crypto/ecc.c

   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 }