 0xe2, 0xb7, 0x9c, 0x02, 0xe9, 0x9e, 0xd2, 0xbc, 0x87,
179 0x2f, 0x3d, 0x9a, 0x1d, 0x8f, 0xc5, 0x72, 0xb8, 0xa2, 0x01, 0xd4, 0x68,
180 0xb1, 0x84, 0x16, 0x10, 0xf6, 0xf3, 0x52, 0x25, 0xd9, 0xdc, 0x4c, 0xdd,
181 0x0f, 0xd6, 0x4a, 0xcf, 0x60, 0x96, 0x7e, 0xcc, 0x42, 0x0f, 0x64, 0x9d,
182 0x72, 0x46, 0x04, 0x07, 0xf2, 0x5b, 0xf4, 0x07, 0xd1, 0xf4, 0x59, 0x71,
183 };
184
185 static const uint8_t kSpakeMSmallPrecomp[15 * 2 * 32] = {
186 0xc8, 0xa6, 0x63, 0xc5, 0x97, 0xf1, 0xee, 0x40, 0xab, 0x62, 0x42, 0xee,
187 0x25, 0x6f, 0x32, 0x6c, 0x75, 0x2c, 0xa7, 0xd3, 0xbd, 0x32, 0x3b, 0x1e,
188 0x11, 0x9c, 0xbd, 0x04, 0xa9, 0x78, 0x6f, 0x45, 0x5a, 0xda, 0x7e, 0x4b,
189 0xf6, 0xdd, 0xd9, 0xad, 0xb6, 0x62, 0x6d, 0x32, 0x13, 0x1c, 0x6b, 0x5c,
190 0x51, 0xa1, 0xe3, 0x47, 0xa3, 0x47, 0x8f, 0x53, 0xcf, 0xcf, 0x44, 0x1b,
191 0x88, 0xee, 0xd1, 0x2e, 0x03, 0x89, 0xaf, 0xc0, 0x61, 0x2d, 0x9e, 0x35,
192 0xeb, 0x0e, 0x03, 0xe0, 0xb7, 0xfb, 0xa5, 0xbc, 0x44, 0xbe, 0x0c, 0x89,
193 0x0a, 0x0f, 0xd6, 0x59, 0x47, 0x9e, 0xe6, 0x3d, 0x36, 0x9d, 0xff, 0x44,
194 0x5e, 0xac, 0xab, 0xe5, 0x3a, 0xd5, 0xb0, 0x35, 0x9f, 0x6d, 0x7f, 0xba,
195 0xc0, 0x85, 0x0e, 0xf4, 0x70, 0x3f, 0x13, 0x90, 0x4c, 0x50, 0x1a, 0xee,
196 0xc5, 0xeb, 0x69, 0xfe, 0x98, 0x42, 0x87, 0x1d, 0xce, 0x6c, 0x29, 0xaa,
197 0x2b, 0x31, 0xc2, 0x38, 0x7b, 0x6b, 0xee, 0x88, 0x0b, 0xba, 0xce, 0xa8,
198 0xca, 0x19, 0x60, 0x1b, 0x16, 0xf1, 0x25, 0x1e, 0xcf, 0x63, 0x66, 0x1e,
199 0xbb, 0x63, 0xeb, 0x7d, 0xca, 0xd2, 0xb4, 0x23, 0x5a, 0x01, 0x6f, 0x05,
200 0xd1, 0xdc, 0x41, 0x73, 0x75, 0xc0, 0xfd, 0x30, 0x91, 0x52, 0x68, 0x96,
201 0x45, 0xb3, 0x66, 0x01, 0x3b, 0x53, 0x89, 0x3c, 0x69, 0xbc, 0x6c, 0x69,
202 0xe3, 0x51, 0x8f, 0xe3, 0xd2, 0x84, 0xd5, 0x28, 0x66, 0xb5, 0xe6, 0x06,
203 0x09, 0xfe, 0x6d, 0xb0, 0x72, 0x16, 0xe0, 0x8a, 0xce, 0x61, 0x65, 0xa9,
204 0x21, 0x32, 0x48, 0xdc, 0x7a, 0x1d, 0xe1, 0x38, 0x7f, 0x8c, 0x75, 0x88,
205 0x3d, 0x08, 0xa9, 0x4a, 0x6f, 0x3d, 0x9f, 0x7f, 0x3f, 0xbd, 0x57, 0x6b,
206 0x19, 0xce, 0x3f, 0x4a, 0xc9, 0xd3, 0xf9, 0x6e, 0x72, 0x7b, 0x5b, 0x74,
207 0xea, 0xbe, 0x9c, 0x7a, 0x6d, 0x9c, 0x40, 0x49, 0xe6, 0xfb, 0x2a, 0x1a,
208 0x75, 0x70, 0xe5, 0x4e, 0xed, 0x74, 0xe0, 0x75, 0xac, 0xc0, 0xb1, 0x11,
209 0x3e, 0xf2, 0xaf, 0x88, 0x4d, 0x66, 0xb6, 0xf6, 0x15, 0x4f, 0x3c, 0x6c,
210 0x77, 0xae, 0x47, 0x51, 0x63, 0x9a, 0xfe, 0xe1, 0xb4, 0x1a, 0x12, 0xdf,
211 0xe9, 0x54, 0x8d, 0x3b, 0x30, 0x2a, 0x75, 0xe3, 0xe5, 0x29, 0xb1, 0x4c,
212 0xb0, 0x7c, 0x6d, 0xb5, 0xae, 0x85, 0xdb, 0x1e, 0x38, 0x55, 0x96, 0xa5,
213 0x5b, 0x9f, 0x15, 0x23, 0x28, 0x36, 0xb8, 0xa2, 0x41, 0xb4, 0xd7, 0x19,
214 0x91, 0x8d, 0x26, 0x3e, 0xca, 0x9c, 0x05, 0x7a, 0x2b, 0x60, 0x45, 0x86,
215 0x8b, 0xee, 0x64, 0x6f, 0x5c, 0x09, 0x4d, 0x4b, 0x5a, 0x7f, 0xb0, 0xc3,
216 0x26, 0x9d, 0x8b, 0xb8, 0x83, 0x69, 0xcf, 0x16, 0x72, 0x62, 0x3e, 0x5e,
217 0x53, 0x4f, 0x9c, 0x73, 0x76, 0xfc, 0x19, 0xef, 0xa0, 0x74, 0x3a, 0x11,
218 0x1e, 0xd0, 0x4d, 0xb7, 0x87, 0xa1, 0xd6, 0x87, 0x6c, 0x0e, 0x6c, 0x8c,
219 0xe9, 0xa0, 0x44, 0xc4, 0x72, 0x3e, 0x73, 0x17, 0x13, 0xd1, 0x4e, 0x3d,
220 0x8e, 0x1d, 0x5a, 0x8b, 0x75, 0xcb, 0x59, 0x2c, 0x47, 0x87, 0x15, 0x41,
221 0xfe, 0x08, 0xe9, 0xa6, 0x97, 0x17, 0x08, 0x26, 0x6a, 0xb5, 0xbb, 0x73,
222 0xaa, 0xb8, 0x5b, 0x65, 0x65, 0x5b, 0x30, 0x9e, 0x62, 0x59, 0x02, 0xf8,
223 0xb8, 0x0f, 0x32, 0x10, 0xc1, 0x36, 0x08, 0x52, 0x98, 0x4a, 0x1e, 0xf0,
224 0xab, 0x21, 0x5e, 0xde, 0x16, 0x0c, 0xda, 0x09, 0x99, 0x6b, 0x9e, 0xc0,
225 0x90, 0xa5, 0x5a, 0xcc, 0xb0, 0xb7, 0xbb, 0xd2, 0x8b, 0x5f, 0xd3, 0x3b,
226 0x3e, 0x8c, 0xa5, 0x71, 0x66, 0x06, 0xe3, 0x28, 0xd4, 0xf8, 0x3f, 0xe5,
227 0x27, 0xdf, 0xfe, 0x0f, 0x09, 0xb2, 0x8a, 0x09, 0x5a, 0x23, 0x61, 0x0d,
228 0x2d, 0xf5, 0x44, 0xf1, 0x5c, 0xf8, 0x82, 0x4e, 0xdc, 0x78, 0x7a, 0xab,
229 0xc3, 0x57, 0x91, 0xaf, 0x65, 0x6e, 0x71, 0xf1, 0x44, 0xbf, 0xed, 0x43,
230 0x50, 0xb4, 0x67, 0x48, 0xef, 0x5a, 0x10, 0x46, 0x81, 0xb4, 0x0c, 0xc8,
231 0x48, 0xed, 0x99, 0x7a, 0x45, 0xa5, 0x92, 0xc3, 0x69, 0xd6, 0xd7, 0x8a,
232 0x20, 0x1b, 0xeb, 0x8f, 0xb2, 0xff, 0xec, 0x6d, 0x76, 0x04, 0xf8, 0xc2,
233 0x58, 0x9b, 0xf2, 0x20, 0x53, 0xc4, 0x74, 0x91, 0x19, 0xdd, 0x2d, 0x12,
234 0x53, 0xc7, 0x6e, 0xd0, 0x02, 0x51, 0x3c, 0xa6, 0x7d, 0x80, 0x75, 0x6b,
235 0x1d, 0xdf, 0xf8, 0x6a, 0x52, 0xbb, 0x81, 0xf8, 0x30, 0x45, 0xef, 0x51,
236 0x85, 0x36, 0xbe, 0x8e, 0xcf, 0x0b, 0x9a, 0x46, 0xe8, 0x3f, 0x99, 0xfd,
237 0xf7, 0xd9, 0x3e, 0x84, 0xe5, 0xe3, 0x37, 0xcf, 0x98, 0x7f, 0xeb, 0x5e,
238 0x5a, 0x53, 0x77, 0x1c, 0x20, 0xdc, 0xf1, 0x20, 0x99, 0xec, 0x60, 0x40,
239 0x93, 0xef, 0x5c, 0x1c, 0x81, 0xe2, 0xa5, 0xad, 0x2a, 0xc2, 0xdb, 0x6b,
240 0xc1, 0x7e, 0x8f, 0xa9, 0x23, 0x5b, 0xd9, 0x0d, 0xfe, 0xa0, 0xac, 0x11,
241 0x28, 0xba, 0x8e, 0x92, 0x07, 0x2d, 0x07, 0x40, 0x83, 0x14, 0x4c, 0x35,
242 0x8d, 0xd0, 0x11, 0xff, 0x98, 0xdb, 0x00, 0x30, 0x6f, 0x65, 0xb6, 0xa0,
243 0x7f, 0x9c, 0x08, 0xb8, 0xce, 0xb3, 0xa8, 0x42, 0xd3, 0x84, 0x45, 0xe1,
244 0xe3, 0x8f, 0xa6, 0x89, 0x21, 0xd7, 0x74, 0x02, 0x4d, 0x64, 0xdf, 0x54,
245 0x15, 0x9e, 0xba, 0x12, 0x49, 0x09, 0x41, 0xf6, 0x10, 0x24, 0xa1, 0x84,
246 0x15, 0xfd, 0x68, 0x6a, 0x57, 0x66, 0xb3, 0x6d, 0x4c, 0xea, 0xbf, 0xbc,
247 0x60, 0x3f, 0x52, 0x1c, 0x44, 0x1b, 0xc0, 0x4a, 0x25, 0xe3, 0xd9, 0x4c,
248 0x9a, 0x74, 0xad, 0xfc, 0x9e, 0x8d, 0x0b, 0x18, 0x66, 0x24, 0xd1, 0x06,
249 0xac, 0x68, 0xc1, 0xae, 0x14, 0xce, 0xb1, 0xf3, 0x86, 0x9f, 0x87, 0x11,
250 0xd7, 0x9f, 0x30, 0x92, 0xdb, 0xec, 0x0b, 0x4a, 0xe8, 0xf6, 0x53, 0x36,
251 0x68, 0x12, 0x11, 0x5e, 0xe0, 0x34, 0xa4, 0xff, 0x00, 0x0a, 0x26, 0xb8,
252 0x62, 0x79, 0x9c, 0x0c, 0xd5, 0xe5, 0xf5, 0x1c, 0x1a, 0x16, 0x84, 0x4d,
253 0x8e, 0x5d, 0x31, 0x7e, 0xf7, 0xe2, 0xd3, 0xa1, 0x41, 0x90, 0x61, 0x5d,
254 0x04, 0xb2, 0x9a, 0x18, 0x9e, 0x54, 0xfb, 0xd1, 0x61, 0x95, 0x1b, 0x08,
255 0xca, 0x7c, 0x49, 0x44, 0x74, 0x1d, 0x2f, 0xca, 0xc4, 0x7a, 0xe1, 0x8b,
256 0x2f, 0xbb, 0x96, 0xee, 0x19, 0x8a, 0x5d, 0xfb, 0x3e, 0x82, 0xe7, 0x15,
257 0xdb, 0x29, 0x14, 0xee, 0xc9, 0x4d, 0x9a, 0xfb, 0x9f, 0x8a, 0xbb, 0x17,
258 0x37, 0x1b, 0x6e, 0x28, 0x6c, 0xf9, 0xff, 0xb5, 0xb5, 0x8b, 0x9d, 0x88,
259 0x20, 0x08, 0x10, 0xd7, 0xca, 0x58, 0xf6, 0xe1, 0x32, 0x91, 0x6f, 0x36,
260 0xc0, 0xad, 0xc1, 0x57, 0x5d, 0x76, 0x31, 0x43, 0xf3, 0xdd, 0xec, 0xf1,
261 0xa9, 0x79, 0xe9, 0xe9, 0x85, 0xd7, 0x91, 0xc7, 0x31, 0x62, 0x3c, 0xd2,
262 0x90, 0x2c, 0x9c, 0xa4, 0x56, 0x37, 0x7b, 0xbe, 0x40, 0x58, 0xc0, 0x81,
263 0x83, 0x22, 0xe8, 0x13, 0x79, 0x18, 0xdb, 0x3a, 0x1b, 0x31, 0x0d, 0x00,
264 0x6c, 0x22, 0x62, 0x75, 0x70, 0xd8, 0x96, 0x59, 0x99, 0x44, 0x79, 0x71,
265 0xa6, 0x76, 0x81, 0x28, 0xb2, 0x65, 0xe8, 0x47, 0x14, 0xc6, 0x39, 0x06,
266 };
267
268 enum spake2_state_t {
269 spake2_state_init = 0,
270 spake2_state_msg_generated,
271 spake2_state_key_generated,
272 };
273
274 struct spake2_ctx_st {
275 uint8_t private_key[32];
276 uint8_t my_msg[32];
277 uint8_t password_scalar[32];
278 uint8_t password_hash[SHA512_DIGEST_LENGTH];
279 uint8_t *my_name;
280 size_t my_name_len;
281 uint8_t *their_name;
282 size_t their_name_len;
283 enum spake2_role_t my_role;
284 enum spake2_state_t state;
285 };
286
SPAKE2_CTX_new(enum spake2_role_t my_role,const uint8_t * my_name,size_t my_name_len,const uint8_t * their_name,size_t their_name_len)287 SPAKE2_CTX *SPAKE2_CTX_new(enum spake2_role_t my_role,
288 const uint8_t *my_name, size_t my_name_len,
289 const uint8_t *their_name, size_t their_name_len) {
290 SPAKE2_CTX *ctx = OPENSSL_malloc(sizeof(SPAKE2_CTX));
291 if (ctx == NULL) {
292 return NULL;
293 }
294
295 OPENSSL_memset(ctx, 0, sizeof(SPAKE2_CTX));
296 ctx->my_role = my_role;
297
298 CBS my_name_cbs, their_name_cbs;
299 CBS_init(&my_name_cbs, my_name, my_name_len);
300 CBS_init(&their_name_cbs, their_name, their_name_len);
301 if (!CBS_stow(&my_name_cbs, &ctx->my_name, &ctx->my_name_len) ||
302 !CBS_stow(&their_name_cbs, &ctx->their_name, &ctx->their_name_len)) {
303 SPAKE2_CTX_free(ctx);
304 return NULL;
305 }
306
307 return ctx;
308 }
309
SPAKE2_CTX_free(SPAKE2_CTX * ctx)310 void SPAKE2_CTX_free(SPAKE2_CTX *ctx) {
311 if (ctx == NULL) {
312 return;
313 }
314
315 OPENSSL_free(ctx->my_name);
316 OPENSSL_free(ctx->their_name);
317 OPENSSL_free(ctx);
318 }
319
320 /* left_shift_3 sets |n| to |n|*8, where |n| is represented in little-endian
321 * order. */
left_shift_3(uint8_t n[32])322 static void left_shift_3(uint8_t n[32]) {
323 uint8_t carry = 0;
324 unsigned i;
325
326 for (i = 0; i < 32; i++) {
327 const uint8_t next_carry = n[i] >> 5;
328 n[i] = (n[i] << 3) | carry;
329 carry = next_carry;
330 }
331 }
332
SPAKE2_generate_msg(SPAKE2_CTX * ctx,uint8_t * out,size_t * out_len,size_t max_out_len,const uint8_t * password,size_t password_len)333 int SPAKE2_generate_msg(SPAKE2_CTX *ctx, uint8_t *out, size_t *out_len,
334 size_t max_out_len, const uint8_t *password,
335 size_t password_len) {
336 if (ctx->state != spake2_state_init) {
337 return 0;
338 }
339
340 if (max_out_len < sizeof(ctx->my_msg)) {
341 return 0;
342 }
343
344 uint8_t private_tmp[64];
345 RAND_bytes(private_tmp, sizeof(private_tmp));
346 x25519_sc_reduce(private_tmp);
347 /* Multiply by the cofactor (eight) so that we'll clear it when operating on
348 * the peer's point later in the protocol. */
349 left_shift_3(private_tmp);
350 OPENSSL_memcpy(ctx->private_key, private_tmp, sizeof(ctx->private_key));
351
352 ge_p3 P;
353 x25519_ge_scalarmult_base(&P, ctx->private_key);
354
355 /* mask = h(password) * <N or M>. */
356 uint8_t password_tmp[SHA512_DIGEST_LENGTH];
357 SHA512(password, password_len, password_tmp);
358 OPENSSL_memcpy(ctx->password_hash, password_tmp, sizeof(ctx->password_hash));
359 x25519_sc_reduce(password_tmp);
360 OPENSSL_memcpy(ctx->password_scalar, password_tmp, sizeof(ctx->password_scalar));
361
362 ge_p3 mask;
363 x25519_ge_scalarmult_small_precomp(&mask, ctx->password_scalar,
364 ctx->my_role == spake2_role_alice
365 ? kSpakeMSmallPrecomp
366 : kSpakeNSmallPrecomp);
367
368 /* P* = P + mask. */
369 ge_cached mask_cached;
370 x25519_ge_p3_to_cached(&mask_cached, &mask);
371 ge_p1p1 Pstar;
372 x25519_ge_add(&Pstar, &P, &mask_cached);
373
374 /* Encode P* */
375 ge_p2 Pstar_proj;
376 x25519_ge_p1p1_to_p2(&Pstar_proj, &Pstar);
377 x25519_ge_tobytes(ctx->my_msg, &Pstar_proj);
378
379 OPENSSL_memcpy(out, ctx->my_msg, sizeof(ctx->my_msg));
380 *out_len = sizeof(ctx->my_msg);
381 ctx->state = spake2_state_msg_generated;
382
383 return 1;
384 }
385
update_with_length_prefix(SHA512_CTX * sha,const uint8_t * data,const size_t len)386 static void update_with_length_prefix(SHA512_CTX *sha, const uint8_t *data,
387 const size_t len) {
388 uint8_t len_le[8];
389 size_t l = len;
390 unsigned i;
391
392 for (i = 0; i < 8; i++) {
393 len_le[i] = l & 0xff;
394 l >>= 8;
395 }
396
397 SHA512_Update(sha, len_le, sizeof(len_le));
398 SHA512_Update(sha, data, len);
399 }
400
SPAKE2_process_msg(SPAKE2_CTX * ctx,uint8_t * out_key,size_t * out_key_len,size_t max_out_key_len,const uint8_t * their_msg,size_t their_msg_len)401 int SPAKE2_process_msg(SPAKE2_CTX *ctx, uint8_t *out_key, size_t *out_key_len,
402 size_t max_out_key_len, const uint8_t *their_msg,
403 size_t their_msg_len) {
404 if (ctx->state != spake2_state_msg_generated ||
405 their_msg_len != 32) {
406 return 0;
407 }
408
409 ge_p3 Qstar;
410 if (0 != x25519_ge_frombytes_vartime(&Qstar, their_msg)) {
411 /* Point received from peer was not on the curve. */
412 return 0;
413 }
414
415 /* Unmask peer's value. */
416 ge_p3 peers_mask;
417 x25519_ge_scalarmult_small_precomp(&peers_mask, ctx->password_scalar,
418 ctx->my_role == spake2_role_alice
419 ? kSpakeNSmallPrecomp
420 : kSpakeMSmallPrecomp);
421
422 ge_cached peers_mask_cached;
423 x25519_ge_p3_to_cached(&peers_mask_cached, &peers_mask);
424
425 ge_p1p1 Q_compl;
426 ge_p3 Q_ext;
427 x25519_ge_sub(&Q_compl, &Qstar, &peers_mask_cached);
428 x25519_ge_p1p1_to_p3(&Q_ext, &Q_compl);
429
430 ge_p2 dh_shared;
431 x25519_ge_scalarmult(&dh_shared, ctx->private_key, &Q_ext);
432
433 uint8_t dh_shared_encoded[32];
434 x25519_ge_tobytes(dh_shared_encoded, &dh_shared);
435
436 SHA512_CTX sha;
437 SHA512_Init(&sha);
438 if (ctx->my_role == spake2_role_alice) {
439 update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len);
440 update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len);
441 update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg));
442 update_with_length_prefix(&sha, their_msg, 32);
443 } else {
444 update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len);
445 update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len);
446 update_with_length_prefix(&sha, their_msg, 32);
447 update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg));
448 }
449 update_with_length_prefix(&sha, dh_shared_encoded, sizeof(dh_shared_encoded));
450 update_with_length_prefix(&sha, ctx->password_hash,
451 sizeof(ctx->password_hash));
452
453 uint8_t key[SHA512_DIGEST_LENGTH];
454 SHA512_Final(key, &sha);
455
456 size_t to_copy = max_out_key_len;
457 if (to_copy > sizeof(key)) {
458 to_copy = sizeof(key);
459 }
460 OPENSSL_memcpy(out_key, key, to_copy);
461 *out_key_len = to_copy;
462 ctx->state = spake2_state_key_generated;
463
464 return 1;
465 }
466