aboutsummaryrefslogtreecommitdiff
path: root/src/external/ge25519.c
blob: b098cc5ea9eacb400da0dae69512b7ea3fb73203 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
/* $OpenBSD: ge25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */

/*
 * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
 * Peter Schwabe, Bo-Yin Yang.
 * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c
 */

#include "libssh/fe25519.h"
#include "libssh/sc25519.h"
#include "libssh/ge25519.h"

/*
 * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
 * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
 * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
 */

/* d */
static const fe25519 ge25519_ecd = {
    {0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75,
     0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
     0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C,
     0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}
};

/* 2*d */
static const fe25519 ge25519_ec2d = {
    {0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB,
     0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00,
     0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19,
     0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}
};

/* sqrt(-1) */
static const fe25519 ge25519_sqrtm1 = {
    {0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4,
     0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F,
     0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B,
     0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}
};

#define ge25519_p3 ge25519

typedef struct {
  fe25519 x;
  fe25519 z;
  fe25519 y;
  fe25519 t;
} ge25519_p1p1;

typedef struct {
  fe25519 x;
  fe25519 y;
  fe25519 z;
} ge25519_p2;

typedef struct {
  fe25519 x;
  fe25519 y;
} ge25519_aff;


/* Packed coordinates of the base point */
const ge25519 ge25519_base = {
    {{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9,
      0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
      0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0,
      0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},
    {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
      0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
      0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
      0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},
    {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
    {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D,
      0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
      0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66,
      0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}
};

/* Multiples of the base point in affine representation */
static const ge25519_aff ge25519_base_multiples_affine[425] = {
#include "ge25519_base.data"
};

static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
{
    fe25519_mul(&r->x, &p->x, &p->t);
    fe25519_mul(&r->y, &p->y, &p->z);
    fe25519_mul(&r->z, &p->z, &p->t);
}

static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
{
    p1p1_to_p2((ge25519_p2 *)r, p);
    fe25519_mul(&r->t, &p->x, &p->y);
}

static void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
{
    fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;
    fe25519_mul(&qt, &q->x, &q->y);
    fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */
    fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */
    fe25519_sub(&t1, &q->y, &q->x);
    fe25519_add(&t2, &q->y, &q->x);
    fe25519_mul(&a, &a, &t1);
    fe25519_mul(&b, &b, &t2);
    fe25519_sub(&e, &b, &a); /* E = B-A */
    fe25519_add(&h, &b, &a); /* H = B+A */
    fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */
    fe25519_mul(&c, &c, &ge25519_ec2d);
    fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */
    fe25519_sub(&f, &d, &c); /* F = D-C */
    fe25519_add(&g, &d, &c); /* G = D+C */
    fe25519_mul(&r->x, &e, &f);
    fe25519_mul(&r->y, &h, &g);
    fe25519_mul(&r->z, &g, &f);
    fe25519_mul(&r->t, &e, &h);
}

static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
{
    fe25519 a, b, c, d, t;

    fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */
    fe25519_sub(&t, &q->y, &q->x);
    fe25519_mul(&a, &a, &t);
    fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */
    fe25519_add(&t, &q->x, &q->y);
    fe25519_mul(&b, &b, &t);
    fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */
    fe25519_mul(&c, &c, &ge25519_ec2d);
    fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */
    fe25519_add(&d, &d, &d);
    fe25519_sub(&r->x, &b, &a); /* E = B-A */
    fe25519_sub(&r->t, &d, &c); /* F = D-C */
    fe25519_add(&r->z, &d, &c); /* G = D+C */
    fe25519_add(&r->y, &b, &a); /* H = B+A */
}

/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
{
    fe25519 a,b,c,d;
    fe25519_square(&a, &p->x);
    fe25519_square(&b, &p->y);
    fe25519_square(&c, &p->z);
    fe25519_add(&c, &c, &c);
    fe25519_neg(&d, &a);

    fe25519_add(&r->x, &p->x, &p->y);
    fe25519_square(&r->x, &r->x);
    fe25519_sub(&r->x, &r->x, &a);
    fe25519_sub(&r->x, &r->x, &b);
    fe25519_add(&r->z, &d, &b);
    fe25519_sub(&r->t, &r->z, &c);
    fe25519_sub(&r->y, &d, &b);
}

/* Constant-time version of: if(b) r = p */
static void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
{
    fe25519_cmov(&r->x, &p->x, b);
    fe25519_cmov(&r->y, &p->y, b);
}

static unsigned char equal(signed char b,signed char c)
{
    unsigned char ub = b;
    unsigned char uc = c;
    unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
    uint32_t y = x; /* 0: yes; 1..255: no */

    y -= 1; /* 4294967295: yes; 0..254: no */
    y >>= 31; /* 1: yes; 0: no */

    return y;
}

static unsigned char negative(signed char b)
{
    unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */

    x >>= 63; /* 1: yes; 0: no */

    return x;
}

static void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
{
    /* constant time */
    fe25519 v;

    *t = ge25519_base_multiples_affine[5 * pos + 0];

    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 1],
             equal(b,1) | equal(b,-1));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 2],
             equal(b,2) | equal(b,-2));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 3],
             equal(b,3) | equal(b,-3));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 4],
             equal(b,-4));

    fe25519_neg(&v, &t->x);
    fe25519_cmov(&t->x, &v, negative(b));
}

static void setneutral(ge25519 *r)
{
    fe25519_setzero(&r->x);
    fe25519_setone(&r->y);
    fe25519_setone(&r->z);
    fe25519_setzero(&r->t);
}

/* ********************************************************************
 *                    EXPORTED FUNCTIONS
 ******************************************************************** */

/* return 0 on success, -1 otherwise */
int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
{
    unsigned char par;

    fe25519 t, chk, num, den, den2, den4, den6;
    fe25519_setone(&r->z);
    par = p[31] >> 7;
    fe25519_unpack(&r->y, p);
    fe25519_square(&num, &r->y); /* x = y^2 */
    fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
    fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
    fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */

    /* Computation of sqrt(num/den) */
    /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
    fe25519_square(&den2, &den);
    fe25519_square(&den4, &den2);
    fe25519_mul(&den6, &den4, &den2);
    fe25519_mul(&t, &den6, &num);
    fe25519_mul(&t, &t, &den);

    fe25519_pow2523(&t, &t);
    /* 2. computation of r->x = t * num * den^3 */
    fe25519_mul(&t, &t, &num);
    fe25519_mul(&t, &t, &den);
    fe25519_mul(&t, &t, &den);
    fe25519_mul(&r->x, &t, &den);

    /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
    fe25519_square(&chk, &r->x);
    fe25519_mul(&chk, &chk, &den);
    if (!fe25519_iseq_vartime(&chk, &num)) {
        fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
    }

    /* 4. Now we have one of the two square roots, except if input was not a square */
    fe25519_square(&chk, &r->x);
    fe25519_mul(&chk, &chk, &den);
    if (!fe25519_iseq_vartime(&chk, &num)) {
        return -1;
    }

    /* 5. Choose the desired square root according to parity: */
    if(fe25519_getparity(&r->x) != (1-par)) {
        fe25519_neg(&r->x, &r->x);
    }

    fe25519_mul(&r->t, &r->x, &r->y);

    return 0;
}

void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
{
    fe25519 tx, ty, zi;

    fe25519_invert(&zi, &p->z);
    fe25519_mul(&tx, &p->x, &zi);
    fe25519_mul(&ty, &p->y, &zi);
    fe25519_pack(r, &ty);

    r[31] ^= fe25519_getparity(&tx) << 7;
}

int ge25519_isneutral_vartime(const ge25519_p3 *p)
{
    int ret = 1;

    if (!fe25519_iszero(&p->x)) {
        ret = 0;
    }

    if (!fe25519_iseq_vartime(&p->y, &p->z)) {
        ret = 0;
    }

    return ret;
}

/* computes [s1]p1 + [s2]p2 */
void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
{
    ge25519_p1p1 tp1p1;
    ge25519_p3 pre[16];
    unsigned char b[127];
    int i;

    /* precomputation                                                        s2 s1 */
    setneutral(pre);                                                      /* 00 00 */
    pre[1] = *p1;                                                         /* 00 01 */
    dbl_p1p1(&tp1p1,(ge25519_p2 *)p1);      p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */
    add_p1p1(&tp1p1,&pre[1], &pre[2]);      p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */
    pre[4] = *p2;                                                         /* 01 00 */
    add_p1p1(&tp1p1,&pre[1], &pre[4]);      p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */
    add_p1p1(&tp1p1,&pre[2], &pre[4]);      p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */
    add_p1p1(&tp1p1,&pre[3], &pre[4]);      p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */
    dbl_p1p1(&tp1p1,(ge25519_p2 *)p2);      p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */
    add_p1p1(&tp1p1,&pre[1], &pre[8]);      p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */
    dbl_p1p1(&tp1p1,(ge25519_p2 *)&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
    add_p1p1(&tp1p1,&pre[3], &pre[8]);      p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
    add_p1p1(&tp1p1,&pre[4], &pre[8]);      p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
    add_p1p1(&tp1p1,&pre[1],&pre[12]);      p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
    add_p1p1(&tp1p1,&pre[2],&pre[12]);      p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
    add_p1p1(&tp1p1,&pre[3],&pre[12]);      p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */

    sc25519_2interleave2(b,s1,s2);

    /* scalar multiplication */
    *r = pre[b[126]];

    for (i = 125; i >= 0; i--) {
        dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
        p1p1_to_p2((ge25519_p2 *) r, &tp1p1);
        dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
        if(b[i] != 0) {
            p1p1_to_p3(r, &tp1p1);
            add_p1p1(&tp1p1, r, &pre[b[i]]);
        }
        if (i != 0) {
            p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
        } else {
            p1p1_to_p3(r, &tp1p1);
        }
    }
}

void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
{
    signed char b[85];
    int i;
    ge25519_aff t;

    sc25519_window3(b,s);

    choose_t((ge25519_aff *)r, 0, b[0]);
    fe25519_setone(&r->z);
    fe25519_mul(&r->t, &r->x, &r->y);
    for (i = 1; i < 85; i++) {
        choose_t(&t, (unsigned long long) i, b[i]);
        ge25519_mixadd2(r, &t);
    }
}