1 /* 2 * Copyright (c) 2013, Kenneth MacKay 3 * All rights reserved. 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/random.h> 28 #include <linux/slab.h> 29 #include <linux/swab.h> 30 #include <linux/fips.h> 31 #include <crypto/ecdh.h> 32 33 #include "ecc.h" 34 #include "ecc_curve_defs.h" 35 36 typedef struct { 37 u64 m_low; 38 u64 m_high; 39 } uint128_t; 40 41 static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id) 42 { 43 switch (curve_id) { 44 /* In FIPS mode only allow P256 and higher */ 45 case ECC_CURVE_NIST_P192: 46 return fips_enabled ? NULL : &nist_p192; 47 case ECC_CURVE_NIST_P256: 48 return &nist_p256; 49 default: 50 return NULL; 51 } 52 } 53 54 static u64 *ecc_alloc_digits_space(unsigned int ndigits) 55 { 56 size_t len = ndigits * sizeof(u64); 57 58 if (!len) 59 return NULL; 60 61 return kmalloc(len, GFP_KERNEL); 62 } 63 64 static void ecc_free_digits_space(u64 *space) 65 { 66 kzfree(space); 67 } 68 69 static struct ecc_point *ecc_alloc_point(unsigned int ndigits) 70 { 71 struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL); 72 73 if (!p) 74 return NULL; 75 76 p->x = ecc_alloc_digits_space(ndigits); 77 if (!p->x) 78 goto err_alloc_x; 79 80 p->y = ecc_alloc_digits_space(ndigits); 81 if (!p->y) 82 goto err_alloc_y; 83 84 p->ndigits = ndigits; 85 86 return p; 87 88 err_alloc_y: 89 ecc_free_digits_space(p->x); 90 err_alloc_x: 91 kfree(p); 92 return NULL; 93 } 94 95 static void ecc_free_point(struct ecc_point *p) 96 { 97 if (!p) 98 return; 99 100 kzfree(p->x); 101 kzfree(p->y); 102 kzfree(p); 103 } 104 105 static void vli_clear(u64 *vli, unsigned int ndigits) 106 { 107 int i; 108 109 for (i = 0; i < ndigits; i++) 110 vli[i] = 0; 111 } 112 113 /* Returns true if vli == 0, false otherwise. */ 114 static bool vli_is_zero(const u64 *vli, unsigned int ndigits) 115 { 116 int i; 117 118 for (i = 0; i < ndigits; i++) { 119 if (vli[i]) 120 return false; 121 } 122 123 return true; 124 } 125 126 /* Returns nonzero if bit bit of vli is set. */ 127 static u64 vli_test_bit(const u64 *vli, unsigned int bit) 128 { 129 return (vli[bit / 64] & ((u64)1 << (bit % 64))); 130 } 131 132 /* Counts the number of 64-bit "digits" in vli. */ 133 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits) 134 { 135 int i; 136 137 /* Search from the end until we find a non-zero digit. 138 * We do it in reverse because we expect that most digits will 139 * be nonzero. 140 */ 141 for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--); 142 143 return (i + 1); 144 } 145 146 /* Counts the number of bits required for vli. */ 147 static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits) 148 { 149 unsigned int i, num_digits; 150 u64 digit; 151 152 num_digits = vli_num_digits(vli, ndigits); 153 if (num_digits == 0) 154 return 0; 155 156 digit = vli[num_digits - 1]; 157 for (i = 0; digit; i++) 158 digit >>= 1; 159 160 return ((num_digits - 1) * 64 + i); 161 } 162 163 /* Sets dest = src. */ 164 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits) 165 { 166 int i; 167 168 for (i = 0; i < ndigits; i++) 169 dest[i] = src[i]; 170 } 171 172 /* Returns sign of left - right. */ 173 static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) 174 { 175 int i; 176 177 for (i = ndigits - 1; i >= 0; i--) { 178 if (left[i] > right[i]) 179 return 1; 180 else if (left[i] < right[i]) 181 return -1; 182 } 183 184 return 0; 185 } 186 187 /* Computes result = in << c, returning carry. Can modify in place 188 * (if result == in). 0 < shift < 64. 189 */ 190 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift, 191 unsigned int ndigits) 192 { 193 u64 carry = 0; 194 int i; 195 196 for (i = 0; i < ndigits; i++) { 197 u64 temp = in[i]; 198 199 result[i] = (temp << shift) | carry; 200 carry = temp >> (64 - shift); 201 } 202 203 return carry; 204 } 205 206 /* Computes vli = vli >> 1. */ 207 static void vli_rshift1(u64 *vli, unsigned int ndigits) 208 { 209 u64 *end = vli; 210 u64 carry = 0; 211 212 vli += ndigits; 213 214 while (vli-- > end) { 215 u64 temp = *vli; 216 *vli = (temp >> 1) | carry; 217 carry = temp << 63; 218 } 219 } 220 221 /* Computes result = left + right, returning carry. Can modify in place. */ 222 static u64 vli_add(u64 *result, const u64 *left, const u64 *right, 223 unsigned int ndigits) 224 { 225 u64 carry = 0; 226 int i; 227 228 for (i = 0; i < ndigits; i++) { 229 u64 sum; 230 231 sum = left[i] + right[i] + carry; 232 if (sum != left[i]) 233 carry = (sum < left[i]); 234 235 result[i] = sum; 236 } 237 238 return carry; 239 } 240 241 /* Computes result = left - right, returning borrow. Can modify in place. */ 242 static u64 vli_sub(u64 *result, const u64 *left, const u64 *right, 243 unsigned int ndigits) 244 { 245 u64 borrow = 0; 246 int i; 247 248 for (i = 0; i < ndigits; i++) { 249 u64 diff; 250 251 diff = left[i] - right[i] - borrow; 252 if (diff != left[i]) 253 borrow = (diff > left[i]); 254 255 result[i] = diff; 256 } 257 258 return borrow; 259 } 260 261 static uint128_t mul_64_64(u64 left, u64 right) 262 { 263 u64 a0 = left & 0xffffffffull; 264 u64 a1 = left >> 32; 265 u64 b0 = right & 0xffffffffull; 266 u64 b1 = right >> 32; 267 u64 m0 = a0 * b0; 268 u64 m1 = a0 * b1; 269 u64 m2 = a1 * b0; 270 u64 m3 = a1 * b1; 271 uint128_t result; 272 273 m2 += (m0 >> 32); 274 m2 += m1; 275 276 /* Overflow */ 277 if (m2 < m1) 278 m3 += 0x100000000ull; 279 280 result.m_low = (m0 & 0xffffffffull) | (m2 << 32); 281 result.m_high = m3 + (m2 >> 32); 282 283 return result; 284 } 285 286 static uint128_t add_128_128(uint128_t a, uint128_t b) 287 { 288 uint128_t result; 289 290 result.m_low = a.m_low + b.m_low; 291 result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low); 292 293 return result; 294 } 295 296 static void vli_mult(u64 *result, const u64 *left, const u64 *right, 297 unsigned int ndigits) 298 { 299 uint128_t r01 = { 0, 0 }; 300 u64 r2 = 0; 301 unsigned int i, k; 302 303 /* Compute each digit of result in sequence, maintaining the 304 * carries. 305 */ 306 for (k = 0; k < ndigits * 2 - 1; k++) { 307 unsigned int min; 308 309 if (k < ndigits) 310 min = 0; 311 else 312 min = (k + 1) - ndigits; 313 314 for (i = min; i <= k && i < ndigits; i++) { 315 uint128_t product; 316 317 product = mul_64_64(left[i], right[k - i]); 318 319 r01 = add_128_128(r01, product); 320 r2 += (r01.m_high < product.m_high); 321 } 322 323 result[k] = r01.m_low; 324 r01.m_low = r01.m_high; 325 r01.m_high = r2; 326 r2 = 0; 327 } 328 329 result[ndigits * 2 - 1] = r01.m_low; 330 } 331 332 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits) 333 { 334 uint128_t r01 = { 0, 0 }; 335 u64 r2 = 0; 336 int i, k; 337 338 for (k = 0; k < ndigits * 2 - 1; k++) { 339 unsigned int min; 340 341 if (k < ndigits) 342 min = 0; 343 else 344 min = (k + 1) - ndigits; 345 346 for (i = min; i <= k && i <= k - i; i++) { 347 uint128_t product; 348 349 product = mul_64_64(left[i], left[k - i]); 350 351 if (i < k - i) { 352 r2 += product.m_high >> 63; 353 product.m_high = (product.m_high << 1) | 354 (product.m_low >> 63); 355 product.m_low <<= 1; 356 } 357 358 r01 = add_128_128(r01, product); 359 r2 += (r01.m_high < product.m_high); 360 } 361 362 result[k] = r01.m_low; 363 r01.m_low = r01.m_high; 364 r01.m_high = r2; 365 r2 = 0; 366 } 367 368 result[ndigits * 2 - 1] = r01.m_low; 369 } 370 371 /* Computes result = (left + right) % mod. 372 * Assumes that left < mod and right < mod, result != mod. 373 */ 374 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right, 375 const u64 *mod, unsigned int ndigits) 376 { 377 u64 carry; 378 379 carry = vli_add(result, left, right, ndigits); 380 381 /* result > mod (result = mod + remainder), so subtract mod to 382 * get remainder. 383 */ 384 if (carry || vli_cmp(result, mod, ndigits) >= 0) 385 vli_sub(result, result, mod, ndigits); 386 } 387 388 /* Computes result = (left - right) % mod. 389 * Assumes that left < mod and right < mod, result != mod. 390 */ 391 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right, 392 const u64 *mod, unsigned int ndigits) 393 { 394 u64 borrow = vli_sub(result, left, right, ndigits); 395 396 /* In this case, p_result == -diff == (max int) - diff. 397 * Since -x % d == d - x, we can get the correct result from 398 * result + mod (with overflow). 399 */ 400 if (borrow) 401 vli_add(result, result, mod, ndigits); 402 } 403 404 /* Computes p_result = p_product % curve_p. 405 * See algorithm 5 and 6 from 406 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf 407 */ 408 static void vli_mmod_fast_192(u64 *result, const u64 *product, 409 const u64 *curve_prime, u64 *tmp) 410 { 411 const unsigned int ndigits = 3; 412 int carry; 413 414 vli_set(result, product, ndigits); 415 416 vli_set(tmp, &product[3], ndigits); 417 carry = vli_add(result, result, tmp, ndigits); 418 419 tmp[0] = 0; 420 tmp[1] = product[3]; 421 tmp[2] = product[4]; 422 carry += vli_add(result, result, tmp, ndigits); 423 424 tmp[0] = tmp[1] = product[5]; 425 tmp[2] = 0; 426 carry += vli_add(result, result, tmp, ndigits); 427 428 while (carry || vli_cmp(curve_prime, result, ndigits) != 1) 429 carry -= vli_sub(result, result, curve_prime, ndigits); 430 } 431 432 /* Computes result = product % curve_prime 433 * from http://www.nsa.gov/ia/_files/nist-routines.pdf 434 */ 435 static void vli_mmod_fast_256(u64 *result, const u64 *product, 436 const u64 *curve_prime, u64 *tmp) 437 { 438 int carry; 439 const unsigned int ndigits = 4; 440 441 /* t */ 442 vli_set(result, product, ndigits); 443 444 /* s1 */ 445 tmp[0] = 0; 446 tmp[1] = product[5] & 0xffffffff00000000ull; 447 tmp[2] = product[6]; 448 tmp[3] = product[7]; 449 carry = vli_lshift(tmp, tmp, 1, ndigits); 450 carry += vli_add(result, result, tmp, ndigits); 451 452 /* s2 */ 453 tmp[1] = product[6] << 32; 454 tmp[2] = (product[6] >> 32) | (product[7] << 32); 455 tmp[3] = product[7] >> 32; 456 carry += vli_lshift(tmp, tmp, 1, ndigits); 457 carry += vli_add(result, result, tmp, ndigits); 458 459 /* s3 */ 460 tmp[0] = product[4]; 461 tmp[1] = product[5] & 0xffffffff; 462 tmp[2] = 0; 463 tmp[3] = product[7]; 464 carry += vli_add(result, result, tmp, ndigits); 465 466 /* s4 */ 467 tmp[0] = (product[4] >> 32) | (product[5] << 32); 468 tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull); 469 tmp[2] = product[7]; 470 tmp[3] = (product[6] >> 32) | (product[4] << 32); 471 carry += vli_add(result, result, tmp, ndigits); 472 473 /* d1 */ 474 tmp[0] = (product[5] >> 32) | (product[6] << 32); 475 tmp[1] = (product[6] >> 32); 476 tmp[2] = 0; 477 tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32); 478 carry -= vli_sub(result, result, tmp, ndigits); 479 480 /* d2 */ 481 tmp[0] = product[6]; 482 tmp[1] = product[7]; 483 tmp[2] = 0; 484 tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull); 485 carry -= vli_sub(result, result, tmp, ndigits); 486 487 /* d3 */ 488 tmp[0] = (product[6] >> 32) | (product[7] << 32); 489 tmp[1] = (product[7] >> 32) | (product[4] << 32); 490 tmp[2] = (product[4] >> 32) | (product[5] << 32); 491 tmp[3] = (product[6] << 32); 492 carry -= vli_sub(result, result, tmp, ndigits); 493 494 /* d4 */ 495 tmp[0] = product[7]; 496 tmp[1] = product[4] & 0xffffffff00000000ull; 497 tmp[2] = product[5]; 498 tmp[3] = product[6] & 0xffffffff00000000ull; 499 carry -= vli_sub(result, result, tmp, ndigits); 500 501 if (carry < 0) { 502 do { 503 carry += vli_add(result, result, curve_prime, ndigits); 504 } while (carry < 0); 505 } else { 506 while (carry || vli_cmp(curve_prime, result, ndigits) != 1) 507 carry -= vli_sub(result, result, curve_prime, ndigits); 508 } 509 } 510 511 /* Computes result = product % curve_prime 512 * from http://www.nsa.gov/ia/_files/nist-routines.pdf 513 */ 514 static bool vli_mmod_fast(u64 *result, u64 *product, 515 const u64 *curve_prime, unsigned int ndigits) 516 { 517 u64 tmp[2 * ndigits]; 518 519 switch (ndigits) { 520 case 3: 521 vli_mmod_fast_192(result, product, curve_prime, tmp); 522 break; 523 case 4: 524 vli_mmod_fast_256(result, product, curve_prime, tmp); 525 break; 526 default: 527 pr_err("unsupports digits size!\n"); 528 return false; 529 } 530 531 return true; 532 } 533 534 /* Computes result = (left * right) % curve_prime. */ 535 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, 536 const u64 *curve_prime, unsigned int ndigits) 537 { 538 u64 product[2 * ndigits]; 539 540 vli_mult(product, left, right, ndigits); 541 vli_mmod_fast(result, product, curve_prime, ndigits); 542 } 543 544 /* Computes result = left^2 % curve_prime. */ 545 static void vli_mod_square_fast(u64 *result, const u64 *left, 546 const u64 *curve_prime, unsigned int ndigits) 547 { 548 u64 product[2 * ndigits]; 549 550 vli_square(product, left, ndigits); 551 vli_mmod_fast(result, product, curve_prime, ndigits); 552 } 553 554 #define EVEN(vli) (!(vli[0] & 1)) 555 /* Computes result = (1 / p_input) % mod. All VLIs are the same size. 556 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" 557 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf 558 */ 559 static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, 560 unsigned int ndigits) 561 { 562 u64 a[ndigits], b[ndigits]; 563 u64 u[ndigits], v[ndigits]; 564 u64 carry; 565 int cmp_result; 566 567 if (vli_is_zero(input, ndigits)) { 568 vli_clear(result, ndigits); 569 return; 570 } 571 572 vli_set(a, input, ndigits); 573 vli_set(b, mod, ndigits); 574 vli_clear(u, ndigits); 575 u[0] = 1; 576 vli_clear(v, ndigits); 577 578 while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) { 579 carry = 0; 580 581 if (EVEN(a)) { 582 vli_rshift1(a, ndigits); 583 584 if (!EVEN(u)) 585 carry = vli_add(u, u, mod, ndigits); 586 587 vli_rshift1(u, ndigits); 588 if (carry) 589 u[ndigits - 1] |= 0x8000000000000000ull; 590 } else if (EVEN(b)) { 591 vli_rshift1(b, ndigits); 592 593 if (!EVEN(v)) 594 carry = vli_add(v, v, mod, ndigits); 595 596 vli_rshift1(v, ndigits); 597 if (carry) 598 v[ndigits - 1] |= 0x8000000000000000ull; 599 } else if (cmp_result > 0) { 600 vli_sub(a, a, b, ndigits); 601 vli_rshift1(a, ndigits); 602 603 if (vli_cmp(u, v, ndigits) < 0) 604 vli_add(u, u, mod, ndigits); 605 606 vli_sub(u, u, v, ndigits); 607 if (!EVEN(u)) 608 carry = vli_add(u, u, mod, ndigits); 609 610 vli_rshift1(u, ndigits); 611 if (carry) 612 u[ndigits - 1] |= 0x8000000000000000ull; 613 } else { 614 vli_sub(b, b, a, ndigits); 615 vli_rshift1(b, ndigits); 616 617 if (vli_cmp(v, u, ndigits) < 0) 618 vli_add(v, v, mod, ndigits); 619 620 vli_sub(v, v, u, ndigits); 621 if (!EVEN(v)) 622 carry = vli_add(v, v, mod, ndigits); 623 624 vli_rshift1(v, ndigits); 625 if (carry) 626 v[ndigits - 1] |= 0x8000000000000000ull; 627 } 628 } 629 630 vli_set(result, u, ndigits); 631 } 632 633 /* ------ Point operations ------ */ 634 635 /* Returns true if p_point is the point at infinity, false otherwise. */ 636 static bool ecc_point_is_zero(const struct ecc_point *point) 637 { 638 return (vli_is_zero(point->x, point->ndigits) && 639 vli_is_zero(point->y, point->ndigits)); 640 } 641 642 /* Point multiplication algorithm using Montgomery's ladder with co-Z 643 * coordinates. From http://eprint.iacr.org/2011/338.pdf 644 */ 645 646 /* Double in place */ 647 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, 648 u64 *curve_prime, unsigned int ndigits) 649 { 650 /* t1 = x, t2 = y, t3 = z */ 651 u64 t4[ndigits]; 652 u64 t5[ndigits]; 653 654 if (vli_is_zero(z1, ndigits)) 655 return; 656 657 /* t4 = y1^2 */ 658 vli_mod_square_fast(t4, y1, curve_prime, ndigits); 659 /* t5 = x1*y1^2 = A */ 660 vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits); 661 /* t4 = y1^4 */ 662 vli_mod_square_fast(t4, t4, curve_prime, ndigits); 663 /* t2 = y1*z1 = z3 */ 664 vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits); 665 /* t3 = z1^2 */ 666 vli_mod_square_fast(z1, z1, curve_prime, ndigits); 667 668 /* t1 = x1 + z1^2 */ 669 vli_mod_add(x1, x1, z1, curve_prime, ndigits); 670 /* t3 = 2*z1^2 */ 671 vli_mod_add(z1, z1, z1, curve_prime, ndigits); 672 /* t3 = x1 - z1^2 */ 673 vli_mod_sub(z1, x1, z1, curve_prime, ndigits); 674 /* t1 = x1^2 - z1^4 */ 675 vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits); 676 677 /* t3 = 2*(x1^2 - z1^4) */ 678 vli_mod_add(z1, x1, x1, curve_prime, ndigits); 679 /* t1 = 3*(x1^2 - z1^4) */ 680 vli_mod_add(x1, x1, z1, curve_prime, ndigits); 681 if (vli_test_bit(x1, 0)) { 682 u64 carry = vli_add(x1, x1, curve_prime, ndigits); 683 684 vli_rshift1(x1, ndigits); 685 x1[ndigits - 1] |= carry << 63; 686 } else { 687 vli_rshift1(x1, ndigits); 688 } 689 /* t1 = 3/2*(x1^2 - z1^4) = B */ 690 691 /* t3 = B^2 */ 692 vli_mod_square_fast(z1, x1, curve_prime, ndigits); 693 /* t3 = B^2 - A */ 694 vli_mod_sub(z1, z1, t5, curve_prime, ndigits); 695 /* t3 = B^2 - 2A = x3 */ 696 vli_mod_sub(z1, z1, t5, curve_prime, ndigits); 697 /* t5 = A - x3 */ 698 vli_mod_sub(t5, t5, z1, curve_prime, ndigits); 699 /* t1 = B * (A - x3) */ 700 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); 701 /* t4 = B * (A - x3) - y1^4 = y3 */ 702 vli_mod_sub(t4, x1, t4, curve_prime, ndigits); 703 704 vli_set(x1, z1, ndigits); 705 vli_set(z1, y1, ndigits); 706 vli_set(y1, t4, ndigits); 707 } 708 709 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ 710 static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime, 711 unsigned int ndigits) 712 { 713 u64 t1[ndigits]; 714 715 vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */ 716 vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */ 717 vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */ 718 vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */ 719 } 720 721 /* P = (x1, y1) => 2P, (x2, y2) => P' */ 722 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2, 723 u64 *p_initial_z, u64 *curve_prime, 724 unsigned int ndigits) 725 { 726 u64 z[ndigits]; 727 728 vli_set(x2, x1, ndigits); 729 vli_set(y2, y1, ndigits); 730 731 vli_clear(z, ndigits); 732 z[0] = 1; 733 734 if (p_initial_z) 735 vli_set(z, p_initial_z, ndigits); 736 737 apply_z(x1, y1, z, curve_prime, ndigits); 738 739 ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits); 740 741 apply_z(x2, y2, z, curve_prime, ndigits); 742 } 743 744 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 745 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) 746 * or P => P', Q => P + Q 747 */ 748 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, 749 unsigned int ndigits) 750 { 751 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 752 u64 t5[ndigits]; 753 754 /* t5 = x2 - x1 */ 755 vli_mod_sub(t5, x2, x1, curve_prime, ndigits); 756 /* t5 = (x2 - x1)^2 = A */ 757 vli_mod_square_fast(t5, t5, curve_prime, ndigits); 758 /* t1 = x1*A = B */ 759 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); 760 /* t3 = x2*A = C */ 761 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); 762 /* t4 = y2 - y1 */ 763 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 764 /* t5 = (y2 - y1)^2 = D */ 765 vli_mod_square_fast(t5, y2, curve_prime, ndigits); 766 767 /* t5 = D - B */ 768 vli_mod_sub(t5, t5, x1, curve_prime, ndigits); 769 /* t5 = D - B - C = x3 */ 770 vli_mod_sub(t5, t5, x2, curve_prime, ndigits); 771 /* t3 = C - B */ 772 vli_mod_sub(x2, x2, x1, curve_prime, ndigits); 773 /* t2 = y1*(C - B) */ 774 vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits); 775 /* t3 = B - x3 */ 776 vli_mod_sub(x2, x1, t5, curve_prime, ndigits); 777 /* t4 = (y2 - y1)*(B - x3) */ 778 vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits); 779 /* t4 = y3 */ 780 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 781 782 vli_set(x2, t5, ndigits); 783 } 784 785 /* Input P = (x1, y1, Z), Q = (x2, y2, Z) 786 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) 787 * or P => P - Q, Q => P + Q 788 */ 789 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime, 790 unsigned int ndigits) 791 { 792 /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ 793 u64 t5[ndigits]; 794 u64 t6[ndigits]; 795 u64 t7[ndigits]; 796 797 /* t5 = x2 - x1 */ 798 vli_mod_sub(t5, x2, x1, curve_prime, ndigits); 799 /* t5 = (x2 - x1)^2 = A */ 800 vli_mod_square_fast(t5, t5, curve_prime, ndigits); 801 /* t1 = x1*A = B */ 802 vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); 803 /* t3 = x2*A = C */ 804 vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); 805 /* t4 = y2 + y1 */ 806 vli_mod_add(t5, y2, y1, curve_prime, ndigits); 807 /* t4 = y2 - y1 */ 808 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 809 810 /* t6 = C - B */ 811 vli_mod_sub(t6, x2, x1, curve_prime, ndigits); 812 /* t2 = y1 * (C - B) */ 813 vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits); 814 /* t6 = B + C */ 815 vli_mod_add(t6, x1, x2, curve_prime, ndigits); 816 /* t3 = (y2 - y1)^2 */ 817 vli_mod_square_fast(x2, y2, curve_prime, ndigits); 818 /* t3 = x3 */ 819 vli_mod_sub(x2, x2, t6, curve_prime, ndigits); 820 821 /* t7 = B - x3 */ 822 vli_mod_sub(t7, x1, x2, curve_prime, ndigits); 823 /* t4 = (y2 - y1)*(B - x3) */ 824 vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits); 825 /* t4 = y3 */ 826 vli_mod_sub(y2, y2, y1, curve_prime, ndigits); 827 828 /* t7 = (y2 + y1)^2 = F */ 829 vli_mod_square_fast(t7, t5, curve_prime, ndigits); 830 /* t7 = x3' */ 831 vli_mod_sub(t7, t7, t6, curve_prime, ndigits); 832 /* t6 = x3' - B */ 833 vli_mod_sub(t6, t7, x1, curve_prime, ndigits); 834 /* t6 = (y2 + y1)*(x3' - B) */ 835 vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits); 836 /* t2 = y3' */ 837 vli_mod_sub(y1, t6, y1, curve_prime, ndigits); 838 839 vli_set(x1, t7, ndigits); 840 } 841 842 static void ecc_point_mult(struct ecc_point *result, 843 const struct ecc_point *point, const u64 *scalar, 844 u64 *initial_z, u64 *curve_prime, 845 unsigned int ndigits) 846 { 847 /* R0 and R1 */ 848 u64 rx[2][ndigits]; 849 u64 ry[2][ndigits]; 850 u64 z[ndigits]; 851 int i, nb; 852 int num_bits = vli_num_bits(scalar, ndigits); 853 854 vli_set(rx[1], point->x, ndigits); 855 vli_set(ry[1], point->y, ndigits); 856 857 xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime, 858 ndigits); 859 860 for (i = num_bits - 2; i > 0; i--) { 861 nb = !vli_test_bit(scalar, i); 862 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime, 863 ndigits); 864 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, 865 ndigits); 866 } 867 868 nb = !vli_test_bit(scalar, 0); 869 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime, 870 ndigits); 871 872 /* Find final 1/Z value. */ 873 /* X1 - X0 */ 874 vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); 875 /* Yb * (X1 - X0) */ 876 vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits); 877 /* xP * Yb * (X1 - X0) */ 878 vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits); 879 880 /* 1 / (xP * Yb * (X1 - X0)) */ 881 vli_mod_inv(z, z, curve_prime, point->ndigits); 882 883 /* yP / (xP * Yb * (X1 - X0)) */ 884 vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits); 885 /* Xb * yP / (xP * Yb * (X1 - X0)) */ 886 vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits); 887 /* End 1/Z calculation */ 888 889 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits); 890 891 apply_z(rx[0], ry[0], z, curve_prime, ndigits); 892 893 vli_set(result->x, rx[0], ndigits); 894 vli_set(result->y, ry[0], ndigits); 895 } 896 897 static inline void ecc_swap_digits(const u64 *in, u64 *out, 898 unsigned int ndigits) 899 { 900 int i; 901 902 for (i = 0; i < ndigits; i++) 903 out[i] = __swab64(in[ndigits - 1 - i]); 904 } 905 906 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, 907 const u8 *private_key, unsigned int private_key_len) 908 { 909 int nbytes; 910 const struct ecc_curve *curve = ecc_get_curve(curve_id); 911 912 if (!private_key) 913 return -EINVAL; 914 915 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 916 917 if (private_key_len != nbytes) 918 return -EINVAL; 919 920 if (vli_is_zero((const u64 *)&private_key[0], ndigits)) 921 return -EINVAL; 922 923 /* Make sure the private key is in the range [1, n-1]. */ 924 if (vli_cmp(curve->n, (const u64 *)&private_key[0], ndigits) != 1) 925 return -EINVAL; 926 927 return 0; 928 } 929 930 int ecdh_make_pub_key(unsigned int curve_id, unsigned int ndigits, 931 const u8 *private_key, unsigned int private_key_len, 932 u8 *public_key, unsigned int public_key_len) 933 { 934 int ret = 0; 935 struct ecc_point *pk; 936 u64 priv[ndigits]; 937 unsigned int nbytes; 938 const struct ecc_curve *curve = ecc_get_curve(curve_id); 939 940 if (!private_key || !curve) { 941 ret = -EINVAL; 942 goto out; 943 } 944 945 ecc_swap_digits((const u64 *)private_key, priv, ndigits); 946 947 pk = ecc_alloc_point(ndigits); 948 if (!pk) { 949 ret = -ENOMEM; 950 goto out; 951 } 952 953 ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits); 954 if (ecc_point_is_zero(pk)) { 955 ret = -EAGAIN; 956 goto err_free_point; 957 } 958 959 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 960 ecc_swap_digits(pk->x, (u64 *)public_key, ndigits); 961 ecc_swap_digits(pk->y, (u64 *)&public_key[nbytes], ndigits); 962 963 err_free_point: 964 ecc_free_point(pk); 965 out: 966 return ret; 967 } 968 969 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, 970 const u8 *private_key, unsigned int private_key_len, 971 const u8 *public_key, unsigned int public_key_len, 972 u8 *secret, unsigned int secret_len) 973 { 974 int ret = 0; 975 struct ecc_point *product, *pk; 976 u64 priv[ndigits]; 977 u64 rand_z[ndigits]; 978 unsigned int nbytes; 979 const struct ecc_curve *curve = ecc_get_curve(curve_id); 980 981 if (!private_key || !public_key || !curve) { 982 ret = -EINVAL; 983 goto out; 984 } 985 986 nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; 987 988 get_random_bytes(rand_z, nbytes); 989 990 pk = ecc_alloc_point(ndigits); 991 if (!pk) { 992 ret = -ENOMEM; 993 goto out; 994 } 995 996 product = ecc_alloc_point(ndigits); 997 if (!product) { 998 ret = -ENOMEM; 999 goto err_alloc_product; 1000 } 1001 1002 ecc_swap_digits((const u64 *)public_key, pk->x, ndigits); 1003 ecc_swap_digits((const u64 *)&public_key[nbytes], pk->y, ndigits); 1004 ecc_swap_digits((const u64 *)private_key, priv, ndigits); 1005 1006 ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits); 1007 1008 ecc_swap_digits(product->x, (u64 *)secret, ndigits); 1009 1010 if (ecc_point_is_zero(product)) 1011 ret = -EFAULT; 1012 1013 ecc_free_point(product); 1014 err_alloc_product: 1015 ecc_free_point(pk); 1016 out: 1017 return ret; 1018 } 1019