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ge25519.c

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1/* $OpenBSD: ge25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */-
2-
3/*-
4 * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,-
5 * Peter Schwabe, Bo-Yin Yang.-
6 * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c-
7 */-
8-
9#include "includes.h"-
10-
11#include "fe25519.h"-
12#include "sc25519.h"-
13#include "ge25519.h"-
14-
15/* -
16 * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2 -
17 * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555-
18 * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);-
19 */-
20-
21/* d */-
22static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00, -
23 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}};-
24/* 2*d */-
25static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00, -
26 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}};-
27/* sqrt(-1) */-
28static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F, -
29 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}};-
30-
31#define ge25519_p3 ge25519-
32-
33typedef struct-
34{-
35 fe25519 x;-
36 fe25519 z;-
37 fe25519 y;-
38 fe25519 t;-
39} ge25519_p1p1;-
40-
41typedef struct-
42{-
43 fe25519 x;-
44 fe25519 y;-
45 fe25519 z;-
46} ge25519_p2;-
47-
48typedef struct-
49{-
50 fe25519 x;-
51 fe25519 y;-
52} ge25519_aff;-
53-
54-
55/* Packed coordinates of the base point */-
56const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69, -
57 0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},-
58 {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, -
59 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},-
60 {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, -
61 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},-
62 {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20, -
63 0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}};-
64-
65/* Multiples of the base point in affine representation */-
66static const ge25519_aff ge25519_base_multiples_affine[425] = {-
67#include "ge25519_base.data"-
68};-
69-
70static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)-
71{-
72 fe25519_mul(&r->x, &p->x, &p->t);-
73 fe25519_mul(&r->y, &p->y, &p->z);-
74 fe25519_mul(&r->z, &p->z, &p->t);-
75}
executed 5340538 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
5340538
76-
77static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)-
78{-
79 p1p1_to_p2((ge25519_p2 *)r, p);-
80 fe25519_mul(&r->t, &p->x, &p->y);-
81}
executed 1846116 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
1846116
82-
83static void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)-
84{-
85 fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;-
86 fe25519_mul(&qt, &q->x, &q->y);-
87 fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */-
88 fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */-
89 fe25519_sub(&t1, &q->y, &q->x);-
90 fe25519_add(&t2, &q->y, &q->x);-
91 fe25519_mul(&a, &a, &t1);-
92 fe25519_mul(&b, &b, &t2);-
93 fe25519_sub(&e, &b, &a); /* E = B-A */-
94 fe25519_add(&h, &b, &a); /* H = B+A */-
95 fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */-
96 fe25519_mul(&c, &c, &ge25519_ec2d);-
97 fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */-
98 fe25519_sub(&f, &d, &c); /* F = D-C */-
99 fe25519_add(&g, &d, &c); /* G = D+C */-
100 fe25519_mul(&r->x, &e, &f);-
101 fe25519_mul(&r->y, &h, &g);-
102 fe25519_mul(&r->z, &g, &f);-
103 fe25519_mul(&r->t, &e, &h);-
104}
executed 6552 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
6552
105-
106static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)-
107{-
108 fe25519 a, b, c, d, t;-
109 -
110 fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */-
111 fe25519_sub(&t, &q->y, &q->x);-
112 fe25519_mul(&a, &a, &t);-
113 fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */-
114 fe25519_add(&t, &q->x, &q->y);-
115 fe25519_mul(&b, &b, &t);-
116 fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */-
117 fe25519_mul(&c, &c, &ge25519_ec2d);-
118 fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */-
119 fe25519_add(&d, &d, &d);-
120 fe25519_sub(&r->x, &b, &a); /* E = B-A */-
121 fe25519_sub(&r->t, &d, &c); /* F = D-C */-
122 fe25519_add(&r->z, &d, &c); /* G = D+C */-
123 fe25519_add(&r->y, &b, &a); /* H = B+A */-
124}
executed 1790428 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
1790428
125-
126/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */-
127static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)-
128{-
129 fe25519 a,b,c,d;-
130 fe25519_square(&a, &p->x);-
131 fe25519_square(&b, &p->y);-
132 fe25519_square(&c, &p->z);-
133 fe25519_add(&c, &c, &c);-
134 fe25519_neg(&d, &a);-
135-
136 fe25519_add(&r->x, &p->x, &p->y);-
137 fe25519_square(&r->x, &r->x);-
138 fe25519_sub(&r->x, &r->x, &a);-
139 fe25519_sub(&r->x, &r->x, &b);-
140 fe25519_add(&r->z, &d, &b);-
141 fe25519_sub(&r->t, &r->z, &c);-
142 fe25519_sub(&r->y, &d, &b);-
143}
executed 3550110 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
3550110
144-
145/* Constant-time version of: if(b) r = p */-
146static void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)-
147{-
148 fe25519_cmov(&r->x, &p->x, b);-
149 fe25519_cmov(&r->y, &p->y, b);-
150}
executed 26520 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
26520
151-
152static unsigned char equal(signed char b,signed char c)-
153{-
154 unsigned char ub = b;-
155 unsigned char uc = c;-
156 unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */-
157 crypto_uint32 y = x; /* 0: yes; 1..255: no */-
158 y -= 1; /* 4294967295: yes; 0..254: no */-
159 y >>= 31; /* 1: yes; 0: no */-
160 return y;
executed 46410 times by 3 tests: return y;
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
46410
161}-
162-
163static unsigned char negative(signed char b)-
164{-
165 unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */-
166 x >>= 63; /* 1: yes; 0: no */-
167 return x;
executed 6630 times by 3 tests: return x;
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
6630
168}-
169-
170static void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)-
171{-
172 /* constant time */-
173 fe25519 v;-
174 *t = ge25519_base_multiples_affine[5*pos+0];-
175 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) | equal(b,-1));-
176 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) | equal(b,-2));-
177 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) | equal(b,-3));-
178 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4));-
179 fe25519_neg(&v, &t->x);-
180 fe25519_cmov(&t->x, &v, negative(b));-
181}
executed 6630 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
6630
182-
183static void setneutral(ge25519 *r)-
184{-
185 fe25519_setzero(&r->x);-
186 fe25519_setone(&r->y);-
187 fe25519_setone(&r->z);-
188 fe25519_setzero(&r->t);-
189}
executed 13922 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
13922
190-
191/* ********************************************************************-
192 * EXPORTED FUNCTIONS-
193 ******************************************************************** */-
194-
195/* return 0 on success, -1 otherwise */-
196int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])-
197{-
198 unsigned char par;-
199 fe25519 t, chk, num, den, den2, den4, den6;-
200 fe25519_setone(&r->z);-
201 par = p[31] >> 7;-
202 fe25519_unpack(&r->y, p); -
203 fe25519_square(&num, &r->y); /* x = y^2 */-
204 fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */-
205 fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */-
206 fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */-
207-
208 /* Computation of sqrt(num/den) */-
209 /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */-
210 fe25519_square(&den2, &den);-
211 fe25519_square(&den4, &den2);-
212 fe25519_mul(&den6, &den4, &den2);-
213 fe25519_mul(&t, &den6, &num);-
214 fe25519_mul(&t, &t, &den);-
215-
216 fe25519_pow2523(&t, &t);-
217 /* 2. computation of r->x = t * num * den^3 */-
218 fe25519_mul(&t, &t, &num);-
219 fe25519_mul(&t, &t, &den);-
220 fe25519_mul(&t, &t, &den);-
221 fe25519_mul(&r->x, &t, &den);-
222-
223 /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */-
224 fe25519_square(&chk, &r->x);-
225 fe25519_mul(&chk, &chk, &den);-
226 if (!fe25519_iseq_vartime(&chk, &num))
!crypto_sign_e...me(&chk, &num)Description
TRUEevaluated 14183 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
FALSEevaluated 216 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
216-14183
227 fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
executed 14183 times by 2 tests: crypto_sign_ed25519_ref_fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
Executed by:
  • test_kex
  • test_sshkey
14183
228-
229 /* 4. Now we have one of the two square roots, except if input was not a square */-
230 fe25519_square(&chk, &r->x);-
231 fe25519_mul(&chk, &chk, &den);-
232 if (!fe25519_iseq_vartime(&chk, &num))
!crypto_sign_e...me(&chk, &num)Description
TRUEevaluated 477 times by 1 test
Evaluated by:
  • test_sshkey
FALSEevaluated 13922 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
477-13922
233 return -1;
executed 477 times by 1 test: return -1;
Executed by:
  • test_sshkey
477
234-
235 /* 5. Choose the desired square root according to parity: */-
236 if(fe25519_getparity(&r->x) != (1-par))
crypto_sign_ed...>x) != (1-par)Description
TRUEevaluated 227 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
FALSEevaluated 13695 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
227-13695
237 fe25519_neg(&r->x, &r->x);
executed 227 times by 2 tests: crypto_sign_ed25519_ref_fe25519_neg(&r->x, &r->x);
Executed by:
  • test_kex
  • test_sshkey
227
238-
239 fe25519_mul(&r->t, &r->x, &r->y);-
240 return 0;
executed 13922 times by 2 tests: return 0;
Executed by:
  • test_kex
  • test_sshkey
13922
241}-
242-
243void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)-
244{-
245 fe25519 tx, ty, zi;-
246 fe25519_invert(&zi, &p->z); -
247 fe25519_mul(&tx, &p->x, &zi);-
248 fe25519_mul(&ty, &p->y, &zi);-
249 fe25519_pack(r, &ty);-
250 r[31] ^= fe25519_getparity(&tx) << 7;-
251}
executed 14000 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
14000
252-
253int ge25519_isneutral_vartime(const ge25519_p3 *p)-
254{-
255 int ret = 1;-
256 if(!fe25519_iszero(&p->x)) ret = 0;
never executed: ret = 0;
!crypto_sign_e..._iszero(&p->x)Description
TRUEnever evaluated
FALSEnever evaluated
0
257 if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0;
never executed: ret = 0;
!crypto_sign_e...(&p->y, &p->z)Description
TRUEnever evaluated
FALSEnever evaluated
0
258 return ret;
never executed: return ret;
0
259}-
260-
261/* computes [s1]p1 + [s2]p2 */-
262void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)-
263{-
264 ge25519_p1p1 tp1p1;-
265 ge25519_p3 pre[16];-
266 unsigned char b[127];-
267 int i;-
268-
269 /* precomputation s2 s1 */-
270 setneutral(pre); /* 00 00 */-
271 pre[1] = *p1; /* 00 01 */-
272 dbl_p1p1(&tp1p1,(ge25519_p2 *)p1); p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */-
273 add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */-
274 pre[4] = *p2; /* 01 00 */-
275 add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */-
276 add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */-
277 add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */-
278 dbl_p1p1(&tp1p1,(ge25519_p2 *)p2); p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */-
279 add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */-
280 dbl_p1p1(&tp1p1,(ge25519_p2 *)&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */-
281 add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */-
282 add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */-
283 add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */-
284 add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */-
285 add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */-
286-
287 sc25519_2interleave2(b,s1,s2);-
288-
289 /* scalar multiplication */-
290 *r = pre[b[126]];-
291 for(i=125;i>=0;i--)
i>=0Description
TRUEevaluated 1754172 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
FALSEevaluated 13922 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
13922-1754172
292 {-
293 dbl_p1p1(&tp1p1, (ge25519_p2 *)r);-
294 p1p1_to_p2((ge25519_p2 *) r, &tp1p1);-
295 dbl_p1p1(&tp1p1, (ge25519_p2 *)r);-
296 if(b[i]!=0)
b[i]!=0Description
TRUEevaluated 1651208 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
FALSEevaluated 102964 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
102964-1651208
297 {-
298 p1p1_to_p3(r, &tp1p1);-
299 add_p1p1(&tp1p1, r, &pre[b[i]]);-
300 }
executed 1651208 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
1651208
301 if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
executed 1740250 times by 2 tests: p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
Executed by:
  • test_kex
  • test_sshkey
i != 0Description
TRUEevaluated 1740250 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
FALSEevaluated 13922 times by 2 tests
Evaluated by:
  • test_kex
  • test_sshkey
13922-1740250
302 else p1p1_to_p3(r, &tp1p1);
executed 13922 times by 2 tests: p1p1_to_p3(r, &tp1p1);
Executed by:
  • test_kex
  • test_sshkey
13922
303 }-
304}
executed 13922 times by 2 tests: end of block
Executed by:
  • test_kex
  • test_sshkey
13922
305-
306void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)-
307{-
308 signed char b[85];-
309 int i;-
310 ge25519_aff t;-
311 sc25519_window3(b,s);-
312-
313 choose_t((ge25519_aff *)r, 0, b[0]);-
314 fe25519_setone(&r->z);-
315 fe25519_mul(&r->t, &r->x, &r->y);-
316 for(i=1;i<85;i++)
i<85Description
TRUEevaluated 6552 times by 3 tests
Evaluated by:
  • ssh-keygen
  • test_kex
  • test_sshkey
FALSEevaluated 78 times by 3 tests
Evaluated by:
  • ssh-keygen
  • test_kex
  • test_sshkey
78-6552
317 {-
318 choose_t(&t, (unsigned long long) i, b[i]);-
319 ge25519_mixadd2(r, &t);-
320 }
executed 6552 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
6552
321}
executed 78 times by 3 tests: end of block
Executed by:
  • ssh-keygen
  • test_kex
  • test_sshkey
78
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