diff options
author | Damien Miller <djm@mindrot.org> | 2013-12-07 11:24:01 +1100 |
---|---|---|
committer | Damien Miller <djm@mindrot.org> | 2013-12-07 11:24:01 +1100 |
commit | 5be9d9e3cbd9c66f24745d25bf2e809c1d158ee0 (patch) | |
tree | d2086d37436014ea44f0f024396a1a8638640b00 /ge25519.c | |
parent | bcd00abd8451f36142ae2ee10cc657202149201e (diff) |
- markus@cvs.openbsd.org 2013/12/06 13:39:49
[authfd.c authfile.c key.c key.h myproposal.h pathnames.h readconf.c]
[servconf.c ssh-agent.c ssh-keygen.c ssh-keyscan.1 ssh-keyscan.c]
[ssh-keysign.c ssh.c ssh_config.5 sshd.8 sshd.c verify.c ssh-ed25519.c]
[sc25519.h sc25519.c hash.c ge25519_base.data ge25519.h ge25519.c]
[fe25519.h fe25519.c ed25519.c crypto_api.h blocks.c]
support ed25519 keys (hostkeys and user identities) using the public
domain ed25519 reference code from SUPERCOP, see
http://ed25519.cr.yp.to/software.html
feedback, help & ok djm@
Diffstat (limited to 'ge25519.c')
-rw-r--r-- | ge25519.c | 315 |
1 files changed, 315 insertions, 0 deletions
diff --git a/ge25519.c b/ge25519.c new file mode 100644 index 000000000..edc97588c --- /dev/null +++ b/ge25519.c | |||
@@ -0,0 +1,315 @@ | |||
1 | /* $OpenBSD: */ | ||
2 | |||
3 | /* Public Domain, from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c */ | ||
4 | |||
5 | #include "fe25519.h" | ||
6 | #include "sc25519.h" | ||
7 | #include "ge25519.h" | ||
8 | |||
9 | /* | ||
10 | * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2 | ||
11 | * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555 | ||
12 | * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960); | ||
13 | */ | ||
14 | |||
15 | /* d */ | ||
16 | static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00, | ||
17 | 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}}; | ||
18 | /* 2*d */ | ||
19 | static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00, | ||
20 | 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}}; | ||
21 | /* sqrt(-1) */ | ||
22 | static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F, | ||
23 | 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}}; | ||
24 | |||
25 | #define ge25519_p3 ge25519 | ||
26 | |||
27 | typedef struct | ||
28 | { | ||
29 | fe25519 x; | ||
30 | fe25519 z; | ||
31 | fe25519 y; | ||
32 | fe25519 t; | ||
33 | } ge25519_p1p1; | ||
34 | |||
35 | typedef struct | ||
36 | { | ||
37 | fe25519 x; | ||
38 | fe25519 y; | ||
39 | fe25519 z; | ||
40 | } ge25519_p2; | ||
41 | |||
42 | typedef struct | ||
43 | { | ||
44 | fe25519 x; | ||
45 | fe25519 y; | ||
46 | } ge25519_aff; | ||
47 | |||
48 | |||
49 | /* Packed coordinates of the base point */ | ||
50 | const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69, | ||
51 | 0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}}, | ||
52 | {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, | ||
53 | 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}}, | ||
54 | {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, | ||
55 | 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, | ||
56 | {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20, | ||
57 | 0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}}; | ||
58 | |||
59 | /* Multiples of the base point in affine representation */ | ||
60 | static const ge25519_aff ge25519_base_multiples_affine[425] = { | ||
61 | #include "ge25519_base.data" | ||
62 | }; | ||
63 | |||
64 | static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p) | ||
65 | { | ||
66 | fe25519_mul(&r->x, &p->x, &p->t); | ||
67 | fe25519_mul(&r->y, &p->y, &p->z); | ||
68 | fe25519_mul(&r->z, &p->z, &p->t); | ||
69 | } | ||
70 | |||
71 | static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p) | ||
72 | { | ||
73 | p1p1_to_p2((ge25519_p2 *)r, p); | ||
74 | fe25519_mul(&r->t, &p->x, &p->y); | ||
75 | } | ||
76 | |||
77 | static void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q) | ||
78 | { | ||
79 | fe25519 a,b,t1,t2,c,d,e,f,g,h,qt; | ||
80 | fe25519_mul(&qt, &q->x, &q->y); | ||
81 | fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */ | ||
82 | fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */ | ||
83 | fe25519_sub(&t1, &q->y, &q->x); | ||
84 | fe25519_add(&t2, &q->y, &q->x); | ||
85 | fe25519_mul(&a, &a, &t1); | ||
86 | fe25519_mul(&b, &b, &t2); | ||
87 | fe25519_sub(&e, &b, &a); /* E = B-A */ | ||
88 | fe25519_add(&h, &b, &a); /* H = B+A */ | ||
89 | fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */ | ||
90 | fe25519_mul(&c, &c, &ge25519_ec2d); | ||
91 | fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */ | ||
92 | fe25519_sub(&f, &d, &c); /* F = D-C */ | ||
93 | fe25519_add(&g, &d, &c); /* G = D+C */ | ||
94 | fe25519_mul(&r->x, &e, &f); | ||
95 | fe25519_mul(&r->y, &h, &g); | ||
96 | fe25519_mul(&r->z, &g, &f); | ||
97 | fe25519_mul(&r->t, &e, &h); | ||
98 | } | ||
99 | |||
100 | static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q) | ||
101 | { | ||
102 | fe25519 a, b, c, d, t; | ||
103 | |||
104 | fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */ | ||
105 | fe25519_sub(&t, &q->y, &q->x); | ||
106 | fe25519_mul(&a, &a, &t); | ||
107 | fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */ | ||
108 | fe25519_add(&t, &q->x, &q->y); | ||
109 | fe25519_mul(&b, &b, &t); | ||
110 | fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */ | ||
111 | fe25519_mul(&c, &c, &ge25519_ec2d); | ||
112 | fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */ | ||
113 | fe25519_add(&d, &d, &d); | ||
114 | fe25519_sub(&r->x, &b, &a); /* E = B-A */ | ||
115 | fe25519_sub(&r->t, &d, &c); /* F = D-C */ | ||
116 | fe25519_add(&r->z, &d, &c); /* G = D+C */ | ||
117 | fe25519_add(&r->y, &b, &a); /* H = B+A */ | ||
118 | } | ||
119 | |||
120 | /* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */ | ||
121 | static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p) | ||
122 | { | ||
123 | fe25519 a,b,c,d; | ||
124 | fe25519_square(&a, &p->x); | ||
125 | fe25519_square(&b, &p->y); | ||
126 | fe25519_square(&c, &p->z); | ||
127 | fe25519_add(&c, &c, &c); | ||
128 | fe25519_neg(&d, &a); | ||
129 | |||
130 | fe25519_add(&r->x, &p->x, &p->y); | ||
131 | fe25519_square(&r->x, &r->x); | ||
132 | fe25519_sub(&r->x, &r->x, &a); | ||
133 | fe25519_sub(&r->x, &r->x, &b); | ||
134 | fe25519_add(&r->z, &d, &b); | ||
135 | fe25519_sub(&r->t, &r->z, &c); | ||
136 | fe25519_sub(&r->y, &d, &b); | ||
137 | } | ||
138 | |||
139 | /* Constant-time version of: if(b) r = p */ | ||
140 | static void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b) | ||
141 | { | ||
142 | fe25519_cmov(&r->x, &p->x, b); | ||
143 | fe25519_cmov(&r->y, &p->y, b); | ||
144 | } | ||
145 | |||
146 | static unsigned char equal(signed char b,signed char c) | ||
147 | { | ||
148 | unsigned char ub = b; | ||
149 | unsigned char uc = c; | ||
150 | unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ | ||
151 | crypto_uint32 y = x; /* 0: yes; 1..255: no */ | ||
152 | y -= 1; /* 4294967295: yes; 0..254: no */ | ||
153 | y >>= 31; /* 1: yes; 0: no */ | ||
154 | return y; | ||
155 | } | ||
156 | |||
157 | static unsigned char negative(signed char b) | ||
158 | { | ||
159 | unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ | ||
160 | x >>= 63; /* 1: yes; 0: no */ | ||
161 | return x; | ||
162 | } | ||
163 | |||
164 | static void choose_t(ge25519_aff *t, unsigned long long pos, signed char b) | ||
165 | { | ||
166 | /* constant time */ | ||
167 | fe25519 v; | ||
168 | *t = ge25519_base_multiples_affine[5*pos+0]; | ||
169 | cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) | equal(b,-1)); | ||
170 | cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) | equal(b,-2)); | ||
171 | cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) | equal(b,-3)); | ||
172 | cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4)); | ||
173 | fe25519_neg(&v, &t->x); | ||
174 | fe25519_cmov(&t->x, &v, negative(b)); | ||
175 | } | ||
176 | |||
177 | static void setneutral(ge25519 *r) | ||
178 | { | ||
179 | fe25519_setzero(&r->x); | ||
180 | fe25519_setone(&r->y); | ||
181 | fe25519_setone(&r->z); | ||
182 | fe25519_setzero(&r->t); | ||
183 | } | ||
184 | |||
185 | /* ******************************************************************** | ||
186 | * EXPORTED FUNCTIONS | ||
187 | ******************************************************************** */ | ||
188 | |||
189 | /* return 0 on success, -1 otherwise */ | ||
190 | int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32]) | ||
191 | { | ||
192 | unsigned char par; | ||
193 | fe25519 t, chk, num, den, den2, den4, den6; | ||
194 | fe25519_setone(&r->z); | ||
195 | par = p[31] >> 7; | ||
196 | fe25519_unpack(&r->y, p); | ||
197 | fe25519_square(&num, &r->y); /* x = y^2 */ | ||
198 | fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */ | ||
199 | fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */ | ||
200 | fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */ | ||
201 | |||
202 | /* Computation of sqrt(num/den) */ | ||
203 | /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */ | ||
204 | fe25519_square(&den2, &den); | ||
205 | fe25519_square(&den4, &den2); | ||
206 | fe25519_mul(&den6, &den4, &den2); | ||
207 | fe25519_mul(&t, &den6, &num); | ||
208 | fe25519_mul(&t, &t, &den); | ||
209 | |||
210 | fe25519_pow2523(&t, &t); | ||
211 | /* 2. computation of r->x = t * num * den^3 */ | ||
212 | fe25519_mul(&t, &t, &num); | ||
213 | fe25519_mul(&t, &t, &den); | ||
214 | fe25519_mul(&t, &t, &den); | ||
215 | fe25519_mul(&r->x, &t, &den); | ||
216 | |||
217 | /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */ | ||
218 | fe25519_square(&chk, &r->x); | ||
219 | fe25519_mul(&chk, &chk, &den); | ||
220 | if (!fe25519_iseq_vartime(&chk, &num)) | ||
221 | fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1); | ||
222 | |||
223 | /* 4. Now we have one of the two square roots, except if input was not a square */ | ||
224 | fe25519_square(&chk, &r->x); | ||
225 | fe25519_mul(&chk, &chk, &den); | ||
226 | if (!fe25519_iseq_vartime(&chk, &num)) | ||
227 | return -1; | ||
228 | |||
229 | /* 5. Choose the desired square root according to parity: */ | ||
230 | if(fe25519_getparity(&r->x) != (1-par)) | ||
231 | fe25519_neg(&r->x, &r->x); | ||
232 | |||
233 | fe25519_mul(&r->t, &r->x, &r->y); | ||
234 | return 0; | ||
235 | } | ||
236 | |||
237 | void ge25519_pack(unsigned char r[32], const ge25519_p3 *p) | ||
238 | { | ||
239 | fe25519 tx, ty, zi; | ||
240 | fe25519_invert(&zi, &p->z); | ||
241 | fe25519_mul(&tx, &p->x, &zi); | ||
242 | fe25519_mul(&ty, &p->y, &zi); | ||
243 | fe25519_pack(r, &ty); | ||
244 | r[31] ^= fe25519_getparity(&tx) << 7; | ||
245 | } | ||
246 | |||
247 | int ge25519_isneutral_vartime(const ge25519_p3 *p) | ||
248 | { | ||
249 | int ret = 1; | ||
250 | if(!fe25519_iszero(&p->x)) ret = 0; | ||
251 | if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0; | ||
252 | return ret; | ||
253 | } | ||
254 | |||
255 | /* computes [s1]p1 + [s2]p2 */ | ||
256 | void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2) | ||
257 | { | ||
258 | ge25519_p1p1 tp1p1; | ||
259 | ge25519_p3 pre[16]; | ||
260 | unsigned char b[127]; | ||
261 | int i; | ||
262 | |||
263 | /* precomputation s2 s1 */ | ||
264 | setneutral(pre); /* 00 00 */ | ||
265 | pre[1] = *p1; /* 00 01 */ | ||
266 | dbl_p1p1(&tp1p1,(ge25519_p2 *)p1); p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */ | ||
267 | add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */ | ||
268 | pre[4] = *p2; /* 01 00 */ | ||
269 | add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */ | ||
270 | add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */ | ||
271 | add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */ | ||
272 | dbl_p1p1(&tp1p1,(ge25519_p2 *)p2); p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */ | ||
273 | add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */ | ||
274 | dbl_p1p1(&tp1p1,(ge25519_p2 *)&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */ | ||
275 | add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */ | ||
276 | add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */ | ||
277 | add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */ | ||
278 | add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */ | ||
279 | add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */ | ||
280 | |||
281 | sc25519_2interleave2(b,s1,s2); | ||
282 | |||
283 | /* scalar multiplication */ | ||
284 | *r = pre[b[126]]; | ||
285 | for(i=125;i>=0;i--) | ||
286 | { | ||
287 | dbl_p1p1(&tp1p1, (ge25519_p2 *)r); | ||
288 | p1p1_to_p2((ge25519_p2 *) r, &tp1p1); | ||
289 | dbl_p1p1(&tp1p1, (ge25519_p2 *)r); | ||
290 | if(b[i]!=0) | ||
291 | { | ||
292 | p1p1_to_p3(r, &tp1p1); | ||
293 | add_p1p1(&tp1p1, r, &pre[b[i]]); | ||
294 | } | ||
295 | if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1); | ||
296 | else p1p1_to_p3(r, &tp1p1); | ||
297 | } | ||
298 | } | ||
299 | |||
300 | void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s) | ||
301 | { | ||
302 | signed char b[85]; | ||
303 | int i; | ||
304 | ge25519_aff t; | ||
305 | sc25519_window3(b,s); | ||
306 | |||
307 | choose_t((ge25519_aff *)r, 0, b[0]); | ||
308 | fe25519_setone(&r->z); | ||
309 | fe25519_mul(&r->t, &r->x, &r->y); | ||
310 | for(i=1;i<85;i++) | ||
311 | { | ||
312 | choose_t(&t, (unsigned long long) i, b[i]); | ||
313 | ge25519_mixadd2(r, &t); | ||
314 | } | ||
315 | } | ||