| 1 |
root |
1.1 |
#include "ge.h" |
| 2 |
|
|
#include "precomp_data.h" |
| 3 |
|
|
|
| 4 |
|
|
|
| 5 |
|
|
/* |
| 6 |
|
|
r = p + q |
| 7 |
|
|
*/ |
| 8 |
|
|
|
| 9 |
|
|
void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 10 |
|
|
fe t0; |
| 11 |
|
|
fe_add(r->X, p->Y, p->X); |
| 12 |
|
|
fe_sub(r->Y, p->Y, p->X); |
| 13 |
|
|
fe_mul(r->Z, r->X, q->YplusX); |
| 14 |
|
|
fe_mul(r->Y, r->Y, q->YminusX); |
| 15 |
|
|
fe_mul(r->T, q->T2d, p->T); |
| 16 |
|
|
fe_mul(r->X, p->Z, q->Z); |
| 17 |
|
|
fe_add(t0, r->X, r->X); |
| 18 |
|
|
fe_sub(r->X, r->Z, r->Y); |
| 19 |
|
|
fe_add(r->Y, r->Z, r->Y); |
| 20 |
|
|
fe_add(r->Z, t0, r->T); |
| 21 |
|
|
fe_sub(r->T, t0, r->T); |
| 22 |
|
|
} |
| 23 |
|
|
|
| 24 |
|
|
|
| 25 |
|
|
static void slide(signed char *r, const unsigned char *a) { |
| 26 |
|
|
int i; |
| 27 |
|
|
int b; |
| 28 |
|
|
int k; |
| 29 |
|
|
|
| 30 |
|
|
for (i = 0; i < 256; ++i) { |
| 31 |
|
|
r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| 32 |
|
|
} |
| 33 |
|
|
|
| 34 |
|
|
for (i = 0; i < 256; ++i) |
| 35 |
|
|
if (r[i]) { |
| 36 |
|
|
for (b = 1; b <= 6 && i + b < 256; ++b) { |
| 37 |
|
|
if (r[i + b]) { |
| 38 |
|
|
if (r[i] + (r[i + b] << b) <= 15) { |
| 39 |
|
|
r[i] += r[i + b] << b; |
| 40 |
|
|
r[i + b] = 0; |
| 41 |
|
|
} else if (r[i] - (r[i + b] << b) >= -15) { |
| 42 |
|
|
r[i] -= r[i + b] << b; |
| 43 |
|
|
|
| 44 |
|
|
for (k = i + b; k < 256; ++k) { |
| 45 |
|
|
if (!r[k]) { |
| 46 |
|
|
r[k] = 1; |
| 47 |
|
|
break; |
| 48 |
|
|
} |
| 49 |
|
|
|
| 50 |
|
|
r[k] = 0; |
| 51 |
|
|
} |
| 52 |
|
|
} else { |
| 53 |
|
|
break; |
| 54 |
|
|
} |
| 55 |
|
|
} |
| 56 |
|
|
} |
| 57 |
|
|
} |
| 58 |
|
|
} |
| 59 |
|
|
|
| 60 |
|
|
/* |
| 61 |
|
|
r = a * A + b * B |
| 62 |
|
|
where a = a[0]+256*a[1]+...+256^31 a[31]. |
| 63 |
|
|
and b = b[0]+256*b[1]+...+256^31 b[31]. |
| 64 |
|
|
B is the Ed25519 base point (x,4/5) with x positive. |
| 65 |
|
|
*/ |
| 66 |
|
|
|
| 67 |
|
|
void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { |
| 68 |
|
|
signed char aslide[256]; |
| 69 |
|
|
signed char bslide[256]; |
| 70 |
|
|
ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
| 71 |
|
|
ge_p1p1 t; |
| 72 |
|
|
ge_p3 u; |
| 73 |
|
|
ge_p3 A2; |
| 74 |
|
|
int i; |
| 75 |
|
|
slide(aslide, a); |
| 76 |
|
|
slide(bslide, b); |
| 77 |
|
|
ge_p3_to_cached(&Ai[0], A); |
| 78 |
|
|
ge_p3_dbl(&t, A); |
| 79 |
|
|
ge_p1p1_to_p3(&A2, &t); |
| 80 |
|
|
ge_add(&t, &A2, &Ai[0]); |
| 81 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 82 |
|
|
ge_p3_to_cached(&Ai[1], &u); |
| 83 |
|
|
ge_add(&t, &A2, &Ai[1]); |
| 84 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 85 |
|
|
ge_p3_to_cached(&Ai[2], &u); |
| 86 |
|
|
ge_add(&t, &A2, &Ai[2]); |
| 87 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 88 |
|
|
ge_p3_to_cached(&Ai[3], &u); |
| 89 |
|
|
ge_add(&t, &A2, &Ai[3]); |
| 90 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 91 |
|
|
ge_p3_to_cached(&Ai[4], &u); |
| 92 |
|
|
ge_add(&t, &A2, &Ai[4]); |
| 93 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 94 |
|
|
ge_p3_to_cached(&Ai[5], &u); |
| 95 |
|
|
ge_add(&t, &A2, &Ai[5]); |
| 96 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 97 |
|
|
ge_p3_to_cached(&Ai[6], &u); |
| 98 |
|
|
ge_add(&t, &A2, &Ai[6]); |
| 99 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 100 |
|
|
ge_p3_to_cached(&Ai[7], &u); |
| 101 |
|
|
ge_p2_0(r); |
| 102 |
|
|
|
| 103 |
|
|
for (i = 255; i >= 0; --i) { |
| 104 |
|
|
if (aslide[i] || bslide[i]) { |
| 105 |
|
|
break; |
| 106 |
|
|
} |
| 107 |
|
|
} |
| 108 |
|
|
|
| 109 |
|
|
for (; i >= 0; --i) { |
| 110 |
|
|
ge_p2_dbl(&t, r); |
| 111 |
|
|
|
| 112 |
|
|
if (aslide[i] > 0) { |
| 113 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 114 |
|
|
ge_add(&t, &u, &Ai[aslide[i] / 2]); |
| 115 |
|
|
} else if (aslide[i] < 0) { |
| 116 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 117 |
|
|
ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); |
| 118 |
|
|
} |
| 119 |
|
|
|
| 120 |
|
|
if (bslide[i] > 0) { |
| 121 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 122 |
|
|
ge_madd(&t, &u, &Bi[bslide[i] / 2]); |
| 123 |
|
|
} else if (bslide[i] < 0) { |
| 124 |
|
|
ge_p1p1_to_p3(&u, &t); |
| 125 |
|
|
ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); |
| 126 |
|
|
} |
| 127 |
|
|
|
| 128 |
|
|
ge_p1p1_to_p2(r, &t); |
| 129 |
|
|
} |
| 130 |
|
|
} |
| 131 |
|
|
|
| 132 |
|
|
|
| 133 |
|
|
static const fe d = { |
| 134 |
|
|
-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 |
| 135 |
|
|
}; |
| 136 |
|
|
|
| 137 |
|
|
static const fe sqrtm1 = { |
| 138 |
|
|
-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 |
| 139 |
|
|
}; |
| 140 |
|
|
|
| 141 |
|
|
int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) { |
| 142 |
|
|
fe u; |
| 143 |
|
|
fe v; |
| 144 |
|
|
fe v3; |
| 145 |
|
|
fe vxx; |
| 146 |
|
|
fe check; |
| 147 |
|
|
fe_frombytes(h->Y, s); |
| 148 |
|
|
fe_1(h->Z); |
| 149 |
|
|
fe_sq(u, h->Y); |
| 150 |
|
|
fe_mul(v, u, d); |
| 151 |
|
|
fe_sub(u, u, h->Z); /* u = y^2-1 */ |
| 152 |
|
|
fe_add(v, v, h->Z); /* v = dy^2+1 */ |
| 153 |
|
|
fe_sq(v3, v); |
| 154 |
|
|
fe_mul(v3, v3, v); /* v3 = v^3 */ |
| 155 |
|
|
fe_sq(h->X, v3); |
| 156 |
|
|
fe_mul(h->X, h->X, v); |
| 157 |
|
|
fe_mul(h->X, h->X, u); /* x = uv^7 */ |
| 158 |
|
|
fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
| 159 |
|
|
fe_mul(h->X, h->X, v3); |
| 160 |
|
|
fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ |
| 161 |
|
|
fe_sq(vxx, h->X); |
| 162 |
|
|
fe_mul(vxx, vxx, v); |
| 163 |
|
|
fe_sub(check, vxx, u); /* vx^2-u */ |
| 164 |
|
|
|
| 165 |
|
|
if (fe_isnonzero(check)) { |
| 166 |
|
|
fe_add(check, vxx, u); /* vx^2+u */ |
| 167 |
|
|
|
| 168 |
|
|
if (fe_isnonzero(check)) { |
| 169 |
|
|
return -1; |
| 170 |
|
|
} |
| 171 |
|
|
|
| 172 |
|
|
fe_mul(h->X, h->X, sqrtm1); |
| 173 |
|
|
} |
| 174 |
|
|
|
| 175 |
|
|
if (fe_isnegative(h->X) == (s[31] >> 7)) { |
| 176 |
|
|
fe_neg(h->X, h->X); |
| 177 |
|
|
} |
| 178 |
|
|
|
| 179 |
|
|
fe_mul(h->T, h->X, h->Y); |
| 180 |
|
|
return 0; |
| 181 |
|
|
} |
| 182 |
|
|
|
| 183 |
|
|
|
| 184 |
|
|
/* |
| 185 |
|
|
r = p + q |
| 186 |
|
|
*/ |
| 187 |
|
|
|
| 188 |
|
|
void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 189 |
|
|
fe t0; |
| 190 |
|
|
fe_add(r->X, p->Y, p->X); |
| 191 |
|
|
fe_sub(r->Y, p->Y, p->X); |
| 192 |
|
|
fe_mul(r->Z, r->X, q->yplusx); |
| 193 |
|
|
fe_mul(r->Y, r->Y, q->yminusx); |
| 194 |
|
|
fe_mul(r->T, q->xy2d, p->T); |
| 195 |
|
|
fe_add(t0, p->Z, p->Z); |
| 196 |
|
|
fe_sub(r->X, r->Z, r->Y); |
| 197 |
|
|
fe_add(r->Y, r->Z, r->Y); |
| 198 |
|
|
fe_add(r->Z, t0, r->T); |
| 199 |
|
|
fe_sub(r->T, t0, r->T); |
| 200 |
|
|
} |
| 201 |
|
|
|
| 202 |
|
|
|
| 203 |
|
|
/* |
| 204 |
|
|
r = p - q |
| 205 |
|
|
*/ |
| 206 |
|
|
|
| 207 |
|
|
void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| 208 |
|
|
fe t0; |
| 209 |
|
|
|
| 210 |
|
|
fe_add(r->X, p->Y, p->X); |
| 211 |
|
|
fe_sub(r->Y, p->Y, p->X); |
| 212 |
|
|
fe_mul(r->Z, r->X, q->yminusx); |
| 213 |
|
|
fe_mul(r->Y, r->Y, q->yplusx); |
| 214 |
|
|
fe_mul(r->T, q->xy2d, p->T); |
| 215 |
|
|
fe_add(t0, p->Z, p->Z); |
| 216 |
|
|
fe_sub(r->X, r->Z, r->Y); |
| 217 |
|
|
fe_add(r->Y, r->Z, r->Y); |
| 218 |
|
|
fe_sub(r->Z, t0, r->T); |
| 219 |
|
|
fe_add(r->T, t0, r->T); |
| 220 |
|
|
} |
| 221 |
|
|
|
| 222 |
|
|
|
| 223 |
|
|
/* |
| 224 |
|
|
r = p |
| 225 |
|
|
*/ |
| 226 |
|
|
|
| 227 |
|
|
void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { |
| 228 |
|
|
fe_mul(r->X, p->X, p->T); |
| 229 |
|
|
fe_mul(r->Y, p->Y, p->Z); |
| 230 |
|
|
fe_mul(r->Z, p->Z, p->T); |
| 231 |
|
|
} |
| 232 |
|
|
|
| 233 |
|
|
|
| 234 |
|
|
|
| 235 |
|
|
/* |
| 236 |
|
|
r = p |
| 237 |
|
|
*/ |
| 238 |
|
|
|
| 239 |
|
|
void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { |
| 240 |
|
|
fe_mul(r->X, p->X, p->T); |
| 241 |
|
|
fe_mul(r->Y, p->Y, p->Z); |
| 242 |
|
|
fe_mul(r->Z, p->Z, p->T); |
| 243 |
|
|
fe_mul(r->T, p->X, p->Y); |
| 244 |
|
|
} |
| 245 |
|
|
|
| 246 |
|
|
|
| 247 |
|
|
void ge_p2_0(ge_p2 *h) { |
| 248 |
|
|
fe_0(h->X); |
| 249 |
|
|
fe_1(h->Y); |
| 250 |
|
|
fe_1(h->Z); |
| 251 |
|
|
} |
| 252 |
|
|
|
| 253 |
|
|
|
| 254 |
|
|
|
| 255 |
|
|
/* |
| 256 |
|
|
r = 2 * p |
| 257 |
|
|
*/ |
| 258 |
|
|
|
| 259 |
|
|
void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { |
| 260 |
|
|
fe t0; |
| 261 |
|
|
|
| 262 |
|
|
fe_sq(r->X, p->X); |
| 263 |
|
|
fe_sq(r->Z, p->Y); |
| 264 |
|
|
fe_sq2(r->T, p->Z); |
| 265 |
|
|
fe_add(r->Y, p->X, p->Y); |
| 266 |
|
|
fe_sq(t0, r->Y); |
| 267 |
|
|
fe_add(r->Y, r->Z, r->X); |
| 268 |
|
|
fe_sub(r->Z, r->Z, r->X); |
| 269 |
|
|
fe_sub(r->X, t0, r->Y); |
| 270 |
|
|
fe_sub(r->T, r->T, r->Z); |
| 271 |
|
|
} |
| 272 |
|
|
|
| 273 |
|
|
|
| 274 |
|
|
void ge_p3_0(ge_p3 *h) { |
| 275 |
|
|
fe_0(h->X); |
| 276 |
|
|
fe_1(h->Y); |
| 277 |
|
|
fe_1(h->Z); |
| 278 |
|
|
fe_0(h->T); |
| 279 |
|
|
} |
| 280 |
|
|
|
| 281 |
|
|
|
| 282 |
|
|
/* |
| 283 |
|
|
r = 2 * p |
| 284 |
|
|
*/ |
| 285 |
|
|
|
| 286 |
|
|
void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { |
| 287 |
|
|
ge_p2 q; |
| 288 |
|
|
ge_p3_to_p2(&q, p); |
| 289 |
|
|
ge_p2_dbl(r, &q); |
| 290 |
|
|
} |
| 291 |
|
|
|
| 292 |
|
|
|
| 293 |
|
|
|
| 294 |
|
|
/* |
| 295 |
|
|
r = p |
| 296 |
|
|
*/ |
| 297 |
|
|
|
| 298 |
|
|
static const fe d2 = { |
| 299 |
|
|
-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 |
| 300 |
|
|
}; |
| 301 |
|
|
|
| 302 |
|
|
void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { |
| 303 |
|
|
fe_add(r->YplusX, p->Y, p->X); |
| 304 |
|
|
fe_sub(r->YminusX, p->Y, p->X); |
| 305 |
|
|
fe_copy(r->Z, p->Z); |
| 306 |
|
|
fe_mul(r->T2d, p->T, d2); |
| 307 |
|
|
} |
| 308 |
|
|
|
| 309 |
|
|
|
| 310 |
|
|
/* |
| 311 |
|
|
r = p |
| 312 |
|
|
*/ |
| 313 |
|
|
|
| 314 |
|
|
void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { |
| 315 |
|
|
fe_copy(r->X, p->X); |
| 316 |
|
|
fe_copy(r->Y, p->Y); |
| 317 |
|
|
fe_copy(r->Z, p->Z); |
| 318 |
|
|
} |
| 319 |
|
|
|
| 320 |
|
|
|
| 321 |
|
|
void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) { |
| 322 |
|
|
fe recip; |
| 323 |
|
|
fe x; |
| 324 |
|
|
fe y; |
| 325 |
|
|
fe_invert(recip, h->Z); |
| 326 |
|
|
fe_mul(x, h->X, recip); |
| 327 |
|
|
fe_mul(y, h->Y, recip); |
| 328 |
|
|
fe_tobytes(s, y); |
| 329 |
|
|
s[31] ^= fe_isnegative(x) << 7; |
| 330 |
|
|
} |
| 331 |
|
|
|
| 332 |
|
|
|
| 333 |
|
|
static unsigned char equal(signed char b, signed char c) { |
| 334 |
|
|
unsigned char ub = b; |
| 335 |
|
|
unsigned char uc = c; |
| 336 |
|
|
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ |
| 337 |
|
|
uint64_t y = x; /* 0: yes; 1..255: no */ |
| 338 |
|
|
y -= 1; /* large: yes; 0..254: no */ |
| 339 |
|
|
y >>= 63; /* 1: yes; 0: no */ |
| 340 |
|
|
return (unsigned char) y; |
| 341 |
|
|
} |
| 342 |
|
|
|
| 343 |
|
|
static unsigned char negative(signed char b) { |
| 344 |
|
|
uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ |
| 345 |
|
|
x >>= 63; /* 1: yes; 0: no */ |
| 346 |
|
|
return (unsigned char) x; |
| 347 |
|
|
} |
| 348 |
|
|
|
| 349 |
root |
1.2 |
static void cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) { |
| 350 |
root |
1.1 |
fe_cmov(t->yplusx, u->yplusx, b); |
| 351 |
|
|
fe_cmov(t->yminusx, u->yminusx, b); |
| 352 |
|
|
fe_cmov(t->xy2d, u->xy2d, b); |
| 353 |
|
|
} |
| 354 |
|
|
|
| 355 |
|
|
|
| 356 |
|
|
static void select(ge_precomp *t, int pos, signed char b) { |
| 357 |
|
|
ge_precomp minust; |
| 358 |
|
|
unsigned char bnegative = negative(b); |
| 359 |
|
|
unsigned char babs = b - (((-bnegative) & b) << 1); |
| 360 |
|
|
fe_1(t->yplusx); |
| 361 |
|
|
fe_1(t->yminusx); |
| 362 |
|
|
fe_0(t->xy2d); |
| 363 |
|
|
cmov(t, &base[pos][0], equal(babs, 1)); |
| 364 |
|
|
cmov(t, &base[pos][1], equal(babs, 2)); |
| 365 |
|
|
cmov(t, &base[pos][2], equal(babs, 3)); |
| 366 |
|
|
cmov(t, &base[pos][3], equal(babs, 4)); |
| 367 |
|
|
cmov(t, &base[pos][4], equal(babs, 5)); |
| 368 |
|
|
cmov(t, &base[pos][5], equal(babs, 6)); |
| 369 |
|
|
cmov(t, &base[pos][6], equal(babs, 7)); |
| 370 |
|
|
cmov(t, &base[pos][7], equal(babs, 8)); |
| 371 |
|
|
fe_copy(minust.yplusx, t->yminusx); |
| 372 |
|
|
fe_copy(minust.yminusx, t->yplusx); |
| 373 |
|
|
fe_neg(minust.xy2d, t->xy2d); |
| 374 |
|
|
cmov(t, &minust, bnegative); |
| 375 |
|
|
} |
| 376 |
|
|
|
| 377 |
|
|
/* |
| 378 |
|
|
h = a * B |
| 379 |
|
|
where a = a[0]+256*a[1]+...+256^31 a[31] |
| 380 |
|
|
B is the Ed25519 base point (x,4/5) with x positive. |
| 381 |
|
|
|
| 382 |
|
|
Preconditions: |
| 383 |
|
|
a[31] <= 127 |
| 384 |
|
|
*/ |
| 385 |
|
|
|
| 386 |
|
|
void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) { |
| 387 |
|
|
signed char e[64]; |
| 388 |
|
|
signed char carry; |
| 389 |
|
|
ge_p1p1 r; |
| 390 |
|
|
ge_p2 s; |
| 391 |
|
|
ge_precomp t; |
| 392 |
|
|
int i; |
| 393 |
|
|
|
| 394 |
|
|
for (i = 0; i < 32; ++i) { |
| 395 |
|
|
e[2 * i + 0] = (a[i] >> 0) & 15; |
| 396 |
|
|
e[2 * i + 1] = (a[i] >> 4) & 15; |
| 397 |
|
|
} |
| 398 |
|
|
|
| 399 |
|
|
/* each e[i] is between 0 and 15 */ |
| 400 |
|
|
/* e[63] is between 0 and 7 */ |
| 401 |
|
|
carry = 0; |
| 402 |
|
|
|
| 403 |
|
|
for (i = 0; i < 63; ++i) { |
| 404 |
|
|
e[i] += carry; |
| 405 |
|
|
carry = e[i] + 8; |
| 406 |
|
|
carry >>= 4; |
| 407 |
|
|
e[i] -= carry << 4; |
| 408 |
|
|
} |
| 409 |
|
|
|
| 410 |
|
|
e[63] += carry; |
| 411 |
|
|
/* each e[i] is between -8 and 8 */ |
| 412 |
|
|
ge_p3_0(h); |
| 413 |
|
|
|
| 414 |
|
|
for (i = 1; i < 64; i += 2) { |
| 415 |
|
|
select(&t, i / 2, e[i]); |
| 416 |
|
|
ge_madd(&r, h, &t); |
| 417 |
|
|
ge_p1p1_to_p3(h, &r); |
| 418 |
|
|
} |
| 419 |
|
|
|
| 420 |
|
|
ge_p3_dbl(&r, h); |
| 421 |
|
|
ge_p1p1_to_p2(&s, &r); |
| 422 |
|
|
ge_p2_dbl(&r, &s); |
| 423 |
|
|
ge_p1p1_to_p2(&s, &r); |
| 424 |
|
|
ge_p2_dbl(&r, &s); |
| 425 |
|
|
ge_p1p1_to_p2(&s, &r); |
| 426 |
|
|
ge_p2_dbl(&r, &s); |
| 427 |
|
|
ge_p1p1_to_p3(h, &r); |
| 428 |
|
|
|
| 429 |
|
|
for (i = 0; i < 64; i += 2) { |
| 430 |
|
|
select(&t, i / 2, e[i]); |
| 431 |
|
|
ge_madd(&r, h, &t); |
| 432 |
|
|
ge_p1p1_to_p3(h, &r); |
| 433 |
|
|
} |
| 434 |
|
|
} |
| 435 |
|
|
|
| 436 |
|
|
|
| 437 |
|
|
/* |
| 438 |
|
|
r = p - q |
| 439 |
|
|
*/ |
| 440 |
|
|
|
| 441 |
|
|
void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| 442 |
|
|
fe t0; |
| 443 |
|
|
|
| 444 |
|
|
fe_add(r->X, p->Y, p->X); |
| 445 |
|
|
fe_sub(r->Y, p->Y, p->X); |
| 446 |
|
|
fe_mul(r->Z, r->X, q->YminusX); |
| 447 |
|
|
fe_mul(r->Y, r->Y, q->YplusX); |
| 448 |
|
|
fe_mul(r->T, q->T2d, p->T); |
| 449 |
|
|
fe_mul(r->X, p->Z, q->Z); |
| 450 |
|
|
fe_add(t0, r->X, r->X); |
| 451 |
|
|
fe_sub(r->X, r->Z, r->Y); |
| 452 |
|
|
fe_add(r->Y, r->Z, r->Y); |
| 453 |
|
|
fe_sub(r->Z, t0, r->T); |
| 454 |
|
|
fe_add(r->T, t0, r->T); |
| 455 |
|
|
} |
| 456 |
|
|
|
| 457 |
|
|
|
| 458 |
|
|
void ge_tobytes(unsigned char *s, const ge_p2 *h) { |
| 459 |
|
|
fe recip; |
| 460 |
|
|
fe x; |
| 461 |
|
|
fe y; |
| 462 |
|
|
fe_invert(recip, h->Z); |
| 463 |
|
|
fe_mul(x, h->X, recip); |
| 464 |
|
|
fe_mul(y, h->Y, recip); |
| 465 |
|
|
fe_tobytes(s, y); |
| 466 |
|
|
s[31] ^= fe_isnegative(x) << 7; |
| 467 |
|
|
} |
