1/* 2 * Copyright 2017-2022 The OpenSSL Project Authors. All Rights Reserved. 3 * Copyright 2015-2016 Cryptography Research, Inc. 4 * 5 * Licensed under the Apache License 2.0 (the "License"). You may not use 6 * this file except in compliance with the License. You can obtain a copy 7 * in the file LICENSE in the source distribution or at 8 * https://www.openssl.org/source/license.html 9 * 10 * Originally written by Mike Hamburg 11 */ 12#include <openssl/crypto.h> 13#include "word.h" 14#include "field.h" 15 16#include "point_448.h" 17#include "ed448.h" 18#include "crypto/ecx.h" 19#include "curve448_local.h" 20 21#define COFACTOR 4 22 23#define C448_WNAF_FIXED_TABLE_BITS 5 24#define C448_WNAF_VAR_TABLE_BITS 3 25 26#define EDWARDS_D (-39081) 27 28static const curve448_scalar_t precomputed_scalarmul_adjustment = { 29 { 30 { 31 SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL), 32 SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL) 33 } 34 } 35}; 36 37#define TWISTED_D (EDWARDS_D - 1) 38 39#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */ 40 41/* Inverse. */ 42static void gf_invert(gf y, const gf x, int assert_nonzero) 43{ 44 mask_t ret; 45 gf t1, t2; 46 47 gf_sqr(t1, x); /* o^2 */ 48 ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */ 49 (void)ret; 50 if (assert_nonzero) 51 assert(ret); 52 gf_sqr(t1, t2); 53 gf_mul(t2, t1, x); /* not direct to y in case of alias. */ 54 gf_copy(y, t2); 55} 56 57/** identity = (0,1) */ 58const curve448_point_t ossl_curve448_point_identity = 59 { {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} }; 60 61static void point_double_internal(curve448_point_t p, const curve448_point_t q, 62 int before_double) 63{ 64 gf a, b, c, d; 65 66 gf_sqr(c, q->x); 67 gf_sqr(a, q->y); 68 gf_add_nr(d, c, a); /* 2+e */ 69 gf_add_nr(p->t, q->y, q->x); /* 2+e */ 70 gf_sqr(b, p->t); 71 gf_subx_nr(b, b, d, 3); /* 4+e */ 72 gf_sub_nr(p->t, a, c); /* 3+e */ 73 gf_sqr(p->x, q->z); 74 gf_add_nr(p->z, p->x, p->x); /* 2+e */ 75 gf_subx_nr(a, p->z, p->t, 4); /* 6+e */ 76 if (GF_HEADROOM == 5) 77 gf_weak_reduce(a); /* or 1+e */ 78 gf_mul(p->x, a, b); 79 gf_mul(p->z, p->t, a); 80 gf_mul(p->y, p->t, d); 81 if (!before_double) 82 gf_mul(p->t, b, d); 83} 84 85void ossl_curve448_point_double(curve448_point_t p, const curve448_point_t q) 86{ 87 point_double_internal(p, q, 0); 88} 89 90/* Operations on [p]niels */ 91static ossl_inline void cond_neg_niels(niels_t n, mask_t neg) 92{ 93 gf_cond_swap(n->a, n->b, neg); 94 gf_cond_neg(n->c, neg); 95} 96 97static void pt_to_pniels(pniels_t b, const curve448_point_t a) 98{ 99 gf_sub(b->n->a, a->y, a->x); 100 gf_add(b->n->b, a->x, a->y); 101 gf_mulw(b->n->c, a->t, 2 * TWISTED_D); 102 gf_add(b->z, a->z, a->z); 103} 104 105static void pniels_to_pt(curve448_point_t e, const pniels_t d) 106{ 107 gf eu; 108 109 gf_add(eu, d->n->b, d->n->a); 110 gf_sub(e->y, d->n->b, d->n->a); 111 gf_mul(e->t, e->y, eu); 112 gf_mul(e->x, d->z, e->y); 113 gf_mul(e->y, d->z, eu); 114 gf_sqr(e->z, d->z); 115} 116 117static void niels_to_pt(curve448_point_t e, const niels_t n) 118{ 119 gf_add(e->y, n->b, n->a); 120 gf_sub(e->x, n->b, n->a); 121 gf_mul(e->t, e->y, e->x); 122 gf_copy(e->z, ONE); 123} 124 125static void add_niels_to_pt(curve448_point_t d, const niels_t e, 126 int before_double) 127{ 128 gf a, b, c; 129 130 gf_sub_nr(b, d->y, d->x); /* 3+e */ 131 gf_mul(a, e->a, b); 132 gf_add_nr(b, d->x, d->y); /* 2+e */ 133 gf_mul(d->y, e->b, b); 134 gf_mul(d->x, e->c, d->t); 135 gf_add_nr(c, a, d->y); /* 2+e */ 136 gf_sub_nr(b, d->y, a); /* 3+e */ 137 gf_sub_nr(d->y, d->z, d->x); /* 3+e */ 138 gf_add_nr(a, d->x, d->z); /* 2+e */ 139 gf_mul(d->z, a, d->y); 140 gf_mul(d->x, d->y, b); 141 gf_mul(d->y, a, c); 142 if (!before_double) 143 gf_mul(d->t, b, c); 144} 145 146static void sub_niels_from_pt(curve448_point_t d, const niels_t e, 147 int before_double) 148{ 149 gf a, b, c; 150 151 gf_sub_nr(b, d->y, d->x); /* 3+e */ 152 gf_mul(a, e->b, b); 153 gf_add_nr(b, d->x, d->y); /* 2+e */ 154 gf_mul(d->y, e->a, b); 155 gf_mul(d->x, e->c, d->t); 156 gf_add_nr(c, a, d->y); /* 2+e */ 157 gf_sub_nr(b, d->y, a); /* 3+e */ 158 gf_add_nr(d->y, d->z, d->x); /* 2+e */ 159 gf_sub_nr(a, d->z, d->x); /* 3+e */ 160 gf_mul(d->z, a, d->y); 161 gf_mul(d->x, d->y, b); 162 gf_mul(d->y, a, c); 163 if (!before_double) 164 gf_mul(d->t, b, c); 165} 166 167static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn, 168 int before_double) 169{ 170 gf L0; 171 172 gf_mul(L0, p->z, pn->z); 173 gf_copy(p->z, L0); 174 add_niels_to_pt(p, pn->n, before_double); 175} 176 177static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn, 178 int before_double) 179{ 180 gf L0; 181 182 gf_mul(L0, p->z, pn->z); 183 gf_copy(p->z, L0); 184 sub_niels_from_pt(p, pn->n, before_double); 185} 186 187c448_bool_t 188ossl_curve448_point_eq(const curve448_point_t p, 189 const curve448_point_t q) 190{ 191 mask_t succ; 192 gf a, b; 193 194 /* equality mod 2-torsion compares x/y */ 195 gf_mul(a, p->y, q->x); 196 gf_mul(b, q->y, p->x); 197 succ = gf_eq(a, b); 198 199 return mask_to_bool(succ); 200} 201 202c448_bool_t 203ossl_curve448_point_valid(const curve448_point_t p) 204{ 205 mask_t out; 206 gf a, b, c; 207 208 gf_mul(a, p->x, p->y); 209 gf_mul(b, p->z, p->t); 210 out = gf_eq(a, b); 211 gf_sqr(a, p->x); 212 gf_sqr(b, p->y); 213 gf_sub(a, b, a); 214 gf_sqr(b, p->t); 215 gf_mulw(c, b, TWISTED_D); 216 gf_sqr(b, p->z); 217 gf_add(b, b, c); 218 out &= gf_eq(a, b); 219 out &= ~gf_eq(p->z, ZERO); 220 return mask_to_bool(out); 221} 222 223static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni, 224 const niels_t * table, 225 int nelts, int idx) 226{ 227 constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx); 228} 229 230void 231ossl_curve448_precomputed_scalarmul(curve448_point_t out, 232 const curve448_precomputed_s * table, 233 const curve448_scalar_t scalar) 234{ 235 unsigned int i, j, k; 236 const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S; 237 niels_t ni; 238 curve448_scalar_t scalar1x; 239 240 ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment); 241 ossl_curve448_scalar_halve(scalar1x, scalar1x); 242 243 for (i = s; i > 0; i--) { 244 if (i != s) 245 point_double_internal(out, out, 0); 246 247 for (j = 0; j < n; j++) { 248 int tab = 0; 249 mask_t invert; 250 251 for (k = 0; k < t; k++) { 252 unsigned int bit = (i - 1) + s * (k + j * t); 253 254 if (bit < C448_SCALAR_BITS) 255 tab |= 256 (scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k; 257 } 258 259 invert = (tab >> (t - 1)) - 1; 260 tab ^= invert; 261 tab &= (1 << (t - 1)) - 1; 262 263 constant_time_lookup_niels(ni, &table->table[j << (t - 1)], 264 1 << (t - 1), tab); 265 266 cond_neg_niels(ni, invert); 267 if ((i != s) || j != 0) 268 add_niels_to_pt(out, ni, j == n - 1 && i != 1); 269 else 270 niels_to_pt(out, ni); 271 } 272 } 273 274 OPENSSL_cleanse(ni, sizeof(ni)); 275 OPENSSL_cleanse(scalar1x, sizeof(scalar1x)); 276} 277 278void 279ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa( 280 uint8_t enc[EDDSA_448_PUBLIC_BYTES], 281 const curve448_point_t p) 282{ 283 gf x, y, z, t; 284 curve448_point_t q; 285 286 /* The point is now on the twisted curve. Move it to untwisted. */ 287 curve448_point_copy(q, p); 288 289 { 290 /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */ 291 gf u; 292 293 gf_sqr(x, q->x); 294 gf_sqr(t, q->y); 295 gf_add(u, x, t); 296 gf_add(z, q->y, q->x); 297 gf_sqr(y, z); 298 gf_sub(y, y, u); 299 gf_sub(z, t, x); 300 gf_sqr(x, q->z); 301 gf_add(t, x, x); 302 gf_sub(t, t, z); 303 gf_mul(x, t, y); 304 gf_mul(y, z, u); 305 gf_mul(z, u, t); 306 OPENSSL_cleanse(u, sizeof(u)); 307 } 308 309 /* Affinize */ 310 gf_invert(z, z, 1); 311 gf_mul(t, x, z); 312 gf_mul(x, y, z); 313 314 /* Encode */ 315 enc[EDDSA_448_PRIVATE_BYTES - 1] = 0; 316 gf_serialize(enc, x, 1); 317 enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t); 318 319 OPENSSL_cleanse(x, sizeof(x)); 320 OPENSSL_cleanse(y, sizeof(y)); 321 OPENSSL_cleanse(z, sizeof(z)); 322 OPENSSL_cleanse(t, sizeof(t)); 323 ossl_curve448_point_destroy(q); 324} 325 326c448_error_t 327ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio( 328 curve448_point_t p, 329 const uint8_t enc[EDDSA_448_PUBLIC_BYTES]) 330{ 331 uint8_t enc2[EDDSA_448_PUBLIC_BYTES]; 332 mask_t low; 333 mask_t succ; 334 335 memcpy(enc2, enc, sizeof(enc2)); 336 337 low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80); 338 enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80; 339 340 succ = gf_deserialize(p->y, enc2, 1, 0); 341 succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]); 342 343 gf_sqr(p->x, p->y); 344 gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */ 345 gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */ 346 gf_sub(p->t, ONE, p->t); /* denom = 1-dy^2 or 1-d + dy^2 */ 347 348 gf_mul(p->x, p->z, p->t); 349 succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */ 350 351 gf_mul(p->x, p->t, p->z); /* sqrt(num / denom) */ 352 gf_cond_neg(p->x, gf_lobit(p->x) ^ low); 353 gf_copy(p->z, ONE); 354 355 { 356 gf a, b, c, d; 357 358 /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */ 359 gf_sqr(c, p->x); 360 gf_sqr(a, p->y); 361 gf_add(d, c, a); 362 gf_add(p->t, p->y, p->x); 363 gf_sqr(b, p->t); 364 gf_sub(b, b, d); 365 gf_sub(p->t, a, c); 366 gf_sqr(p->x, p->z); 367 gf_add(p->z, p->x, p->x); 368 gf_sub(a, p->z, d); 369 gf_mul(p->x, a, b); 370 gf_mul(p->z, p->t, a); 371 gf_mul(p->y, p->t, d); 372 gf_mul(p->t, b, d); 373 OPENSSL_cleanse(a, sizeof(a)); 374 OPENSSL_cleanse(b, sizeof(b)); 375 OPENSSL_cleanse(c, sizeof(c)); 376 OPENSSL_cleanse(d, sizeof(d)); 377 } 378 379 OPENSSL_cleanse(enc2, sizeof(enc2)); 380 assert(ossl_curve448_point_valid(p) || ~succ); 381 382 return c448_succeed_if(mask_to_bool(succ)); 383} 384 385c448_error_t 386ossl_x448_int(uint8_t out[X_PUBLIC_BYTES], 387 const uint8_t base[X_PUBLIC_BYTES], 388 const uint8_t scalar[X_PRIVATE_BYTES]) 389{ 390 gf x1, x2, z2, x3, z3, t1, t2; 391 int t; 392 mask_t swap = 0; 393 mask_t nz; 394 395 (void)gf_deserialize(x1, base, 1, 0); 396 gf_copy(x2, ONE); 397 gf_copy(z2, ZERO); 398 gf_copy(x3, x1); 399 gf_copy(z3, ONE); 400 401 for (t = X_PRIVATE_BITS - 1; t >= 0; t--) { 402 uint8_t sb = scalar[t / 8]; 403 mask_t k_t; 404 405 /* Scalar conditioning */ 406 if (t / 8 == 0) 407 sb &= -(uint8_t)COFACTOR; 408 else if (t == X_PRIVATE_BITS - 1) 409 sb = -1; 410 411 k_t = (sb >> (t % 8)) & 1; 412 k_t = 0 - k_t; /* set to all 0s or all 1s */ 413 414 swap ^= k_t; 415 gf_cond_swap(x2, x3, swap); 416 gf_cond_swap(z2, z3, swap); 417 swap = k_t; 418 419 /* 420 * The "_nr" below skips coefficient reduction. In the following 421 * comments, "2+e" is saying that the coefficients are at most 2+epsilon 422 * times the reduction limit. 423 */ 424 gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */ 425 gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */ 426 gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */ 427 gf_mul(x2, t1, z2); /* DA */ 428 gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */ 429 gf_mul(x3, t2, z2); /* CB */ 430 gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */ 431 gf_sqr(z2, z3); /* (DA-CB)^2 */ 432 gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */ 433 gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */ 434 gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */ 435 436 gf_sqr(z2, t1); /* AA = A^2 */ 437 gf_sqr(t1, t2); /* BB = B^2 */ 438 gf_mul(x2, z2, t1); /* x2 = AA*BB */ 439 gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */ 440 441 gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */ 442 gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */ 443 gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */ 444 } 445 446 /* Finish */ 447 gf_cond_swap(x2, x3, swap); 448 gf_cond_swap(z2, z3, swap); 449 gf_invert(z2, z2, 0); 450 gf_mul(x1, x2, z2); 451 gf_serialize(out, x1, 1); 452 nz = ~gf_eq(x1, ZERO); 453 454 OPENSSL_cleanse(x1, sizeof(x1)); 455 OPENSSL_cleanse(x2, sizeof(x2)); 456 OPENSSL_cleanse(z2, sizeof(z2)); 457 OPENSSL_cleanse(x3, sizeof(x3)); 458 OPENSSL_cleanse(z3, sizeof(z3)); 459 OPENSSL_cleanse(t1, sizeof(t1)); 460 OPENSSL_cleanse(t2, sizeof(t2)); 461 462 return c448_succeed_if(mask_to_bool(nz)); 463} 464 465void 466ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t 467 out[X_PUBLIC_BYTES], 468 const curve448_point_t p) 469{ 470 curve448_point_t q; 471 472 curve448_point_copy(q, p); 473 gf_invert(q->t, q->x, 0); /* 1/x */ 474 gf_mul(q->z, q->t, q->y); /* y/x */ 475 gf_sqr(q->y, q->z); /* (y/x)^2 */ 476 gf_serialize(out, q->y, 1); 477 ossl_curve448_point_destroy(q); 478} 479 480void ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES], 481 const uint8_t scalar[X_PRIVATE_BYTES]) 482{ 483 /* Scalar conditioning */ 484 uint8_t scalar2[X_PRIVATE_BYTES]; 485 curve448_scalar_t the_scalar; 486 curve448_point_t p; 487 unsigned int i; 488 489 memcpy(scalar2, scalar, sizeof(scalar2)); 490 scalar2[0] &= -(uint8_t)COFACTOR; 491 492 scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8)); 493 scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8); 494 495 ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2)); 496 497 /* Compensate for the encoding ratio */ 498 for (i = 1; i < X448_ENCODE_RATIO; i <<= 1) 499 ossl_curve448_scalar_halve(the_scalar, the_scalar); 500 501 ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base, 502 the_scalar); 503 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p); 504 ossl_curve448_point_destroy(p); 505} 506 507/* Control for variable-time scalar multiply algorithms. */ 508struct smvt_control { 509 int power, addend; 510}; 511 512#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3)) 513# define NUMTRAILINGZEROS __builtin_ctz 514#else 515# define NUMTRAILINGZEROS numtrailingzeros 516static uint32_t numtrailingzeros(uint32_t i) 517{ 518 uint32_t tmp; 519 uint32_t num = 31; 520 521 if (i == 0) 522 return 32; 523 524 tmp = i << 16; 525 if (tmp != 0) { 526 i = tmp; 527 num -= 16; 528 } 529 tmp = i << 8; 530 if (tmp != 0) { 531 i = tmp; 532 num -= 8; 533 } 534 tmp = i << 4; 535 if (tmp != 0) { 536 i = tmp; 537 num -= 4; 538 } 539 tmp = i << 2; 540 if (tmp != 0) { 541 i = tmp; 542 num -= 2; 543 } 544 tmp = i << 1; 545 if (tmp != 0) 546 num--; 547 548 return num; 549} 550#endif 551 552static int recode_wnaf(struct smvt_control *control, 553 /* [nbits/(table_bits + 1) + 3] */ 554 const curve448_scalar_t scalar, 555 unsigned int table_bits) 556{ 557 unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3; 558 int position = table_size - 1; /* at the end */ 559 uint64_t current = scalar->limb[0] & 0xFFFF; 560 uint32_t mask = (1 << (table_bits + 1)) - 1; 561 unsigned int w; 562 const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2; 563 unsigned int n, i; 564 565 /* place the end marker */ 566 control[position].power = -1; 567 control[position].addend = 0; 568 position--; 569 570 /* 571 * PERF: Could negate scalar if it's large. But then would need more cases 572 * in the actual code that uses it, all for an expected reduction of like 573 * 1/5 op. Probably not worth it. 574 */ 575 576 for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) { 577 if (w < (C448_SCALAR_BITS - 1) / 16 + 1) { 578 /* Refill the 16 high bits of current */ 579 current += (uint32_t)((scalar->limb[w / B_OVER_16] 580 >> (16 * (w % B_OVER_16))) << 16); 581 } 582 583 while (current & 0xFFFF) { 584 uint32_t pos = NUMTRAILINGZEROS((uint32_t)current); 585 uint32_t odd = (uint32_t)current >> pos; 586 int32_t delta = odd & mask; 587 588 assert(position >= 0); 589 assert(pos < 32); /* can't fail since current & 0xFFFF != 0 */ 590 if (odd & (1 << (table_bits + 1))) 591 delta -= (1 << (table_bits + 1)); 592 current -= delta * (1 << pos); 593 control[position].power = pos + 16 * (w - 1); 594 control[position].addend = delta; 595 position--; 596 } 597 current >>= 16; 598 } 599 assert(current == 0); 600 601 position++; 602 n = table_size - position; 603 for (i = 0; i < n; i++) 604 control[i] = control[i + position]; 605 606 return n - 1; 607} 608 609static void prepare_wnaf_table(pniels_t * output, 610 const curve448_point_t working, 611 unsigned int tbits) 612{ 613 curve448_point_t tmp; 614 int i; 615 pniels_t twop; 616 617 pt_to_pniels(output[0], working); 618 619 if (tbits == 0) 620 return; 621 622 ossl_curve448_point_double(tmp, working); 623 pt_to_pniels(twop, tmp); 624 625 add_pniels_to_pt(tmp, output[0], 0); 626 pt_to_pniels(output[1], tmp); 627 628 for (i = 2; i < 1 << tbits; i++) { 629 add_pniels_to_pt(tmp, twop, 0); 630 pt_to_pniels(output[i], tmp); 631 } 632 633 ossl_curve448_point_destroy(tmp); 634 OPENSSL_cleanse(twop, sizeof(twop)); 635} 636 637void 638ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo, 639 const curve448_scalar_t scalar1, 640 const curve448_point_t base2, 641 const curve448_scalar_t scalar2) 642{ 643 const int table_bits_var = C448_WNAF_VAR_TABLE_BITS; 644 const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS; 645 struct smvt_control control_var[C448_SCALAR_BITS / 646 (C448_WNAF_VAR_TABLE_BITS + 1) + 3]; 647 struct smvt_control control_pre[C448_SCALAR_BITS / 648 (C448_WNAF_FIXED_TABLE_BITS + 1) + 3]; 649 int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre); 650 int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var); 651 pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS]; 652 int contp = 0, contv = 0, i; 653 654 prepare_wnaf_table(precmp_var, base2, table_bits_var); 655 i = control_var[0].power; 656 657 if (i < 0) { 658 curve448_point_copy(combo, ossl_curve448_point_identity); 659 return; 660 } 661 if (i > control_pre[0].power) { 662 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]); 663 contv++; 664 } else if (i == control_pre[0].power && i >= 0) { 665 pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]); 666 add_niels_to_pt(combo, 667 ossl_curve448_wnaf_base[control_pre[0].addend >> 1], 668 i); 669 contv++; 670 contp++; 671 } else { 672 i = control_pre[0].power; 673 niels_to_pt(combo, ossl_curve448_wnaf_base[control_pre[0].addend >> 1]); 674 contp++; 675 } 676 677 for (i--; i >= 0; i--) { 678 int cv = (i == control_var[contv].power); 679 int cp = (i == control_pre[contp].power); 680 681 point_double_internal(combo, combo, i && !(cv || cp)); 682 683 if (cv) { 684 assert(control_var[contv].addend); 685 686 if (control_var[contv].addend > 0) 687 add_pniels_to_pt(combo, 688 precmp_var[control_var[contv].addend >> 1], 689 i && !cp); 690 else 691 sub_pniels_from_pt(combo, 692 precmp_var[(-control_var[contv].addend) 693 >> 1], i && !cp); 694 contv++; 695 } 696 697 if (cp) { 698 assert(control_pre[contp].addend); 699 700 if (control_pre[contp].addend > 0) 701 add_niels_to_pt(combo, 702 ossl_curve448_wnaf_base[control_pre[contp].addend 703 >> 1], i); 704 else 705 sub_niels_from_pt(combo, 706 ossl_curve448_wnaf_base[(-control_pre 707 [contp].addend) >> 1], i); 708 contp++; 709 } 710 } 711 712 /* This function is non-secret, but whatever this is cheap. */ 713 OPENSSL_cleanse(control_var, sizeof(control_var)); 714 OPENSSL_cleanse(control_pre, sizeof(control_pre)); 715 OPENSSL_cleanse(precmp_var, sizeof(precmp_var)); 716 717 assert(contv == ncb_var); 718 (void)ncb_var; 719 assert(contp == ncb_pre); 720 (void)ncb_pre; 721} 722 723void ossl_curve448_point_destroy(curve448_point_t point) 724{ 725 OPENSSL_cleanse(point, sizeof(curve448_point_t)); 726} 727 728int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56], 729 const uint8_t peer_public_value[56]) 730{ 731 return ossl_x448_int(out_shared_key, peer_public_value, private_key) 732 == C448_SUCCESS; 733} 734 735void ossl_x448_public_from_private(uint8_t out_public_value[56], 736 const uint8_t private_key[56]) 737{ 738 ossl_x448_derive_public_key(out_public_value, private_key); 739} 740