1/* 2 * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved. 3 * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org> 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions are 7 * met: 8 * * Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * * Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 15 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 16 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 17 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 18 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 19 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 20 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 24 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27#include <linux/module.h> 28#include <linux/random.h> 29#include <linux/slab.h> 30#include <linux/swab.h> 31#include <linux/fips.h> 32#include <crypto/ecdh.h> 33#include <crypto/rng.h> 34#include <asm/unaligned.h> 35#include <linux/ratelimit.h> 36 37#include "ecc.h" 38#include "ecc_curve_defs.h" 39 40typedef struct { 41 u64 m_low; 42 u64 m_high; 43} uint128_t; 44 45const struct ecc_curve *ecc_get_curve(unsigned int curve_id) 46{ 47 switch (curve_id) { 48 /* In FIPS mode only allow P256 and higher */ 49 case ECC_CURVE_NIST_P192: 50 return fips_enabled ? NULL : &nist_p192; 51 case ECC_CURVE_NIST_P256: 52 return &nist_p256; 53 case ECC_CURVE_NIST_P384: 54 return &nist_p384; 55 default: 56 return NULL; 57 } 58} 59EXPORT_SYMBOL(ecc_get_curve); 60 61static u64 *ecc_alloc_digits_space(unsigned int ndigits) 62{ 63 size_t len = ndigits * sizeof(u64); 64 65 if (!len) 66 return NULL; 67 68 return kmalloc(len, GFP_KERNEL); 69} 70 71static void ecc_free_digits_space(u64 *space) 72{ 73 kfree_sensitive(space); 74} 75 76static struct ecc_point *ecc_alloc_point(unsigned int ndigits) 77{ 78 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL); 79 80 if (!p) 81 return NULL; 82 83 p->x = ecc_alloc_digits_space(ndigits); 84 if (!p->x) 85 goto err_alloc_x; 86 87 p->y = ecc_alloc_digits_space(ndigits); 88 if (!p->y) 89 goto err_alloc_y; 90 91 p->ndigits = ndigits; 92 93 return p; 94 95err_alloc_y: 96 ecc_free_digits_space(p->x); 97err_alloc_x: 98 kfree(p); 99 return NULL; 100} 101 102static void ecc_free_point(struct ecc_point *p) 103{ 104 if (!p) 105 return; 106 107 kfree_sensitive(p->x); 108 kfree_sensitive(p->y); 109 kfree_sensitive(p); 110} 111 112static void vli_clear(u64 *vli, unsigned int ndigits) 113{ 114 int i; 115 116 for (i = 0; i < ndigits; i++) 117 vli[i] = 0; 118} 119 120/* Returns true if vli == 0, false otherwise. */ 121bool vli_is_zero(const u64 *vli, unsigned int ndigits) 122{ 123 int i; 124 125 for (i = 0; i < ndigits; i++) { 126 if (vli[i]) 127 return false; 128 } 129 130 return true; 131} 132EXPORT_SYMBOL(vli_is_zero); 133 134/* Returns nonzero if bit bit of vli is set. */ 135static u64 vli_test_bit(const u64 *vli, unsigned int bit) 136{ 137 return (vli[bit / 64] & ((u64)1 << (bit % 64))); 138} 139 140static bool vli_is_negative(const u64 *vli, unsigned int ndigits) 141{ 142 return vli_test_bit(vli, ndigits * 64 - 1); 143} 144 145/* Counts the number of 64-bit "digits" in vli. */ 146static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits) 147{ 148 int i; 149 150 /* Search from the end until we find a non-zero digit. 151 * We do it in reverse because we expect that most digits will 152 * be nonzero. 153 */ 154 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--); 155 156 return (i + 1); 157} 158 159/* Counts the number of bits required for vli. */ 160static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits) 161{ 162 unsigned int i, num_digits; 163 u64 digit; 164 165 num_digits = vli_num_digits(vli, ndigits); 166 if (num_digits == 0) 167 return 0; 168 169 digit = vli[num_digits - 1]; 170 for (i = 0; digit; i++) 171 digit >>= 1; 172 173 return ((num_digits - 1) * 64 + i); 174} 175 176/* Set dest from unaligned bit string src. */ 177void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits) 178{ 179 int i; 180 const u64 *from = src; 181 182 for (i = 0; i < ndigits; i++) 183 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]); 184} 185EXPORT_SYMBOL(vli_from_be64); 186 187void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits) 188{ 189 int i; 190 const u64 *from = src; 191 192 for (i = 0; i < ndigits; i++) 193 dest[i] = get_unaligned_le64(&from[i]); 194} 195EXPORT_SYMBOL(vli_from_le64); 196 197/* Sets dest = src. */ 198static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits) 199{ 200 int i; 201 202 for (i = 0; i < ndigits; i++) 203 dest[i] = src[i]; 204} 205 206/* Returns sign of left - right. */ 207int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) 208{ 209 int i; 210 211 for (i = ndigits - 1; i >= 0; i--) { 212 if (left[i] > right[i]) 213 return 1; 214 else if (left[i] < right[i]) 215 return -1; 216 } 217 218 return 0; 219} 220EXPORT_SYMBOL(vli_cmp); 221 222/* Computes result = in << c, returning carry. Can modify in place 223 * (if result == in). 0 < shift < 64. 224 */ 225static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift, 226 unsigned int ndigits) 227{ 228 u64 carry = 0; 229 int i; 230 231 for (i = 0; i < ndigits; i++) { 232 u64 temp = in[i]; 233 234 result[i] = (temp << shift) | carry; 235 carry = temp >> (64 - shift); 236 } 237 238 return carry; 239} 240 241/* Computes vli = vli >> 1. */ 242static void vli_rshift1(u64 *vli, unsigned int ndigits) 243{ 244 u64 *end = vli; 245 u64 carry = 0; 246 247 vli += ndigits; 248 249 while (vli-- > end) { 250 u64 temp = *vli; 251 *vli = (temp >> 1) | carry; 252 carry = temp << 63; 253 } 254} 255 256/* Computes result = left + right, returning carry. Can modify in place. */ 257static u64 vli_add(u64 *result, const u64 *left, const u64 *right, 258 unsigned int ndigits) 259{ 260 u64 carry = 0; 261 int i; 262 263 for (i = 0; i < ndigits; i++) { 264 u64 sum; 265 266 sum = left[i] + right[i] + carry; 267 if (sum != left[i]) 268 carry = (sum < left[i]); 269 270 result[i] = sum; 271 } 272 273 return carry; 274} 275 276/* Computes result = left + right, returning carry. Can modify in place. */ 277static u64 vli_uadd(u64 *result, const u64 *left, u64 right, 278 unsigned int ndigits) 279{ 280 u64 carry = right; 281 int i; 282 283 for (i = 0; i < ndigits; i++) { 284 u64 sum; 285 286 sum = left[i] + carry; 287 if (sum != left[i]) 288 carry = (sum < left[i]); 289 else 290 carry = !!carry; 291 292 result[i] = sum; 293 } 294 295 return carry; 296} 297 298/* Computes result = left - right, returning borrow. Can modify in place. */ 299u64 vli_sub(u64 *result, const u64 *left, const u64 *right, 300 unsigned int ndigits) 301{ 302 u64 borrow = 0; 303 int i; 304 305 for (i = 0; i < ndigits; i++) { 306 u64 diff; 307 308 diff = left[i] - right[i] - borrow; 309 if (diff != left[i]) 310 borrow = (diff > left[i]); 311 312 result[i] = diff; 313 } 314 315 return borrow; 316} 317EXPORT_SYMBOL(vli_sub); 318 319/* Computes result = left - right, returning borrow. Can modify in place. */ 320static u64 vli_usub(u64 *result, const u64 *left, u64 right, 321 unsigned int ndigits) 322{ 323 u64 borrow = right; 324 int i; 325 326 for (i = 0; i < ndigits; i++) { 327 u64 diff; 328 329 diff = left[i] - borrow; 330 if (diff != left[i]) 331 borrow = (diff > left[i]); 332 333 result[i] = diff; 334 } 335 336 return borrow; 337} 338 339static uint128_t mul_64_64(u64 left, u64 right) 340{ 341 uint128_t result; 342#if defined(CONFIG_ARCH_SUPPORTS_INT128) 343 unsigned __int128 m = (unsigned __int128)left * right; 344 345 result.m_low = m; 346 result.m_high = m >> 64; 347#else 348 u64 a0 = left & 0xffffffffull; 349 u64 a1 = left >> 32; 350 u64 b0 = right & 0xffffffffull; 351 u64 b1 = right >> 32; 352 u64 m0 = a0 * b0; 353 u64 m1 = a0 * b1; 354 u64 m2 = a1 * b0; 355 u64 m3 = a1 * b1; 356 357 m2 += (m0 >> 32); 358 m2 += m1; 359 360 /* Overflow */ 361 if (m2 < m1) 362 m3 += 0x100000000ull; 363 364 result.m_low = (m0 & 0xffffffffull) | (m2 << 32); 365 result.m_high = m3 + (m2 >> 32); 366#endif 367 return result; 368} 369 370static uint128_t add_128_128(uint128_t a, uint128_t b) 371{ 372 uint128_t result; 373 374 result.m_low = a.m_low + b.m_low; 375 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low); 376 377 return result; 378} 379 380static void vli_mult(u64 *result, const u64 *left, const u64 *right, 381 unsigned int ndigits) 382{ 383 uint128_t r01 = { 0, 0 }; 384 u64 r2 = 0; 385 unsigned int i, k; 386 387 /* Compute each digit of result in sequence, maintaining the 388 * carries. 389 */ 390 for (k = 0; k < ndigits * 2 - 1; k++) { 391 unsigned int min; 392 393 if (k < ndigits) 394 min = 0; 395 else 396 min = (k + 1) - ndigits; 397 398 for (i = min; i <= k && i < ndigits; i++) { 399 uint128_t product; 400 401 product = mul_64_64(left[i], right[k - i]); 402 403 r01 = add_128_128(r01, product); 404 r2 += (r01.m_high < product.m_high); 405 } 406 407 result[k] = r01.m_low; 408 r01.m_low = r01.m_high; 409 r01.m_high = r2; 410 r2 = 0; 411 } 412 413 result[ndigits * 2 - 1] = r01.m_low; 414} 415 416/* Compute product = left * right, for a small right value. */ 417static void vli_umult(u64 *result, const u64 *left, u32 right, 418 unsigned int ndigits) 419{ 420 uint128_t r01 = { 0 }; 421 unsigned int k; 422 423 for (k = 0; k < ndigits; k++) { 424 uint128_t product; 425 426 product = mul_64_64(left[k], right); 427 r01 = add_128_128(r01, product); 428 /* no carry */ 429 result[k] = r01.m_low; 430 r01.m_low = r01.m_high; 431 r01.m_high = 0; 432 } 433 result[k] = r01.m_low; 434 for (++k; k < ndigits * 2; k++) 435 result[k] = 0; 436} 437 438static void vli_square(u64 *result, const u64 *left, unsigned int ndigits) 439{ 440 uint128_t r01 = { 0, 0 }; 441 u64 r2 = 0; 442 int i, k; 443 444 for (k = 0; k < ndigits * 2 - 1; k++) { 445 unsigned int min; 446 447 if (k < ndigits) 448 min = 0; 449 else 450 min = (k + 1) - ndigits; 451 452 for (i = min; i <= k && i <= k - i; i++) { 453 uint128_t product; 454 455 product = mul_64_64(left[i], left[k - i]); 456 457 if (i < k - i) { 458 r2 += product.m_high >> 63; 459 product.m_high = (product.m_high << 1) | 460 (product.m_low >> 63); 461 product.m_low <<= 1; 462 } 463 464 r01 = add_128_128(r01, product); 465 r2 += (r01.m_high < product.m_high); 466 } 467 468 result[k] = r01.m_low; 469 r01.m_low = r01.m_high; 470 r01.m_high = r2; 471 r2 = 0; 472 } 473 474 result[ndigits * 2 - 1] = r01.m_low; 475} 476 477/* Computes result = (left + right) % mod. 478 * Assumes that left < mod and right < mod, result != mod. 479 */ 480static void vli_mod_add(u64 *result, const u64 *left, const u64 *right, 481 const u64 *mod, unsigned int ndigits) 482{ 483 u64 carry; 484 485 carry = vli_add(result, left, right, ndigits); 486 487 /* result > mod (result = mod + remainder), so subtract mod to 488 * get remainder. 489 */ 490 if (carry || vli_cmp(result, mod, ndigits) >= 0) 491 vli_sub(result, result, mod, ndigits); 492} 493 494/* Computes result = (left - right) % mod. 495 * Assumes that left < mod and right < mod, result != mod. 496 */ 497static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right, 498 const u64 *mod, unsigned int ndigits) 499{ 500 u64 borrow = vli_sub(result, left, right, ndigits); 501 502 /* In this case, p_result == -diff == (max int) - diff. 503 * Since -x % d == d - x, we can get the correct result from 504 * result + mod (with overflow). 505 */ 506 if (borrow) 507 vli_add(result, result, mod, ndigits); 508} 509 510/* 511 * Computes result = product % mod 512 * for special form moduli: p = 2^k-c, for small c (note the minus sign) 513 * 514 * References: 515 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective. 516 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form 517 * Algorithm 9.2.13 (Fast mod operation for special-form moduli). 518 */ 519static void vli_mmod_special(u64 *result, const u64 *product, 520 const u64 *mod, unsigned int ndigits) 521{ 522 u64 c = -mod[0]; 523 u64 t[ECC_MAX_DIGITS * 2]; 524 u64 r[ECC_MAX_DIGITS * 2]; 525 526 vli_set(r, product, ndigits * 2); 527 while (!vli_is_zero(r + ndigits, ndigits)) { 528 vli_umult(t, r + ndigits, c, ndigits); 529 vli_clear(r + ndigits, ndigits); 530 vli_add(r, r, t, ndigits * 2); 531 } 532 vli_set(t, mod, ndigits); 533 vli_clear(t + ndigits, ndigits); 534 while (vli_cmp(r, t, ndigits * 2) >= 0) 535 vli_sub(r, r, t, ndigits * 2); 536 vli_set(result, r, ndigits); 537} 538 539/* 540 * Computes result = product % mod 541 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign) 542 * where k-1 does not fit into qword boundary by -1 bit (such as 255). 543 544 * References (loosely based on): 545 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography. 546 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47. 547 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf 548 * 549 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren. 550 * Handbook of Elliptic and Hyperelliptic Curve Cryptography. 551 * Algorithm 10.25 Fast reduction for special form moduli 552 */ 553static void vli_mmod_special2(u64 *result, const u64 *product, 554 const u64 *mod, unsigned int ndigits) 555{ 556 u64 c2 = mod[0] * 2; 557 u64 q[ECC_MAX_DIGITS]; 558 u64 r[ECC_MAX_DIGITS * 2]; 559 u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */ 560 int carry; /* last bit that doesn't fit into q */ 561 int i; 562 563 vli_set(m, mod, ndigits); 564 vli_clear(m + ndigits, ndigits); 565 566 vli_set(r, product, ndigits); 567 /* q and carry are top bits */ 568 vli_set(q, product + ndigits, ndigits); 569 vli_clear(r + ndigits, ndigits); 570 carry = vli_is_negative(r, ndigits); 571 if (carry) 572 r[ndigits - 1] &= (1ull << 63) - 1; 573 for (i = 1; carry || !vli_is_zero(q, ndigits); i++) { 574 u64 qc[ECC_MAX_DIGITS * 2]; 575 576 vli_umult(qc, q, c2, ndigits); 577 if (carry) 578 vli_uadd(qc, qc, mod[0], ndigits * 2); 579 vli_set(q, qc + ndigits, ndigits); 580 vli_clear(qc + ndigits, ndigits); 581 carry = vli_is_negative(qc, ndigits); 582 if (carry) 583 qc[ndigits - 1] &= (1ull << 63) - 1; 584 if (i & 1) 585 vli_sub(r, r, qc, ndigits * 2); 586 else 587 vli_add(r, r, qc, ndigits * 2); 588 } 589 while (vli_is_negative(r, ndigits * 2)) 590 vli_add(r, r, m, ndigits * 2); 591 while (vli_cmp(r, m, ndigits * 2) >= 0) 592 vli_sub(r, r, m, ndigits * 2); 593 594 vli_set(result, r, ndigits); 595} 596 597/* 598 * Computes result = product % mod, where product is 2N words long. 599 * Reference: Ken MacKay's micro-ecc. 600 * Currently only designed to work for curve_p or curve_n. 601 */ 602static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod, 603 unsigned int ndigits) 604{ 605 u64 mod_m[2 * ECC_MAX_DIGITS]; 606 u64 tmp[2 * ECC_MAX_DIGITS]; 607 u64 *v[2] = { tmp, product }; 608 u64 carry = 0; 609 unsigned int i; 610 /* Shift mod so its highest set bit is at the maximum position. */ 611 int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits); 612 int word_shift = shift / 64; 613 int bit_shift = shift % 64; 614 615 vli_clear(mod_m, word_shift); 616 if (bit_shift > 0) { 617 for (i = 0; i < ndigits; ++i) { 618 mod_m[word_shift + i] = (mod[i] << bit_shift) | carry; 619 carry = mod[i] >> (64 - bit_shift); 620 } 621 } else 622 vli_set(mod_m + word_shift, mod, ndigits); 623 624 for (i = 1; shift >= 0; --shift) { 625 u64 borrow = 0; 626 unsigned int j; 627 628 for (j = 0; j < ndigits * 2; ++j) { 629 u64 diff = v[i][j] - mod_m[j] - borrow; 630 631 if (diff != v[i][j]) 632 borrow = (diff > v[i][j]); 633 v[1 - i][j] = diff; 634 } 635 i = !(i ^ borrow); /* Swap the index if there was no borrow */ 636 vli_rshift1(mod_m, ndigits); 637 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1); 638 vli_rshift1(mod_m + ndigits, ndigits); 639 } 640 vli_set(result, v[i], ndigits); 641} 642 643/* Computes result = product % mod using Barrett's reduction with precomputed 644 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have 645 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits 646 * boundary. 647 * 648 * Reference: 649 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010. 650 * 2.4.1 Barrett's algorithm. Algorithm 2.5. 651 */ 652static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod, 653 unsigned int ndigits) 654{ 655 u64 q[ECC_MAX_DIGITS * 2]; 656 u64 r[ECC_MAX_DIGITS * 2]; 657 const u64 *mu = mod + ndigits; 658 659 vli_mult(q, product + ndigits, mu, ndigits); 660 if (mu[ndigits]) 661 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits); 662 vli_mult(r, mod, q + ndigits, ndigits); 663 vli_sub(r, product, r, ndigits * 2); 664 while (!vli_is_zero(r + ndigits, ndigits) || 665 vli_cmp(r, mod, ndigits) != -1) { 666 u64 carry; 667 668 carry = vli_sub(r, r, mod, ndigits); 669 vli_usub(r + ndigits, r + ndigits, carry, ndigits); 670 } 671 vli_set(result, r, ndigits); 672} 673 674/* Computes p_result = p_product % curve_p. 675 * See algorithm 5 and 6 from 676 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf 677 */ 678static void vli_mmod_fast_192(u64 *result, const u64 *product, 679 const u64 *curve_prime, u64 *tmp) 680{ 681 const unsigned int ndigits = 3; 682 int carry; 683 684 vli_set(result, product, ndigits); 685 686 vli_set(tmp, &product[3], ndigits); 687 carry = vli_add(result, result, tmp, ndigits); 688 689 tmp[0] = 0; 690 tmp[1] = product[3]; 691 tmp[2] = product[4]; 692 carry += vli_add(result, result, tmp, ndigits); 693 694 tmp[0] = tmp[1] = product[5]; 695 tmp[2] = 0; 696 carry += vli_add(result, result, tmp, ndigits); 697 698 while (carry || vli_cmp(curve_prime, result, ndigits) != 1) 699 carry -= vli_sub(result, result, curve_prime, ndigits); 700} 701 702/* Computes result = product % curve_prime 703 * from http://www.nsa.gov/ia/_files/nist-routines.pdf 704 */ 705static void vli_mmod_fast_256(u64 *result, const u64 *product, 706 const u64 *curve_prime, u64 *tmp) 707{ 708 int carry; 709 const unsigned int ndigits = 4; 710 711 /* t */ 712 vli_set(result, product, ndigits); 713 714 /* s1 */ 715 tmp[0] = 0; 716 tmp[1] = product[5] & 0xffffffff00000000ull; 717 tmp[2] = product[6]; 718 tmp[3] = product[7]; 719 carry = vli_lshift(tmp, tmp, 1, ndigits); 720 carry += vli_add(result, result, tmp, ndigits); 721 722 /* s2 */ 723 tmp[1] = product[6] << 32; 724 tmp[2] = (product[6] >> 32) | (product[7] << 32); 725 tmp[3] = product[7] >> 32; 726 carry += vli_lshift(tmp, tmp, 1, ndigits); 727 carry += vli_add(result, result, tmp, ndigits); 728 729 /* s3 */ 730 tmp[0] = product[4]; 731 tmp[1] = product[5] & 0xffffffff; 732 tmp[2] = 0; 733 tmp[3] = product[7]; 734 carry += vli_add(result, result, tmp, ndigits); 735 736 /* s4 */ 737 tmp[0] = (product[4] >> 32) | (product[5] << 32); 738 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); 739 tmp[2] = product[7]; 740 tmp[3] = (product[6] >> 32) | (product[4] << 32); 741 carry += vli_add(result, result, tmp, ndigits); 742 743 /* d1 */ 744 tmp[0] = (product[5] >> 32) | (product[6] << 32); 745 tmp[1] = (product[6] >> 32); 746 tmp[2] = 0; 747 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); 748 carry -= vli_sub(result, result, tmp, ndigits); 749 750 /* d2 */ 751 tmp[0] = product[6]; 752 tmp[1] = product[7]; 753 tmp[2] = 0; 754 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); 755 carry -= vli_sub(result, result, tmp, ndigits); 756 757 /* d3 */ 758 tmp[0] = (product[6] >> 32) | (product[7] << 32); 759 tmp[1] = (product[7] >> 32) | (product[4] << 32); 760 tmp[2] = (product[4] >> 32) | (product[5] << 32); 761 tmp[3] = (product[6] << 32); 762 carry -= vli_sub(result, result, tmp, ndigits); 763 764 /* d4 */ 765 tmp[0] = product[7]; 766 tmp[1] = product[4] & 0xffffffff00000000ull; 767 tmp[2] = product[5]; 768 tmp[3] = product[6] & 0xffffffff00000000ull; 769 carry -= vli_sub(result, result, tmp, ndigits); 770 771 if (carry < 0) { 772 do { 773 carry += vli_add(result, result, curve_prime, ndigits); 774 } while (carry < 0); 775 } else { 776 while (carry || vli_cmp(curve_prime, result, ndigits) != 1) 777 carry -= vli_sub(result, result, curve_prime, ndigits); 778 } 779} 780 781#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32) 782#define AND64H(x64) (x64 & 0xffFFffFF00000000ull) 783#define AND64L(x64) (x64 & 0x00000000ffFFffFFull) 784 785/* Computes result = product % curve_prime 786 * from "Mathematical routines for the NIST prime elliptic curves" 787 */ 788static void vli_mmod_fast_384(u64 *result, const u64 *product, 789 const u64 *curve_prime, u64 *tmp) 790{ 791 int carry; 792 const unsigned int ndigits = 6; 793 794 /* t */ 795 vli_set(result, product, ndigits); 796 797 /* s1 */ 798 tmp[0] = 0; // 0 || 0 799 tmp[1] = 0; // 0 || 0 800 tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 801 tmp[3] = product[11]>>32; // 0 ||a23 802 tmp[4] = 0; // 0 || 0 803 tmp[5] = 0; // 0 || 0 804 carry = vli_lshift(tmp, tmp, 1, ndigits); 805 carry += vli_add(result, result, tmp, ndigits); 806 807 /* s2 */ 808 tmp[0] = product[6]; //a13||a12 809 tmp[1] = product[7]; //a15||a14 810 tmp[2] = product[8]; //a17||a16 811 tmp[3] = product[9]; //a19||a18 812 tmp[4] = product[10]; //a21||a20 813 tmp[5] = product[11]; //a23||a22 814 carry += vli_add(result, result, tmp, ndigits); 815 816 /* s3 */ 817 tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 818 tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 819 tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13 820 tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 821 tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 822 tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 823 carry += vli_add(result, result, tmp, ndigits); 824 825 /* s4 */ 826 tmp[0] = AND64H(product[11]); //a23|| 0 827 tmp[1] = (product[10]<<32); //a20|| 0 828 tmp[2] = product[6]; //a13||a12 829 tmp[3] = product[7]; //a15||a14 830 tmp[4] = product[8]; //a17||a16 831 tmp[5] = product[9]; //a19||a18 832 carry += vli_add(result, result, tmp, ndigits); 833 834 /* s5 */ 835 tmp[0] = 0; // 0|| 0 836 tmp[1] = 0; // 0|| 0 837 tmp[2] = product[10]; //a21||a20 838 tmp[3] = product[11]; //a23||a22 839 tmp[4] = 0; // 0|| 0 840 tmp[5] = 0; // 0|| 0 841 carry += vli_add(result, result, tmp, ndigits); 842 843 /* s6 */ 844 tmp[0] = AND64L(product[10]); // 0 ||a20 845 tmp[1] = AND64H(product[10]); //a21|| 0 846 tmp[2] = product[11]; //a23||a22 847 tmp[3] = 0; // 0 || 0 848 tmp[4] = 0; // 0 || 0 849 tmp[5] = 0; // 0 || 0 850 carry += vli_add(result, result, tmp, ndigits); 851 852 /* d1 */ 853 tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 854 tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13 855 tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 856 tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 857 tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 858 tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 859 carry -= vli_sub(result, result, tmp, ndigits); 860 861 /* d2 */ 862 tmp[0] = (product[10]<<32); //a20|| 0 863 tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 864 tmp[2] = (product[11]>>32); // 0 ||a23 865 tmp[3] = 0; // 0 || 0 866 tmp[4] = 0; // 0 || 0 867 tmp[5] = 0; // 0 || 0 868 carry -= vli_sub(result, result, tmp, ndigits); 869 870 /* d3 */ 871 tmp[0] = 0; // 0 || 0 872 tmp[1] = AND64H(product[11]); //a23|| 0 873 tmp[2] = product[11]>>32; // 0 ||a23 874 tmp[3] = 0; // 0 || 0 875 tmp[4] = 0; // 0 || 0 876 tmp[5] = 0; // 0 || 0 877 carry -= vli_sub(result, result, tmp, ndigits); 878 879 if (carry < 0) { 880 do { 881 carry += vli_add(result, result, curve_prime, ndigits); 882 } while (carry < 0); 883 } else { 884 while (carry || vli_cmp(curve_prime, result, ndigits) != 1) 885 carry -= vli_sub(result, result, curve_prime, ndigits); 886 } 887 888} 889 890#undef SL32OR32 891#undef AND64H 892#undef AND64L 893 894/* Computes result = product % curve_prime for different curve_primes. 895 * 896 * Note that curve_primes are distinguished just by heuristic check and 897 * not by complete conformance check. 898 */ 899static bool vli_mmod_fast(u64 *result, u64 *product, 900 const struct ecc_curve *curve) 901{ 902 u64 tmp[2 * ECC_MAX_DIGITS]; 903 const u64 *curve_prime = curve->p; 904 const unsigned int ndigits = curve->g.ndigits; 905 906 /* All NIST curves have name prefix 'nist_' */ 907 if (strncmp(curve->name, "nist_", 5) != 0) { 908 /* Try to handle Pseudo-Marsenne primes. */ 909 if (curve_prime[ndigits - 1] == -1ull) { 910 vli_mmod_special(result, product, curve_prime, 911 ndigits); 912 return true; 913 } else if (curve_prime[ndigits - 1] == 1ull << 63 && 914 curve_prime[ndigits - 2] == 0) { 915 vli_mmod_special2(result, product, curve_prime, 916 ndigits); 917 return true; 918 } 919 vli_mmod_barrett(result, product, curve_prime, ndigits); 920 return true; 921 } 922 923 switch (ndigits) { 924 case 3: 925 vli_mmod_fast_192(result, product, curve_prime, tmp); 926 break; 927 case 4: 928 vli_mmod_fast_256(result, product, curve_prime, tmp); 929 break; 930 case 6: 931 vli_mmod_fast_384(result, product, curve_prime, tmp); 932 break; 933 default: 934 pr_err_ratelimited("ecc: unsupported digits size!\n"); 935 return false; 936 } 937 938 return true; 939} 940 941/* Computes result = (left * right) % mod. 942 * Assumes that mod is big enough curve order. 943 */ 944void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right, 945 const u64 *mod, unsigned int ndigits) 946{ 947 u64 product[ECC_MAX_DIGITS * 2]; 948 949 vli_mult(product, left, right, ndigits); 950 vli_mmod_slow(result, product, mod, ndigits); 951} 952EXPORT_SYMBOL(vli_mod_mult_slow); 953 954/* Computes result = (left * right) % curve_prime. */ 955static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, 956 const struct ecc_curve *curve) 957{ 958 u64 product[2 * ECC_MAX_DIGITS]; 959 960 vli_mult(product, left, right, curve->g.ndigits); 961 vli_mmod_fast(result, product, curve); 962} 963 964/* Computes result = left^2 % curve_prime. */ 965static void vli_mod_square_fast(u64 *result, const u64 *left, 966 const struct ecc_curve *curve) 967{ 968 u64 product[2 * ECC_MAX_DIGITS]; 969 970 vli_square(product, left, curve->g.ndigits); 971 vli_mmod_fast(result, product, curve); 972} 973 974#define EVEN(vli) (!(vli[0] & 1)) 975/* Computes result = (1 / p_input) % mod. All VLIs are the same size. 976 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" 977 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf 978 */ 979void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, 980 unsigned int ndigits) 981{ 982 u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS]; 983 u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS]; 984 u64 carry; 985 int cmp_result; 986 987 if (vli_is_zero(input, ndigits)) { 988 vli_clear(result, ndigits); 989 return; 990 } 991 992 vli_set(a, input, ndigits); 993 vli_set(b, mod, ndigits); 994 vli_clear(u, ndigits); 995 u[0] = 1; 996 vli_clear(v, ndigits); 997 998 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) { 999 carry = 0; 1000 1001 if (EVEN(a)) { 1002 vli_rshift1(a, ndigits); 1003 1004 if (!EVEN(u)) 1005 carry = vli_add(u, u, mod, ndigits); 1006 1007 vli_rshift1(u, ndigits); 1008 if (carry) 1009 u[ndigits - 1] |= 0x8000000000000000ull; 1010 } else if (EVEN(b)) { 1011 vli_rshift1(b, ndigits); 1012 1013 if (!EVEN(v)) 1014 carry = vli_add(v, v, mod, ndigits); 1015 1016 vli_rshift1(v, ndigits); 1017 if (carry) 1018 v[ndigits - 1] |= 0x8000000000000000ull; 1019 } else if (cmp_result > 0) { 1020 vli_sub(a, a, b, ndigits); 1021 vli_rshift1(a, ndigits); 1022 1023 if (vli_cmp(u, v, ndigits) < 0) 1024 vli_add(u, u, mod, ndigits); 1025 1026 vli_sub(u, u, v, ndigits); 1027 if (!EVEN(u)) 1028 carry = vli_add(u, u, mod, ndigits); 1029 1030 vli_rshift1(u, ndigits); 1031 if (carry) 1032 u[ndigits - 1] |= 0x8000000000000000ull; 1033 } else { 1034 vli_sub(b, b, a, ndigits); 1035 vli_rshift1(b, ndigits); 1036 1037 if (vli_cmp(v, u, ndigits) < 0) 1038 vli_add(v, v, mod, ndigits); 1039 1040 vli_sub(v, v, u, ndigits); 1041 if (!EVEN(v)) 1042 carry = vli_add(v, v, mod, ndigits); 1043 1044 vli_rshift1(v, ndigits); 1045 if (carry) 1046 v[ndigits - 1] |= 0x8000000000000000ull; 1047 } 1048 } 1049 1050 vli_set(result, u, ndigits); 1051} 1052EXPORT_SYMBOL(vli_mod_inv); 1053 1054/* ------ Point operations ------ */ 1055 1056/* Returns true if p_point is the point at infinity, false otherwise. */ 1057static bool ecc_point_is_zero(const struct ecc_point *point) 1058{ 1059 return (vli_is_zero(point->x, point->ndigits) && 1060 vli_is_zero(point->y, point->ndigits)); 1061} 1062 1063/* Point multiplication algorithm using Montgomery's ladder with co-Z 1064 * coordinates. From https://eprint.iacr.org/2011/338.pdf 1065 */ 1066 1067/* Double in place */ 1068static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, 1069 const struct ecc_curve *curve) 1070{ 1071 /* t1 = x, t2 = y, t3 = z */ 1072 u64 t4[ECC_MAX_DIGITS]; 1073 u64 t5[ECC_MAX_DIGITS]; 1074 const u64 *curve_prime = curve->p; 1075 const unsigned int ndigits = curve->g.ndigits; 1076 1077 if (vli_is_zero(z1, ndigits)) 1078 return; 1079 1080 /* t4 = y1^2 */ 1081 vli_mod_square_fast(t4, y1, curve); 1082 /* t5 = x1*y1^2 = A */ 1083 vli_mod_mult_fast(t5, x1, t4, curve); 1084 /* t4 = y1^4 */ 1085 vli_mod_square_fast(t4, t4, curve); 1086 /* t2 = y1*z1 = z3 */ 1087 vli_mod_mult_fast(y1, y1, z1, curve); 1088 /* t3 = z1^2 */ 1089 vli_mod_square_fast(z1, z1, curve); 1090 1091 /* t1 = x1 + z1^2 */ 1092 vli_mod_add(x1, x1, z1, curve_prime, ndigits); 1093 /* t3 = 2*z1^2 */ 1094 vli_mod_add(z1, z1, z1, curve_prime, ndigits); 1095 /* t3 = x1 - z1^2 */ 1096 vli_mod_sub(z1, x1, z1, curve_prime, ndigits); 1097 /* t1 = x1^2 - z1^4 */ 1098 vli_mod_mult_fast(x1, x1, z1, curve); 1099 1100 /* t3 = 2*(x1^2 - z1^4) */ 1101 vli_mod_add(z1, x1, x1, curve_prime, ndigits); 1102 /* t1 = 3*(x1^2 - z1^4) */ 1103 vli_mod_add(x1, x1, z1, curve_prime, ndigits); 1104 if (vli_test_bit(x1, 0)) { 1105 u64 carry = vli_add(x1, x1, curve_prime, ndigits); 1106 1107 vli_rshift1(x1, ndigits); 1108 x1[ndigits - 1] |= carry << 63; 1109 } else { 1110 vli_rshift1(x1, ndigits); 1111 } 1112 /* t1 = 3/2*(x1^2 - z1^4) = B */ 1113 1114 /* t3 = B^2 */ 1115 vli_mod_square_fast(z1, x1, curve); 1116 /* t3 = B^2 - A */ 1117 vli_mod_sub(z1, z1, t5, curve_prime, ndigits); 1118 /* t3 = B^2 - 2A = x3 */ 1119 vli_mod_sub(z1, z1, t5, curve_prime, ndigits); 1120 /* t5 = A - x3 */ 1121 vli_mod_sub(t5, t5, z1, curve_prime, ndigits); 1122 /* t1 = B * (A - x3) */ 1123 vli_mod_mult_fast(x1, x1, t5, curve); 1124 /* t4 = B * (A - x3) - y1^4 = y3 */ 1125 vli_mod_sub(t4, x1, t4, curve_prime, ndigits); 1126 1127 vli_set(x1, z1, ndigits); 1128 vli_set(z1, y1, ndigits); 1129 vli_set(y1, t4, ndigits); 1130} 1131 1132/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ 1133static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve) 1134{ 1135 u64 t1[ECC_MAX_DIGITS]; 1136 1137 vli_mod_square_fast(t1, z, curve); /* z^2 */ 1138 vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */ 1139 vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */ 1140 vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */ 1141} 1142 1143/* P = (x1, y1) => 2P, (x2, y2) => P' */ 1144static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, 1145 u64 *p_initial_z, const struct ecc_curve *curve) 1146{ 1147 u64 z[ECC_MAX_DIGITS]; 1148 const unsigned int ndigits = curve->g.ndigits; 1149 1150 vli_set(x2, x1, ndigits); 1151 vli_set(y2, y1, ndigits); 1152 1153 vli_clear(z, ndigits); 1154 z[0] = 1; 1155 1156 if (p_initial_z) 1157 vli_set(z, p_initial_z, ndigits); 1158 1159 apply_z(x1, y1, z, curve); 1160 1161 ecc_point_double_jacobian(x1, y1, z, curve); 1162 1163 apply_z(x2, y2, z, curve); 1164} 1165 1166/* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1167 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) 1168 * or P => P', Q => P + Q 1169 */ 1170static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, 1171 const struct ecc_curve *curve) 1172{ 1173 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1174 u64 t5[ECC_MAX_DIGITS]; 1175 const u64 *curve_prime = curve->p; 1176 const unsigned int ndigits = curve->g.ndigits; 1177 1178 /* t5 = x2 - x1 */ 1179 vli_mod_sub(t5, x2, x1, curve_prime, ndigits); 1180 /* t5 = (x2 - x1)^2 = A */ 1181 vli_mod_square_fast(t5, t5, curve); 1182 /* t1 = x1*A = B */ 1183 vli_mod_mult_fast(x1, x1, t5, curve); 1184 /* t3 = x2*A = C */ 1185 vli_mod_mult_fast(x2, x2, t5, curve); 1186 /* t4 = y2 - y1 */ 1187 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 1188 /* t5 = (y2 - y1)^2 = D */ 1189 vli_mod_square_fast(t5, y2, curve); 1190 1191 /* t5 = D - B */ 1192 vli_mod_sub(t5, t5, x1, curve_prime, ndigits); 1193 /* t5 = D - B - C = x3 */ 1194 vli_mod_sub(t5, t5, x2, curve_prime, ndigits); 1195 /* t3 = C - B */ 1196 vli_mod_sub(x2, x2, x1, curve_prime, ndigits); 1197 /* t2 = y1*(C - B) */ 1198 vli_mod_mult_fast(y1, y1, x2, curve); 1199 /* t3 = B - x3 */ 1200 vli_mod_sub(x2, x1, t5, curve_prime, ndigits); 1201 /* t4 = (y2 - y1)*(B - x3) */ 1202 vli_mod_mult_fast(y2, y2, x2, curve); 1203 /* t4 = y3 */ 1204 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 1205 1206 vli_set(x2, t5, ndigits); 1207} 1208 1209/* Input P = (x1, y1, Z), Q = (x2, y2, Z) 1210 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) 1211 * or P => P - Q, Q => P + Q 1212 */ 1213static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, 1214 const struct ecc_curve *curve) 1215{ 1216 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 1217 u64 t5[ECC_MAX_DIGITS]; 1218 u64 t6[ECC_MAX_DIGITS]; 1219 u64 t7[ECC_MAX_DIGITS]; 1220 const u64 *curve_prime = curve->p; 1221 const unsigned int ndigits = curve->g.ndigits; 1222 1223 /* t5 = x2 - x1 */ 1224 vli_mod_sub(t5, x2, x1, curve_prime, ndigits); 1225 /* t5 = (x2 - x1)^2 = A */ 1226 vli_mod_square_fast(t5, t5, curve); 1227 /* t1 = x1*A = B */ 1228 vli_mod_mult_fast(x1, x1, t5, curve); 1229 /* t3 = x2*A = C */ 1230 vli_mod_mult_fast(x2, x2, t5, curve); 1231 /* t4 = y2 + y1 */ 1232 vli_mod_add(t5, y2, y1, curve_prime, ndigits); 1233 /* t4 = y2 - y1 */ 1234 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 1235 1236 /* t6 = C - B */ 1237 vli_mod_sub(t6, x2, x1, curve_prime, ndigits); 1238 /* t2 = y1 * (C - B) */ 1239 vli_mod_mult_fast(y1, y1, t6, curve); 1240 /* t6 = B + C */ 1241 vli_mod_add(t6, x1, x2, curve_prime, ndigits); 1242 /* t3 = (y2 - y1)^2 */ 1243 vli_mod_square_fast(x2, y2, curve); 1244 /* t3 = x3 */ 1245 vli_mod_sub(x2, x2, t6, curve_prime, ndigits); 1246 1247 /* t7 = B - x3 */ 1248 vli_mod_sub(t7, x1, x2, curve_prime, ndigits); 1249 /* t4 = (y2 - y1)*(B - x3) */ 1250 vli_mod_mult_fast(y2, y2, t7, curve); 1251 /* t4 = y3 */ 1252 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 1253 1254 /* t7 = (y2 + y1)^2 = F */ 1255 vli_mod_square_fast(t7, t5, curve); 1256 /* t7 = x3' */ 1257 vli_mod_sub(t7, t7, t6, curve_prime, ndigits); 1258 /* t6 = x3' - B */ 1259 vli_mod_sub(t6, t7, x1, curve_prime, ndigits); 1260 /* t6 = (y2 + y1)*(x3' - B) */ 1261 vli_mod_mult_fast(t6, t6, t5, curve); 1262 /* t2 = y3' */ 1263 vli_mod_sub(y1, t6, y1, curve_prime, ndigits); 1264 1265 vli_set(x1, t7, ndigits); 1266} 1267 1268static void ecc_point_mult(struct ecc_point *result, 1269 const struct ecc_point *point, const u64 *scalar, 1270 u64 *initial_z, const struct ecc_curve *curve, 1271 unsigned int ndigits) 1272{ 1273 /* R0 and R1 */ 1274 u64 rx[2][ECC_MAX_DIGITS]; 1275 u64 ry[2][ECC_MAX_DIGITS]; 1276 u64 z[ECC_MAX_DIGITS]; 1277 u64 sk[2][ECC_MAX_DIGITS]; 1278 u64 *curve_prime = curve->p; 1279 int i, nb; 1280 int num_bits; 1281 int carry; 1282 1283 carry = vli_add(sk[0], scalar, curve->n, ndigits); 1284 vli_add(sk[1], sk[0], curve->n, ndigits); 1285 scalar = sk[!carry]; 1286 num_bits = sizeof(u64) * ndigits * 8 + 1; 1287 1288 vli_set(rx[1], point->x, ndigits); 1289 vli_set(ry[1], point->y, ndigits); 1290 1291 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve); 1292 1293 for (i = num_bits - 2; i > 0; i--) { 1294 nb = !vli_test_bit(scalar, i); 1295 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); 1296 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); 1297 } 1298 1299 nb = !vli_test_bit(scalar, 0); 1300 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); 1301 1302 /* Find final 1/Z value. */ 1303 /* X1 - X0 */ 1304 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); 1305 /* Yb * (X1 - X0) */ 1306 vli_mod_mult_fast(z, z, ry[1 - nb], curve); 1307 /* xP * Yb * (X1 - X0) */ 1308 vli_mod_mult_fast(z, z, point->x, curve); 1309 1310 /* 1 / (xP * Yb * (X1 - X0)) */ 1311 vli_mod_inv(z, z, curve_prime, point->ndigits); 1312 1313 /* yP / (xP * Yb * (X1 - X0)) */ 1314 vli_mod_mult_fast(z, z, point->y, curve); 1315 /* Xb * yP / (xP * Yb * (X1 - X0)) */ 1316 vli_mod_mult_fast(z, z, rx[1 - nb], curve); 1317 /* End 1/Z calculation */ 1318 1319 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); 1320 1321 apply_z(rx[0], ry[0], z, curve); 1322 1323 vli_set(result->x, rx[0], ndigits); 1324 vli_set(result->y, ry[0], ndigits); 1325} 1326 1327/* Computes R = P + Q mod p */ 1328static void ecc_point_add(const struct ecc_point *result, 1329 const struct ecc_point *p, const struct ecc_point *q, 1330 const struct ecc_curve *curve) 1331{ 1332 u64 z[ECC_MAX_DIGITS]; 1333 u64 px[ECC_MAX_DIGITS]; 1334 u64 py[ECC_MAX_DIGITS]; 1335 unsigned int ndigits = curve->g.ndigits; 1336 1337 vli_set(result->x, q->x, ndigits); 1338 vli_set(result->y, q->y, ndigits); 1339 vli_mod_sub(z, result->x, p->x, curve->p, ndigits); 1340 vli_set(px, p->x, ndigits); 1341 vli_set(py, p->y, ndigits); 1342 xycz_add(px, py, result->x, result->y, curve); 1343 vli_mod_inv(z, z, curve->p, ndigits); 1344 apply_z(result->x, result->y, z, curve); 1345} 1346 1347/* Computes R = u1P + u2Q mod p using Shamir's trick. 1348 * Based on: Kenneth MacKay's micro-ecc (2014). 1349 */ 1350void ecc_point_mult_shamir(const struct ecc_point *result, 1351 const u64 *u1, const struct ecc_point *p, 1352 const u64 *u2, const struct ecc_point *q, 1353 const struct ecc_curve *curve) 1354{ 1355 u64 z[ECC_MAX_DIGITS]; 1356 u64 sump[2][ECC_MAX_DIGITS]; 1357 u64 *rx = result->x; 1358 u64 *ry = result->y; 1359 unsigned int ndigits = curve->g.ndigits; 1360 unsigned int num_bits; 1361 struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits); 1362 const struct ecc_point *points[4]; 1363 const struct ecc_point *point; 1364 unsigned int idx; 1365 int i; 1366 1367 ecc_point_add(&sum, p, q, curve); 1368 points[0] = NULL; 1369 points[1] = p; 1370 points[2] = q; 1371 points[3] = ∑ 1372 1373 num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits)); 1374 i = num_bits - 1; 1375 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); 1376 point = points[idx]; 1377 1378 vli_set(rx, point->x, ndigits); 1379 vli_set(ry, point->y, ndigits); 1380 vli_clear(z + 1, ndigits - 1); 1381 z[0] = 1; 1382 1383 for (--i; i >= 0; i--) { 1384 ecc_point_double_jacobian(rx, ry, z, curve); 1385 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1); 1386 point = points[idx]; 1387 if (point) { 1388 u64 tx[ECC_MAX_DIGITS]; 1389 u64 ty[ECC_MAX_DIGITS]; 1390 u64 tz[ECC_MAX_DIGITS]; 1391 1392 vli_set(tx, point->x, ndigits); 1393 vli_set(ty, point->y, ndigits); 1394 apply_z(tx, ty, z, curve); 1395 vli_mod_sub(tz, rx, tx, curve->p, ndigits); 1396 xycz_add(tx, ty, rx, ry, curve); 1397 vli_mod_mult_fast(z, z, tz, curve); 1398 } 1399 } 1400 vli_mod_inv(z, z, curve->p, ndigits); 1401 apply_z(rx, ry, z, curve); 1402} 1403EXPORT_SYMBOL(ecc_point_mult_shamir); 1404 1405static int __ecc_is_key_valid(const struct ecc_curve *curve, 1406 const u64 *private_key, unsigned int ndigits) 1407{ 1408 u64 one[ECC_MAX_DIGITS] = { 1, }; 1409 u64 res[ECC_MAX_DIGITS]; 1410 1411 if (!private_key) 1412 return -EINVAL; 1413 1414 if (curve->g.ndigits != ndigits) 1415 return -EINVAL; 1416 1417 /* Make sure the private key is in the range [2, n-3]. */ 1418 if (vli_cmp(one, private_key, ndigits) != -1) 1419 return -EINVAL; 1420 vli_sub(res, curve->n, one, ndigits); 1421 vli_sub(res, res, one, ndigits); 1422 if (vli_cmp(res, private_key, ndigits) != 1) 1423 return -EINVAL; 1424 1425 return 0; 1426} 1427 1428int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, 1429 const u64 *private_key, unsigned int private_key_len) 1430{ 1431 int nbytes; 1432 const struct ecc_curve *curve = ecc_get_curve(curve_id); 1433 1434 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 1435 1436 if (private_key_len != nbytes) 1437 return -EINVAL; 1438 1439 return __ecc_is_key_valid(curve, private_key, ndigits); 1440} 1441EXPORT_SYMBOL(ecc_is_key_valid); 1442 1443/* 1444 * ECC private keys are generated using the method of extra random bits, 1445 * equivalent to that described in FIPS 186-4, Appendix B.4.1. 1446 * 1447 * d = (c mod(n–1)) + 1 where c is a string of random bits, 64 bits longer 1448 * than requested 1449 * 0 <= c mod(n-1) <= n-2 and implies that 1450 * 1 <= d <= n-1 1451 * 1452 * This method generates a private key uniformly distributed in the range 1453 * [1, n-1]. 1454 */ 1455int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey) 1456{ 1457 const struct ecc_curve *curve = ecc_get_curve(curve_id); 1458 u64 priv[ECC_MAX_DIGITS]; 1459 unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 1460 unsigned int nbits = vli_num_bits(curve->n, ndigits); 1461 int err; 1462 1463 /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */ 1464 if (nbits < 160 || ndigits > ARRAY_SIZE(priv)) 1465 return -EINVAL; 1466 1467 /* 1468 * FIPS 186-4 recommends that the private key should be obtained from a 1469 * RBG with a security strength equal to or greater than the security 1470 * strength associated with N. 1471 * 1472 * The maximum security strength identified by NIST SP800-57pt1r4 for 1473 * ECC is 256 (N >= 512). 1474 * 1475 * This condition is met by the default RNG because it selects a favored 1476 * DRBG with a security strength of 256. 1477 */ 1478 if (crypto_get_default_rng()) 1479 return -EFAULT; 1480 1481 err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes); 1482 crypto_put_default_rng(); 1483 if (err) 1484 return err; 1485 1486 /* Make sure the private key is in the valid range. */ 1487 if (__ecc_is_key_valid(curve, priv, ndigits)) 1488 return -EINVAL; 1489 1490 ecc_swap_digits(priv, privkey, ndigits); 1491 1492 return 0; 1493} 1494EXPORT_SYMBOL(ecc_gen_privkey); 1495 1496int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits, 1497 const u64 *private_key, u64 *public_key) 1498{ 1499 int ret = 0; 1500 struct ecc_point *pk; 1501 u64 priv[ECC_MAX_DIGITS]; 1502 const struct ecc_curve *curve = ecc_get_curve(curve_id); 1503 1504 if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) { 1505 ret = -EINVAL; 1506 goto out; 1507 } 1508 1509 ecc_swap_digits(private_key, priv, ndigits); 1510 1511 pk = ecc_alloc_point(ndigits); 1512 if (!pk) { 1513 ret = -ENOMEM; 1514 goto out; 1515 } 1516 1517 ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits); 1518 1519 /* SP800-56A rev 3 5.6.2.1.3 key check */ 1520 if (ecc_is_pubkey_valid_full(curve, pk)) { 1521 ret = -EAGAIN; 1522 goto err_free_point; 1523 } 1524 1525 ecc_swap_digits(pk->x, public_key, ndigits); 1526 ecc_swap_digits(pk->y, &public_key[ndigits], ndigits); 1527 1528err_free_point: 1529 ecc_free_point(pk); 1530out: 1531 return ret; 1532} 1533EXPORT_SYMBOL(ecc_make_pub_key); 1534 1535/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */ 1536int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, 1537 struct ecc_point *pk) 1538{ 1539 u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS]; 1540 1541 if (WARN_ON(pk->ndigits != curve->g.ndigits)) 1542 return -EINVAL; 1543 1544 /* Check 1: Verify key is not the zero point. */ 1545 if (ecc_point_is_zero(pk)) 1546 return -EINVAL; 1547 1548 /* Check 2: Verify key is in the range [1, p-1]. */ 1549 if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1) 1550 return -EINVAL; 1551 if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1) 1552 return -EINVAL; 1553 1554 /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */ 1555 vli_mod_square_fast(yy, pk->y, curve); /* y^2 */ 1556 vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */ 1557 vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */ 1558 vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */ 1559 vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */ 1560 vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */ 1561 if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */ 1562 return -EINVAL; 1563 1564 return 0; 1565} 1566EXPORT_SYMBOL(ecc_is_pubkey_valid_partial); 1567 1568/* SP800-56A section 5.6.2.3.3 full verification */ 1569int ecc_is_pubkey_valid_full(const struct ecc_curve *curve, 1570 struct ecc_point *pk) 1571{ 1572 struct ecc_point *nQ; 1573 1574 /* Checks 1 through 3 */ 1575 int ret = ecc_is_pubkey_valid_partial(curve, pk); 1576 1577 if (ret) 1578 return ret; 1579 1580 /* Check 4: Verify that nQ is the zero point. */ 1581 nQ = ecc_alloc_point(pk->ndigits); 1582 if (!nQ) 1583 return -ENOMEM; 1584 1585 ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits); 1586 if (!ecc_point_is_zero(nQ)) 1587 ret = -EINVAL; 1588 1589 ecc_free_point(nQ); 1590 1591 return ret; 1592} 1593EXPORT_SYMBOL(ecc_is_pubkey_valid_full); 1594 1595int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, 1596 const u64 *private_key, const u64 *public_key, 1597 u64 *secret) 1598{ 1599 int ret = 0; 1600 struct ecc_point *product, *pk; 1601 u64 priv[ECC_MAX_DIGITS]; 1602 u64 rand_z[ECC_MAX_DIGITS]; 1603 unsigned int nbytes; 1604 const struct ecc_curve *curve = ecc_get_curve(curve_id); 1605 1606 if (!private_key || !public_key || !curve || 1607 ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) { 1608 ret = -EINVAL; 1609 goto out; 1610 } 1611 1612 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 1613 1614 get_random_bytes(rand_z, nbytes); 1615 1616 pk = ecc_alloc_point(ndigits); 1617 if (!pk) { 1618 ret = -ENOMEM; 1619 goto out; 1620 } 1621 1622 ecc_swap_digits(public_key, pk->x, ndigits); 1623 ecc_swap_digits(&public_key[ndigits], pk->y, ndigits); 1624 ret = ecc_is_pubkey_valid_partial(curve, pk); 1625 if (ret) 1626 goto err_alloc_product; 1627 1628 ecc_swap_digits(private_key, priv, ndigits); 1629 1630 product = ecc_alloc_point(ndigits); 1631 if (!product) { 1632 ret = -ENOMEM; 1633 goto err_alloc_product; 1634 } 1635 1636 ecc_point_mult(product, pk, priv, rand_z, curve, ndigits); 1637 1638 if (ecc_point_is_zero(product)) { 1639 ret = -EFAULT; 1640 goto err_validity; 1641 } 1642 1643 ecc_swap_digits(product->x, secret, ndigits); 1644 1645err_validity: 1646 memzero_explicit(priv, sizeof(priv)); 1647 memzero_explicit(rand_z, sizeof(rand_z)); 1648 ecc_free_point(product); 1649err_alloc_product: 1650 ecc_free_point(pk); 1651out: 1652 return ret; 1653} 1654EXPORT_SYMBOL(crypto_ecdh_shared_secret); 1655 1656MODULE_LICENSE("Dual BSD/GPL"); 1657