crypto/ecc.c

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This source file includes following definitions.
ecc_get_curve
ecc_alloc_digits_space
ecc_free_digits_space
ecc_alloc_point
ecc_free_point
vli_clear
vli_is_zero
vli_test_bit
vli_is_negative
vli_num_digits
vli_num_bits
vli_from_be64
vli_from_le64
vli_set
vli_cmp
vli_lshift
vli_rshift1
vli_add
vli_uadd
vli_sub
vli_usub
mul_64_64
add_128_128
vli_mult
vli_umult
vli_square
vli_mod_add
vli_mod_sub
vli_mmod_special
vli_mmod_special2
vli_mmod_slow
vli_mmod_barrett
vli_mmod_fast_192
vli_mmod_fast_256
vli_mmod_fast
vli_mod_mult_slow
vli_mod_mult_fast
vli_mod_square_fast
vli_mod_inv
ecc_point_is_zero
ecc_point_double_jacobian
apply_z
xycz_initial_double
xycz_add
xycz_add_c
ecc_point_mult
ecc_point_add
ecc_point_mult_shamir
ecc_swap_digits
__ecc_is_key_valid
ecc_is_key_valid
ecc_gen_privkey
ecc_make_pub_key
ecc_is_pubkey_valid_partial
crypto_ecdh_shared_secret
   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 
  40 typedef struct {
  41         u64 m_low;
  42         u64 m_high;
  43 } uint128_t;
  44 
  45 static inline const 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         default:
  54                 return NULL;
  55         }
  56 }
  57 
  58 static u64 *ecc_alloc_digits_space(unsigned int ndigits)
  59 {
  60         size_t len = ndigits * sizeof(u64);
  61 
  62         if (!len)
  63                 return NULL;
  64 
  65         return kmalloc(len, GFP_KERNEL);
  66 }
  67 
  68 static void ecc_free_digits_space(u64 *space)
  69 {
  70         kzfree(space);
  71 }
  72 
  73 static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
  74 {
  75         struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
  76 
  77         if (!p)
  78                 return NULL;
  79 
  80         p->x = ecc_alloc_digits_space(ndigits);
  81         if (!p->x)
  82                 goto err_alloc_x;
  83 
  84         p->y = ecc_alloc_digits_space(ndigits);
  85         if (!p->y)
  86                 goto err_alloc_y;
  87 
  88         p->ndigits = ndigits;
  89 
  90         return p;
  91 
  92 err_alloc_y:
  93         ecc_free_digits_space(p->x);
  94 err_alloc_x:
  95         kfree(p);
  96         return NULL;
  97 }
  98 
  99 static void ecc_free_point(struct ecc_point *p)
 100 {
 101         if (!p)
 102                 return;
 103 
 104         kzfree(p->x);
 105         kzfree(p->y);
 106         kzfree(p);
 107 }
 108 
 109 static void vli_clear(u64 *vli, unsigned int ndigits)
 110 {
 111         int i;
 112 
 113         for (i = 0; i < ndigits; i++)
 114                 vli[i] = 0;
 115 }
 116 
 117 /* Returns true if vli == 0, false otherwise. */
 118 bool vli_is_zero(const u64 *vli, unsigned int ndigits)
 119 {
 120         int i;
 121 
 122         for (i = 0; i < ndigits; i++) {
 123                 if (vli[i])
 124                         return false;
 125         }
 126 
 127         return true;
 128 }
 129 EXPORT_SYMBOL(vli_is_zero);
 130 
 131 /* Returns nonzero if bit bit of vli is set. */
 132 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
 133 {
 134         return (vli[bit / 64] & ((u64)1 << (bit % 64)));
 135 }
 136 
 137 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
 138 {
 139         return vli_test_bit(vli, ndigits * 64 - 1);
 140 }
 141 
 142 /* Counts the number of 64-bit "digits" in vli. */
 143 static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
 144 {
 145         int i;
 146 
 147         /* Search from the end until we find a non-zero digit.
 148          * We do it in reverse because we expect that most digits will
 149          * be nonzero.
 150          */
 151         for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);
 152 
 153         return (i + 1);
 154 }
 155 
 156 /* Counts the number of bits required for vli. */
 157 static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
 158 {
 159         unsigned int i, num_digits;
 160         u64 digit;
 161 
 162         num_digits = vli_num_digits(vli, ndigits);
 163         if (num_digits == 0)
 164                 return 0;
 165 
 166         digit = vli[num_digits - 1];
 167         for (i = 0; digit; i++)
 168                 digit >>= 1;
 169 
 170         return ((num_digits - 1) * 64 + i);
 171 }
 172 
 173 /* Set dest from unaligned bit string src. */
 174 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
 175 {
 176         int i;
 177         const u64 *from = src;
 178 
 179         for (i = 0; i < ndigits; i++)
 180                 dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
 181 }
 182 EXPORT_SYMBOL(vli_from_be64);
 183 
 184 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
 185 {
 186         int i;
 187         const u64 *from = src;
 188 
 189         for (i = 0; i < ndigits; i++)
 190                 dest[i] = get_unaligned_le64(&from[i]);
 191 }
 192 EXPORT_SYMBOL(vli_from_le64);
 193 
 194 /* Sets dest = src. */
 195 static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
 196 {
 197         int i;
 198 
 199         for (i = 0; i < ndigits; i++)
 200                 dest[i] = src[i];
 201 }
 202 
 203 /* Returns sign of left - right. */
 204 int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
 205 {
 206         int i;
 207 
 208         for (i = ndigits - 1; i >= 0; i--) {
 209                 if (left[i] > right[i])
 210                         return 1;
 211                 else if (left[i] < right[i])
 212                         return -1;
 213         }
 214 
 215         return 0;
 216 }
 217 EXPORT_SYMBOL(vli_cmp);
 218 
 219 /* Computes result = in << c, returning carry. Can modify in place
 220  * (if result == in). 0 < shift < 64.
 221  */
 222 static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
 223                       unsigned int ndigits)
 224 {
 225         u64 carry = 0;
 226         int i;
 227 
 228         for (i = 0; i < ndigits; i++) {
 229                 u64 temp = in[i];
 230 
 231                 result[i] = (temp << shift) | carry;
 232                 carry = temp >> (64 - shift);
 233         }
 234 
 235         return carry;
 236 }
 237 
 238 /* Computes vli = vli >> 1. */
 239 static void vli_rshift1(u64 *vli, unsigned int ndigits)
 240 {
 241         u64 *end = vli;
 242         u64 carry = 0;
 243 
 244         vli += ndigits;
 245 
 246         while (vli-- > end) {
 247                 u64 temp = *vli;
 248                 *vli = (temp >> 1) | carry;
 249                 carry = temp << 63;
 250         }
 251 }
 252 
 253 /* Computes result = left + right, returning carry. Can modify in place. */
 254 static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
 255                    unsigned int ndigits)
 256 {
 257         u64 carry = 0;
 258         int i;
 259 
 260         for (i = 0; i < ndigits; i++) {
 261                 u64 sum;
 262 
 263                 sum = left[i] + right[i] + carry;
 264                 if (sum != left[i])
 265                         carry = (sum < left[i]);
 266 
 267                 result[i] = sum;
 268         }
 269 
 270         return carry;
 271 }
 272 
 273 /* Computes result = left + right, returning carry. Can modify in place. */
 274 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
 275                     unsigned int ndigits)
 276 {
 277         u64 carry = right;
 278         int i;
 279 
 280         for (i = 0; i < ndigits; i++) {
 281                 u64 sum;
 282 
 283                 sum = left[i] + carry;
 284                 if (sum != left[i])
 285                         carry = (sum < left[i]);
 286                 else
 287                         carry = !!carry;
 288 
 289                 result[i] = sum;
 290         }
 291 
 292         return carry;
 293 }
 294 
 295 /* Computes result = left - right, returning borrow. Can modify in place. */
 296 u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
 297                    unsigned int ndigits)
 298 {
 299         u64 borrow = 0;
 300         int i;
 301 
 302         for (i = 0; i < ndigits; i++) {
 303                 u64 diff;
 304 
 305                 diff = left[i] - right[i] - borrow;
 306                 if (diff != left[i])
 307                         borrow = (diff > left[i]);
 308 
 309                 result[i] = diff;
 310         }
 311 
 312         return borrow;
 313 }
 314 EXPORT_SYMBOL(vli_sub);
 315 
 316 /* Computes result = left - right, returning borrow. Can modify in place. */
 317 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
 318              unsigned int ndigits)
 319 {
 320         u64 borrow = right;
 321         int i;
 322 
 323         for (i = 0; i < ndigits; i++) {
 324                 u64 diff;
 325 
 326                 diff = left[i] - borrow;
 327                 if (diff != left[i])
 328                         borrow = (diff > left[i]);
 329 
 330                 result[i] = diff;
 331         }
 332 
 333         return borrow;
 334 }
 335 
 336 static uint128_t mul_64_64(u64 left, u64 right)
 337 {
 338         uint128_t result;
 339 #if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
 340         unsigned __int128 m = (unsigned __int128)left * right;
 341 
 342         result.m_low  = m;
 343         result.m_high = m >> 64;
 344 #else
 345         u64 a0 = left & 0xffffffffull;
 346         u64 a1 = left >> 32;
 347         u64 b0 = right & 0xffffffffull;
 348         u64 b1 = right >> 32;
 349         u64 m0 = a0 * b0;
 350         u64 m1 = a0 * b1;
 351         u64 m2 = a1 * b0;
 352         u64 m3 = a1 * b1;
 353 
 354         m2 += (m0 >> 32);
 355         m2 += m1;
 356 
 357         /* Overflow */
 358         if (m2 < m1)
 359                 m3 += 0x100000000ull;
 360 
 361         result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
 362         result.m_high = m3 + (m2 >> 32);
 363 #endif
 364         return result;
 365 }
 366 
 367 static uint128_t add_128_128(uint128_t a, uint128_t b)
 368 {
 369         uint128_t result;
 370 
 371         result.m_low = a.m_low + b.m_low;
 372         result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
 373 
 374         return result;
 375 }
 376 
 377 static void vli_mult(u64 *result, const u64 *left, const u64 *right,
 378                      unsigned int ndigits)
 379 {
 380         uint128_t r01 = { 0, 0 };
 381         u64 r2 = 0;
 382         unsigned int i, k;
 383 
 384         /* Compute each digit of result in sequence, maintaining the
 385          * carries.
 386          */
 387         for (k = 0; k < ndigits * 2 - 1; k++) {
 388                 unsigned int min;
 389 
 390                 if (k < ndigits)
 391                         min = 0;
 392                 else
 393                         min = (k + 1) - ndigits;
 394 
 395                 for (i = min; i <= k && i < ndigits; i++) {
 396                         uint128_t product;
 397 
 398                         product = mul_64_64(left[i], right[k - i]);
 399 
 400                         r01 = add_128_128(r01, product);
 401                         r2 += (r01.m_high < product.m_high);
 402                 }
 403 
 404                 result[k] = r01.m_low;
 405                 r01.m_low = r01.m_high;
 406                 r01.m_high = r2;
 407                 r2 = 0;
 408         }
 409 
 410         result[ndigits * 2 - 1] = r01.m_low;
 411 }
 412 
 413 /* Compute product = left * right, for a small right value. */
 414 static void vli_umult(u64 *result, const u64 *left, u32 right,
 415                       unsigned int ndigits)
 416 {
 417         uint128_t r01 = { 0 };
 418         unsigned int k;
 419 
 420         for (k = 0; k < ndigits; k++) {
 421                 uint128_t product;
 422 
 423                 product = mul_64_64(left[k], right);
 424                 r01 = add_128_128(r01, product);
 425                 /* no carry */
 426                 result[k] = r01.m_low;
 427                 r01.m_low = r01.m_high;
 428                 r01.m_high = 0;
 429         }
 430         result[k] = r01.m_low;
 431         for (++k; k < ndigits * 2; k++)
 432                 result[k] = 0;
 433 }
 434 
 435 static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
 436 {
 437         uint128_t r01 = { 0, 0 };
 438         u64 r2 = 0;
 439         int i, k;
 440 
 441         for (k = 0; k < ndigits * 2 - 1; k++) {
 442                 unsigned int min;
 443 
 444                 if (k < ndigits)
 445                         min = 0;
 446                 else
 447                         min = (k + 1) - ndigits;
 448 
 449                 for (i = min; i <= k && i <= k - i; i++) {
 450                         uint128_t product;
 451 
 452                         product = mul_64_64(left[i], left[k - i]);
 453 
 454                         if (i < k - i) {
 455                                 r2 += product.m_high >> 63;
 456                                 product.m_high = (product.m_high << 1) |
 457                                                  (product.m_low >> 63);
 458                                 product.m_low <<= 1;
 459                         }
 460 
 461                         r01 = add_128_128(r01, product);
 462                         r2 += (r01.m_high < product.m_high);
 463                 }
 464 
 465                 result[k] = r01.m_low;
 466                 r01.m_low = r01.m_high;
 467                 r01.m_high = r2;
 468                 r2 = 0;
 469         }
 470 
 471         result[ndigits * 2 - 1] = r01.m_low;
 472 }
 473 
 474 /* Computes result = (left + right) % mod.
 475  * Assumes that left < mod and right < mod, result != mod.
 476  */
 477 static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
 478                         const u64 *mod, unsigned int ndigits)
 479 {
 480         u64 carry;
 481 
 482         carry = vli_add(result, left, right, ndigits);
 483 
 484         /* result > mod (result = mod + remainder), so subtract mod to
 485          * get remainder.
 486          */
 487         if (carry || vli_cmp(result, mod, ndigits) >= 0)
 488                 vli_sub(result, result, mod, ndigits);
 489 }
 490 
 491 /* Computes result = (left - right) % mod.
 492  * Assumes that left < mod and right < mod, result != mod.
 493  */
 494 static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
 495                         const u64 *mod, unsigned int ndigits)
 496 {
 497         u64 borrow = vli_sub(result, left, right, ndigits);
 498 
 499         /* In this case, p_result == -diff == (max int) - diff.
 500          * Since -x % d == d - x, we can get the correct result from
 501          * result + mod (with overflow).
 502          */
 503         if (borrow)
 504                 vli_add(result, result, mod, ndigits);
 505 }
 506 
 507 /*
 508  * Computes result = product % mod
 509  * for special form moduli: p = 2^k-c, for small c (note the minus sign)
 510  *
 511  * References:
 512  * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
 513  * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
 514  * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
 515  */
 516 static void vli_mmod_special(u64 *result, const u64 *product,
 517                               const u64 *mod, unsigned int ndigits)
 518 {
 519         u64 c = -mod[0];
 520         u64 t[ECC_MAX_DIGITS * 2];
 521         u64 r[ECC_MAX_DIGITS * 2];
 522 
 523         vli_set(r, product, ndigits * 2);
 524         while (!vli_is_zero(r + ndigits, ndigits)) {
 525                 vli_umult(t, r + ndigits, c, ndigits);
 526                 vli_clear(r + ndigits, ndigits);
 527                 vli_add(r, r, t, ndigits * 2);
 528         }
 529         vli_set(t, mod, ndigits);
 530         vli_clear(t + ndigits, ndigits);
 531         while (vli_cmp(r, t, ndigits * 2) >= 0)
 532                 vli_sub(r, r, t, ndigits * 2);
 533         vli_set(result, r, ndigits);
 534 }
 535 
 536 /*
 537  * Computes result = product % mod
 538  * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
 539  * where k-1 does not fit into qword boundary by -1 bit (such as 255).
 540 
 541  * References (loosely based on):
 542  * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
 543  * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
 544  * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
 545  *
 546  * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
 547  * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
 548  * Algorithm 10.25 Fast reduction for special form moduli
 549  */
 550 static void vli_mmod_special2(u64 *result, const u64 *product,
 551                                const u64 *mod, unsigned int ndigits)
 552 {
 553         u64 c2 = mod[0] * 2;
 554         u64 q[ECC_MAX_DIGITS];
 555         u64 r[ECC_MAX_DIGITS * 2];
 556         u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
 557         int carry; /* last bit that doesn't fit into q */
 558         int i;
 559 
 560         vli_set(m, mod, ndigits);
 561         vli_clear(m + ndigits, ndigits);
 562 
 563         vli_set(r, product, ndigits);
 564         /* q and carry are top bits */
 565         vli_set(q, product + ndigits, ndigits);
 566         vli_clear(r + ndigits, ndigits);
 567         carry = vli_is_negative(r, ndigits);
 568         if (carry)
 569                 r[ndigits - 1] &= (1ull << 63) - 1;
 570         for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
 571                 u64 qc[ECC_MAX_DIGITS * 2];
 572 
 573                 vli_umult(qc, q, c2, ndigits);
 574                 if (carry)
 575                         vli_uadd(qc, qc, mod[0], ndigits * 2);
 576                 vli_set(q, qc + ndigits, ndigits);
 577                 vli_clear(qc + ndigits, ndigits);
 578                 carry = vli_is_negative(qc, ndigits);
 579                 if (carry)
 580                         qc[ndigits - 1] &= (1ull << 63) - 1;
 581                 if (i & 1)
 582                         vli_sub(r, r, qc, ndigits * 2);
 583                 else
 584                         vli_add(r, r, qc, ndigits * 2);
 585         }
 586         while (vli_is_negative(r, ndigits * 2))
 587                 vli_add(r, r, m, ndigits * 2);
 588         while (vli_cmp(r, m, ndigits * 2) >= 0)
 589                 vli_sub(r, r, m, ndigits * 2);
 590 
 591         vli_set(result, r, ndigits);
 592 }
 593 
 594 /*
 595  * Computes result = product % mod, where product is 2N words long.
 596  * Reference: Ken MacKay's micro-ecc.
 597  * Currently only designed to work for curve_p or curve_n.
 598  */
 599 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
 600                           unsigned int ndigits)
 601 {
 602         u64 mod_m[2 * ECC_MAX_DIGITS];
 603         u64 tmp[2 * ECC_MAX_DIGITS];
 604         u64 *v[2] = { tmp, product };
 605         u64 carry = 0;
 606         unsigned int i;
 607         /* Shift mod so its highest set bit is at the maximum position. */
 608         int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
 609         int word_shift = shift / 64;
 610         int bit_shift = shift % 64;
 611 
 612         vli_clear(mod_m, word_shift);
 613         if (bit_shift > 0) {
 614                 for (i = 0; i < ndigits; ++i) {
 615                         mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
 616                         carry = mod[i] >> (64 - bit_shift);
 617                 }
 618         } else
 619                 vli_set(mod_m + word_shift, mod, ndigits);
 620 
 621         for (i = 1; shift >= 0; --shift) {
 622                 u64 borrow = 0;
 623                 unsigned int j;
 624 
 625                 for (j = 0; j < ndigits * 2; ++j) {
 626                         u64 diff = v[i][j] - mod_m[j] - borrow;
 627 
 628                         if (diff != v[i][j])
 629                                 borrow = (diff > v[i][j]);
 630                         v[1 - i][j] = diff;
 631                 }
 632                 i = !(i ^ borrow); /* Swap the index if there was no borrow */
 633                 vli_rshift1(mod_m, ndigits);
 634                 mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
 635                 vli_rshift1(mod_m + ndigits, ndigits);
 636         }
 637         vli_set(result, v[i], ndigits);
 638 }
 639 
 640 /* Computes result = product % mod using Barrett's reduction with precomputed
 641  * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
 642  * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
 643  * boundary.
 644  *
 645  * Reference:
 646  * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
 647  * 2.4.1 Barrett's algorithm. Algorithm 2.5.
 648  */
 649 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
 650                              unsigned int ndigits)
 651 {
 652         u64 q[ECC_MAX_DIGITS * 2];
 653         u64 r[ECC_MAX_DIGITS * 2];
 654         const u64 *mu = mod + ndigits;
 655 
 656         vli_mult(q, product + ndigits, mu, ndigits);
 657         if (mu[ndigits])
 658                 vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
 659         vli_mult(r, mod, q + ndigits, ndigits);
 660         vli_sub(r, product, r, ndigits * 2);
 661         while (!vli_is_zero(r + ndigits, ndigits) ||
 662                vli_cmp(r, mod, ndigits) != -1) {
 663                 u64 carry;
 664 
 665                 carry = vli_sub(r, r, mod, ndigits);
 666                 vli_usub(r + ndigits, r + ndigits, carry, ndigits);
 667         }
 668         vli_set(result, r, ndigits);
 669 }
 670 
 671 /* Computes p_result = p_product % curve_p.
 672  * See algorithm 5 and 6 from
 673  * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
 674  */
 675 static void vli_mmod_fast_192(u64 *result, const u64 *product,
 676                               const u64 *curve_prime, u64 *tmp)
 677 {
 678         const unsigned int ndigits = 3;
 679         int carry;
 680 
 681         vli_set(result, product, ndigits);
 682 
 683         vli_set(tmp, &product[3], ndigits);
 684         carry = vli_add(result, result, tmp, ndigits);
 685 
 686         tmp[0] = 0;
 687         tmp[1] = product[3];
 688         tmp[2] = product[4];
 689         carry += vli_add(result, result, tmp, ndigits);
 690 
 691         tmp[0] = tmp[1] = product[5];
 692         tmp[2] = 0;
 693         carry += vli_add(result, result, tmp, ndigits);
 694 
 695         while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
 696                 carry -= vli_sub(result, result, curve_prime, ndigits);
 697 }
 698 
 699 /* Computes result = product % curve_prime
 700  * from http://www.nsa.gov/ia/_files/nist-routines.pdf
 701  */
 702 static void vli_mmod_fast_256(u64 *result, const u64 *product,
 703                               const u64 *curve_prime, u64 *tmp)
 704 {
 705         int carry;
 706         const unsigned int ndigits = 4;
 707 
 708         /* t */
 709         vli_set(result, product, ndigits);
 710 
 711         /* s1 */
 712         tmp[0] = 0;
 713         tmp[1] = product[5] & 0xffffffff00000000ull;
 714         tmp[2] = product[6];
 715         tmp[3] = product[7];
 716         carry = vli_lshift(tmp, tmp, 1, ndigits);
 717         carry += vli_add(result, result, tmp, ndigits);
 718 
 719         /* s2 */
 720         tmp[1] = product[6] << 32;
 721         tmp[2] = (product[6] >> 32) | (product[7] << 32);
 722         tmp[3] = product[7] >> 32;
 723         carry += vli_lshift(tmp, tmp, 1, ndigits);
 724         carry += vli_add(result, result, tmp, ndigits);
 725 
 726         /* s3 */
 727         tmp[0] = product[4];
 728         tmp[1] = product[5] & 0xffffffff;
 729         tmp[2] = 0;
 730         tmp[3] = product[7];
 731         carry += vli_add(result, result, tmp, ndigits);
 732 
 733         /* s4 */
 734         tmp[0] = (product[4] >> 32) | (product[5] << 32);
 735         tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
 736         tmp[2] = product[7];
 737         tmp[3] = (product[6] >> 32) | (product[4] << 32);
 738         carry += vli_add(result, result, tmp, ndigits);
 739 
 740         /* d1 */
 741         tmp[0] = (product[5] >> 32) | (product[6] << 32);
 742         tmp[1] = (product[6] >> 32);
 743         tmp[2] = 0;
 744         tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
 745         carry -= vli_sub(result, result, tmp, ndigits);
 746 
 747         /* d2 */
 748         tmp[0] = product[6];
 749         tmp[1] = product[7];
 750         tmp[2] = 0;
 751         tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
 752         carry -= vli_sub(result, result, tmp, ndigits);
 753 
 754         /* d3 */
 755         tmp[0] = (product[6] >> 32) | (product[7] << 32);
 756         tmp[1] = (product[7] >> 32) | (product[4] << 32);
 757         tmp[2] = (product[4] >> 32) | (product[5] << 32);
 758         tmp[3] = (product[6] << 32);
 759         carry -= vli_sub(result, result, tmp, ndigits);
 760 
 761         /* d4 */
 762         tmp[0] = product[7];
 763         tmp[1] = product[4] & 0xffffffff00000000ull;
 764         tmp[2] = product[5];
 765         tmp[3] = product[6] & 0xffffffff00000000ull;
 766         carry -= vli_sub(result, result, tmp, ndigits);
 767 
 768         if (carry < 0) {
 769                 do {
 770                         carry += vli_add(result, result, curve_prime, ndigits);
 771                 } while (carry < 0);
 772         } else {
 773                 while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
 774                         carry -= vli_sub(result, result, curve_prime, ndigits);
 775         }
 776 }
 777 
 778 /* Computes result = product % curve_prime for different curve_primes.
 779  *
 780  * Note that curve_primes are distinguished just by heuristic check and
 781  * not by complete conformance check.
 782  */
 783 static bool vli_mmod_fast(u64 *result, u64 *product,
 784                           const u64 *curve_prime, unsigned int ndigits)
 785 {
 786         u64 tmp[2 * ECC_MAX_DIGITS];
 787 
 788         /* Currently, both NIST primes have -1 in lowest qword. */
 789         if (curve_prime[0] != -1ull) {
 790                 /* Try to handle Pseudo-Marsenne primes. */
 791                 if (curve_prime[ndigits - 1] == -1ull) {
 792                         vli_mmod_special(result, product, curve_prime,
 793                                          ndigits);
 794                         return true;
 795                 } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
 796                            curve_prime[ndigits - 2] == 0) {
 797                         vli_mmod_special2(result, product, curve_prime,
 798                                           ndigits);
 799                         return true;
 800                 }
 801                 vli_mmod_barrett(result, product, curve_prime, ndigits);
 802                 return true;
 803         }
 804 
 805         switch (ndigits) {
 806         case 3:
 807                 vli_mmod_fast_192(result, product, curve_prime, tmp);
 808                 break;
 809         case 4:
 810                 vli_mmod_fast_256(result, product, curve_prime, tmp);
 811                 break;
 812         default:
 813                 pr_err_ratelimited("ecc: unsupported digits size!\n");
 814                 return false;
 815         }
 816 
 817         return true;
 818 }
 819 
 820 /* Computes result = (left * right) % mod.
 821  * Assumes that mod is big enough curve order.
 822  */
 823 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
 824                        const u64 *mod, unsigned int ndigits)
 825 {
 826         u64 product[ECC_MAX_DIGITS * 2];
 827 
 828         vli_mult(product, left, right, ndigits);
 829         vli_mmod_slow(result, product, mod, ndigits);
 830 }
 831 EXPORT_SYMBOL(vli_mod_mult_slow);
 832 
 833 /* Computes result = (left * right) % curve_prime. */
 834 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
 835                               const u64 *curve_prime, unsigned int ndigits)
 836 {
 837         u64 product[2 * ECC_MAX_DIGITS];
 838 
 839         vli_mult(product, left, right, ndigits);
 840         vli_mmod_fast(result, product, curve_prime, ndigits);
 841 }
 842 
 843 /* Computes result = left^2 % curve_prime. */
 844 static void vli_mod_square_fast(u64 *result, const u64 *left,
 845                                 const u64 *curve_prime, unsigned int ndigits)
 846 {
 847         u64 product[2 * ECC_MAX_DIGITS];
 848 
 849         vli_square(product, left, ndigits);
 850         vli_mmod_fast(result, product, curve_prime, ndigits);
 851 }
 852 
 853 #define EVEN(vli) (!(vli[0] & 1))
 854 /* Computes result = (1 / p_input) % mod. All VLIs are the same size.
 855  * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
 856  * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
 857  */
 858 void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
 859                         unsigned int ndigits)
 860 {
 861         u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
 862         u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
 863         u64 carry;
 864         int cmp_result;
 865 
 866         if (vli_is_zero(input, ndigits)) {
 867                 vli_clear(result, ndigits);
 868                 return;
 869         }
 870 
 871         vli_set(a, input, ndigits);
 872         vli_set(b, mod, ndigits);
 873         vli_clear(u, ndigits);
 874         u[0] = 1;
 875         vli_clear(v, ndigits);
 876 
 877         while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
 878                 carry = 0;
 879 
 880                 if (EVEN(a)) {
 881                         vli_rshift1(a, ndigits);
 882 
 883                         if (!EVEN(u))
 884                                 carry = vli_add(u, u, mod, ndigits);
 885 
 886                         vli_rshift1(u, ndigits);
 887                         if (carry)
 888                                 u[ndigits - 1] |= 0x8000000000000000ull;
 889                 } else if (EVEN(b)) {
 890                         vli_rshift1(b, ndigits);
 891 
 892                         if (!EVEN(v))
 893                                 carry = vli_add(v, v, mod, ndigits);
 894 
 895                         vli_rshift1(v, ndigits);
 896                         if (carry)
 897                                 v[ndigits - 1] |= 0x8000000000000000ull;
 898                 } else if (cmp_result > 0) {
 899                         vli_sub(a, a, b, ndigits);
 900                         vli_rshift1(a, ndigits);
 901 
 902                         if (vli_cmp(u, v, ndigits) < 0)
 903                                 vli_add(u, u, mod, ndigits);
 904 
 905                         vli_sub(u, u, v, ndigits);
 906                         if (!EVEN(u))
 907                                 carry = vli_add(u, u, mod, ndigits);
 908 
 909                         vli_rshift1(u, ndigits);
 910                         if (carry)
 911                                 u[ndigits - 1] |= 0x8000000000000000ull;
 912                 } else {
 913                         vli_sub(b, b, a, ndigits);
 914                         vli_rshift1(b, ndigits);
 915 
 916                         if (vli_cmp(v, u, ndigits) < 0)
 917                                 vli_add(v, v, mod, ndigits);
 918 
 919                         vli_sub(v, v, u, ndigits);
 920                         if (!EVEN(v))
 921                                 carry = vli_add(v, v, mod, ndigits);
 922 
 923                         vli_rshift1(v, ndigits);
 924                         if (carry)
 925                                 v[ndigits - 1] |= 0x8000000000000000ull;
 926                 }
 927         }
 928 
 929         vli_set(result, u, ndigits);
 930 }
 931 EXPORT_SYMBOL(vli_mod_inv);
 932 
 933 /* ------ Point operations ------ */
 934 
 935 /* Returns true if p_point is the point at infinity, false otherwise. */
 936 static bool ecc_point_is_zero(const struct ecc_point *point)
 937 {
 938         return (vli_is_zero(point->x, point->ndigits) &&
 939                 vli_is_zero(point->y, point->ndigits));
 940 }
 941 
 942 /* Point multiplication algorithm using Montgomery's ladder with co-Z
 943  * coordinates. From http://eprint.iacr.org/2011/338.pdf
 944  */
 945 
 946 /* Double in place */
 947 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
 948                                       u64 *curve_prime, unsigned int ndigits)
 949 {
 950         /* t1 = x, t2 = y, t3 = z */
 951         u64 t4[ECC_MAX_DIGITS];
 952         u64 t5[ECC_MAX_DIGITS];
 953 
 954         if (vli_is_zero(z1, ndigits))
 955                 return;
 956 
 957         /* t4 = y1^2 */
 958         vli_mod_square_fast(t4, y1, curve_prime, ndigits);
 959         /* t5 = x1*y1^2 = A */
 960         vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
 961         /* t4 = y1^4 */
 962         vli_mod_square_fast(t4, t4, curve_prime, ndigits);
 963         /* t2 = y1*z1 = z3 */
 964         vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
 965         /* t3 = z1^2 */
 966         vli_mod_square_fast(z1, z1, curve_prime, ndigits);
 967 
 968         /* t1 = x1 + z1^2 */
 969         vli_mod_add(x1, x1, z1, curve_prime, ndigits);
 970         /* t3 = 2*z1^2 */
 971         vli_mod_add(z1, z1, z1, curve_prime, ndigits);
 972         /* t3 = x1 - z1^2 */
 973         vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
 974         /* t1 = x1^2 - z1^4 */
 975         vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
 976 
 977         /* t3 = 2*(x1^2 - z1^4) */
 978         vli_mod_add(z1, x1, x1, curve_prime, ndigits);
 979         /* t1 = 3*(x1^2 - z1^4) */
 980         vli_mod_add(x1, x1, z1, curve_prime, ndigits);
 981         if (vli_test_bit(x1, 0)) {
 982                 u64 carry = vli_add(x1, x1, curve_prime, ndigits);
 983 
 984                 vli_rshift1(x1, ndigits);
 985                 x1[ndigits - 1] |= carry << 63;
 986         } else {
 987                 vli_rshift1(x1, ndigits);
 988         }
 989         /* t1 = 3/2*(x1^2 - z1^4) = B */
 990 
 991         /* t3 = B^2 */
 992         vli_mod_square_fast(z1, x1, curve_prime, ndigits);
 993         /* t3 = B^2 - A */
 994         vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
 995         /* t3 = B^2 - 2A = x3 */
 996         vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
 997         /* t5 = A - x3 */
 998         vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
 999         /* t1 = B * (A - x3) */
1000         vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1001         /* t4 = B * (A - x3) - y1^4 = y3 */
1002         vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
1003 
1004         vli_set(x1, z1, ndigits);
1005         vli_set(z1, y1, ndigits);
1006         vli_set(y1, t4, ndigits);
1007 }
1008 
1009 /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1010 static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
1011                     unsigned int ndigits)
1012 {
1013         u64 t1[ECC_MAX_DIGITS];
1014 
1015         vli_mod_square_fast(t1, z, curve_prime, ndigits);    /* z^2 */
1016         vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
1017         vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits);  /* z^3 */
1018         vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */
1019 }
1020 
1021 /* P = (x1, y1) => 2P, (x2, y2) => P' */
1022 static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1023                                 u64 *p_initial_z, u64 *curve_prime,
1024                                 unsigned int ndigits)
1025 {
1026         u64 z[ECC_MAX_DIGITS];
1027 
1028         vli_set(x2, x1, ndigits);
1029         vli_set(y2, y1, ndigits);
1030 
1031         vli_clear(z, ndigits);
1032         z[0] = 1;
1033 
1034         if (p_initial_z)
1035                 vli_set(z, p_initial_z, ndigits);
1036 
1037         apply_z(x1, y1, z, curve_prime, ndigits);
1038 
1039         ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
1040 
1041         apply_z(x2, y2, z, curve_prime, ndigits);
1042 }
1043 
1044 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1045  * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
1046  * or P => P', Q => P + Q
1047  */
1048 static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
1049                      unsigned int ndigits)
1050 {
1051         /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1052         u64 t5[ECC_MAX_DIGITS];
1053 
1054         /* t5 = x2 - x1 */
1055         vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1056         /* t5 = (x2 - x1)^2 = A */
1057         vli_mod_square_fast(t5, t5, curve_prime, ndigits);
1058         /* t1 = x1*A = B */
1059         vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1060         /* t3 = x2*A = C */
1061         vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
1062         /* t4 = y2 - y1 */
1063         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1064         /* t5 = (y2 - y1)^2 = D */
1065         vli_mod_square_fast(t5, y2, curve_prime, ndigits);
1066 
1067         /* t5 = D - B */
1068         vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
1069         /* t5 = D - B - C = x3 */
1070         vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
1071         /* t3 = C - B */
1072         vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
1073         /* t2 = y1*(C - B) */
1074         vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
1075         /* t3 = B - x3 */
1076         vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
1077         /* t4 = (y2 - y1)*(B - x3) */
1078         vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
1079         /* t4 = y3 */
1080         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1081 
1082         vli_set(x2, t5, ndigits);
1083 }
1084 
1085 /* Input P = (x1, y1, Z), Q = (x2, y2, Z)
1086  * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
1087  * or P => P - Q, Q => P + Q
1088  */
1089 static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
1090                        unsigned int ndigits)
1091 {
1092         /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1093         u64 t5[ECC_MAX_DIGITS];
1094         u64 t6[ECC_MAX_DIGITS];
1095         u64 t7[ECC_MAX_DIGITS];
1096 
1097         /* t5 = x2 - x1 */
1098         vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
1099         /* t5 = (x2 - x1)^2 = A */
1100         vli_mod_square_fast(t5, t5, curve_prime, ndigits);
1101         /* t1 = x1*A = B */
1102         vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
1103         /* t3 = x2*A = C */
1104         vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
1105         /* t4 = y2 + y1 */
1106         vli_mod_add(t5, y2, y1, curve_prime, ndigits);
1107         /* t4 = y2 - y1 */
1108         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1109 
1110         /* t6 = C - B */
1111         vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
1112         /* t2 = y1 * (C - B) */
1113         vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
1114         /* t6 = B + C */
1115         vli_mod_add(t6, x1, x2, curve_prime, ndigits);
1116         /* t3 = (y2 - y1)^2 */
1117         vli_mod_square_fast(x2, y2, curve_prime, ndigits);
1118         /* t3 = x3 */
1119         vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
1120 
1121         /* t7 = B - x3 */
1122         vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
1123         /* t4 = (y2 - y1)*(B - x3) */
1124         vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
1125         /* t4 = y3 */
1126         vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
1127 
1128         /* t7 = (y2 + y1)^2 = F */
1129         vli_mod_square_fast(t7, t5, curve_prime, ndigits);
1130         /* t7 = x3' */
1131         vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
1132         /* t6 = x3' - B */
1133         vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
1134         /* t6 = (y2 + y1)*(x3' - B) */
1135         vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
1136         /* t2 = y3' */
1137         vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
1138 
1139         vli_set(x1, t7, ndigits);
1140 }
1141 
1142 static void ecc_point_mult(struct ecc_point *result,
1143                            const struct ecc_point *point, const u64 *scalar,
1144                            u64 *initial_z, const struct ecc_curve *curve,
1145                            unsigned int ndigits)
1146 {
1147         /* R0 and R1 */
1148         u64 rx[2][ECC_MAX_DIGITS];
1149         u64 ry[2][ECC_MAX_DIGITS];
1150         u64 z[ECC_MAX_DIGITS];
1151         u64 sk[2][ECC_MAX_DIGITS];
1152         u64 *curve_prime = curve->p;
1153         int i, nb;
1154         int num_bits;
1155         int carry;
1156 
1157         carry = vli_add(sk[0], scalar, curve->n, ndigits);
1158         vli_add(sk[1], sk[0], curve->n, ndigits);
1159         scalar = sk[!carry];
1160         num_bits = sizeof(u64) * ndigits * 8 + 1;
1161 
1162         vli_set(rx[1], point->x, ndigits);
1163         vli_set(ry[1], point->y, ndigits);
1164 
1165         xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
1166                             ndigits);
1167 
1168         for (i = num_bits - 2; i > 0; i--) {
1169                 nb = !vli_test_bit(scalar, i);
1170                 xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
1171                            ndigits);
1172                 xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
1173                          ndigits);
1174         }
1175 
1176         nb = !vli_test_bit(scalar, 0);
1177         xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
1178                    ndigits);
1179 
1180         /* Find final 1/Z value. */
1181         /* X1 - X0 */
1182         vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
1183         /* Yb * (X1 - X0) */
1184         vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
1185         /* xP * Yb * (X1 - X0) */
1186         vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
1187 
1188         /* 1 / (xP * Yb * (X1 - X0)) */
1189         vli_mod_inv(z, z, curve_prime, point->ndigits);
1190 
1191         /* yP / (xP * Yb * (X1 - X0)) */
1192         vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
1193         /* Xb * yP / (xP * Yb * (X1 - X0)) */
1194         vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
1195         /* End 1/Z calculation */
1196 
1197         xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
1198 
1199         apply_z(rx[0], ry[0], z, curve_prime, ndigits);
1200 
1201         vli_set(result->x, rx[0], ndigits);
1202         vli_set(result->y, ry[0], ndigits);
1203 }
1204 
1205 /* Computes R = P + Q mod p */
1206 static void ecc_point_add(const struct ecc_point *result,
1207                    const struct ecc_point *p, const struct ecc_point *q,
1208                    const struct ecc_curve *curve)
1209 {
1210         u64 z[ECC_MAX_DIGITS];
1211         u64 px[ECC_MAX_DIGITS];
1212         u64 py[ECC_MAX_DIGITS];
1213         unsigned int ndigits = curve->g.ndigits;
1214 
1215         vli_set(result->x, q->x, ndigits);
1216         vli_set(result->y, q->y, ndigits);
1217         vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
1218         vli_set(px, p->x, ndigits);
1219         vli_set(py, p->y, ndigits);
1220         xycz_add(px, py, result->x, result->y, curve->p, ndigits);
1221         vli_mod_inv(z, z, curve->p, ndigits);
1222         apply_z(result->x, result->y, z, curve->p, ndigits);
1223 }
1224 
1225 /* Computes R = u1P + u2Q mod p using Shamir's trick.
1226  * Based on: Kenneth MacKay's micro-ecc (2014).
1227  */
1228 void ecc_point_mult_shamir(const struct ecc_point *result,
1229                            const u64 *u1, const struct ecc_point *p,
1230                            const u64 *u2, const struct ecc_point *q,
1231                            const struct ecc_curve *curve)
1232 {
1233         u64 z[ECC_MAX_DIGITS];
1234         u64 sump[2][ECC_MAX_DIGITS];
1235         u64 *rx = result->x;
1236         u64 *ry = result->y;
1237         unsigned int ndigits = curve->g.ndigits;
1238         unsigned int num_bits;
1239         struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
1240         const struct ecc_point *points[4];
1241         const struct ecc_point *point;
1242         unsigned int idx;
1243         int i;
1244 
1245         ecc_point_add(&sum, p, q, curve);
1246         points[0] = NULL;
1247         points[1] = p;
1248         points[2] = q;
1249         points[3] = &sum;
1250 
1251         num_bits = max(vli_num_bits(u1, ndigits),
1252                        vli_num_bits(u2, ndigits));
1253         i = num_bits - 1;
1254         idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1255         point = points[idx];
1256 
1257         vli_set(rx, point->x, ndigits);
1258         vli_set(ry, point->y, ndigits);
1259         vli_clear(z + 1, ndigits - 1);
1260         z[0] = 1;
1261 
1262         for (--i; i >= 0; i--) {
1263                 ecc_point_double_jacobian(rx, ry, z, curve->p, ndigits);
1264                 idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
1265                 point = points[idx];
1266                 if (point) {
1267                         u64 tx[ECC_MAX_DIGITS];
1268                         u64 ty[ECC_MAX_DIGITS];
1269                         u64 tz[ECC_MAX_DIGITS];
1270 
1271                         vli_set(tx, point->x, ndigits);
1272                         vli_set(ty, point->y, ndigits);
1273                         apply_z(tx, ty, z, curve->p, ndigits);
1274                         vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1275                         xycz_add(tx, ty, rx, ry, curve->p, ndigits);
1276                         vli_mod_mult_fast(z, z, tz, curve->p, ndigits);
1277                 }
1278         }
1279         vli_mod_inv(z, z, curve->p, ndigits);
1280         apply_z(rx, ry, z, curve->p, ndigits);
1281 }
1282 EXPORT_SYMBOL(ecc_point_mult_shamir);
1283 
1284 static inline void ecc_swap_digits(const u64 *in, u64 *out,
1285                                    unsigned int ndigits)
1286 {
1287         const __be64 *src = (__force __be64 *)in;
1288         int i;
1289 
1290         for (i = 0; i < ndigits; i++)
1291                 out[i] = be64_to_cpu(src[ndigits - 1 - i]);
1292 }
1293 
1294 static int __ecc_is_key_valid(const struct ecc_curve *curve,
1295                               const u64 *private_key, unsigned int ndigits)
1296 {
1297         u64 one[ECC_MAX_DIGITS] = { 1, };
1298         u64 res[ECC_MAX_DIGITS];
1299 
1300         if (!private_key)
1301                 return -EINVAL;
1302 
1303         if (curve->g.ndigits != ndigits)
1304                 return -EINVAL;
1305 
1306         /* Make sure the private key is in the range [2, n-3]. */
1307         if (vli_cmp(one, private_key, ndigits) != -1)
1308                 return -EINVAL;
1309         vli_sub(res, curve->n, one, ndigits);
1310         vli_sub(res, res, one, ndigits);
1311         if (vli_cmp(res, private_key, ndigits) != 1)
1312                 return -EINVAL;
1313 
1314         return 0;
1315 }
1316 
1317 int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
1318                      const u64 *private_key, unsigned int private_key_len)
1319 {
1320         int nbytes;
1321         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1322 
1323         nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1324 
1325         if (private_key_len != nbytes)
1326                 return -EINVAL;
1327 
1328         return __ecc_is_key_valid(curve, private_key, ndigits);
1329 }
1330 EXPORT_SYMBOL(ecc_is_key_valid);
1331 
1332 /*
1333  * ECC private keys are generated using the method of extra random bits,
1334  * equivalent to that described in FIPS 186-4, Appendix B.4.1.
1335  *
1336  * d = (c mod(n–1)) + 1    where c is a string of random bits, 64 bits longer
1337  *                         than requested
1338  * 0 <= c mod(n-1) <= n-2  and implies that
1339  * 1 <= d <= n-1
1340  *
1341  * This method generates a private key uniformly distributed in the range
1342  * [1, n-1].
1343  */
1344 int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
1345 {
1346         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1347         u64 priv[ECC_MAX_DIGITS];
1348         unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1349         unsigned int nbits = vli_num_bits(curve->n, ndigits);
1350         int err;
1351 
1352         /* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */
1353         if (nbits < 160 || ndigits > ARRAY_SIZE(priv))
1354                 return -EINVAL;
1355 
1356         /*
1357          * FIPS 186-4 recommends that the private key should be obtained from a
1358          * RBG with a security strength equal to or greater than the security
1359          * strength associated with N.
1360          *
1361          * The maximum security strength identified by NIST SP800-57pt1r4 for
1362          * ECC is 256 (N >= 512).
1363          *
1364          * This condition is met by the default RNG because it selects a favored
1365          * DRBG with a security strength of 256.
1366          */
1367         if (crypto_get_default_rng())
1368                 return -EFAULT;
1369 
1370         err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
1371         crypto_put_default_rng();
1372         if (err)
1373                 return err;
1374 
1375         /* Make sure the private key is in the valid range. */
1376         if (__ecc_is_key_valid(curve, priv, ndigits))
1377                 return -EINVAL;
1378 
1379         ecc_swap_digits(priv, privkey, ndigits);
1380 
1381         return 0;
1382 }
1383 EXPORT_SYMBOL(ecc_gen_privkey);
1384 
1385 int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
1386                      const u64 *private_key, u64 *public_key)
1387 {
1388         int ret = 0;
1389         struct ecc_point *pk;
1390         u64 priv[ECC_MAX_DIGITS];
1391         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1392 
1393         if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {
1394                 ret = -EINVAL;
1395                 goto out;
1396         }
1397 
1398         ecc_swap_digits(private_key, priv, ndigits);
1399 
1400         pk = ecc_alloc_point(ndigits);
1401         if (!pk) {
1402                 ret = -ENOMEM;
1403                 goto out;
1404         }
1405 
1406         ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1407         if (ecc_point_is_zero(pk)) {
1408                 ret = -EAGAIN;
1409                 goto err_free_point;
1410         }
1411 
1412         ecc_swap_digits(pk->x, public_key, ndigits);
1413         ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1414 
1415 err_free_point:
1416         ecc_free_point(pk);
1417 out:
1418         return ret;
1419 }
1420 EXPORT_SYMBOL(ecc_make_pub_key);
1421 
1422 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1423 int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
1424                                 struct ecc_point *pk)
1425 {
1426         u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
1427 
1428         if (WARN_ON(pk->ndigits != curve->g.ndigits))
1429                 return -EINVAL;
1430 
1431         /* Check 1: Verify key is not the zero point. */
1432         if (ecc_point_is_zero(pk))
1433                 return -EINVAL;
1434 
1435         /* Check 2: Verify key is in the range [1, p-1]. */
1436         if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
1437                 return -EINVAL;
1438         if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
1439                 return -EINVAL;
1440 
1441         /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1442         vli_mod_square_fast(yy, pk->y, curve->p, pk->ndigits); /* y^2 */
1443         vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */
1444         vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */
1445         vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* a·x */
1446         vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
1447         vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
1448         if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
1449                 return -EINVAL;
1450 
1451         return 0;
1452 }
1453 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1454 
1455 int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1456                               const u64 *private_key, const u64 *public_key,
1457                               u64 *secret)
1458 {
1459         int ret = 0;
1460         struct ecc_point *product, *pk;
1461         u64 priv[ECC_MAX_DIGITS];
1462         u64 rand_z[ECC_MAX_DIGITS];
1463         unsigned int nbytes;
1464         const struct ecc_curve *curve = ecc_get_curve(curve_id);
1465 
1466         if (!private_key || !public_key || !curve ||
1467             ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1468                 ret = -EINVAL;
1469                 goto out;
1470         }
1471 
1472         nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1473 
1474         get_random_bytes(rand_z, nbytes);
1475 
1476         pk = ecc_alloc_point(ndigits);
1477         if (!pk) {
1478                 ret = -ENOMEM;
1479                 goto out;
1480         }
1481 
1482         ecc_swap_digits(public_key, pk->x, ndigits);
1483         ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
1484         ret = ecc_is_pubkey_valid_partial(curve, pk);
1485         if (ret)
1486                 goto err_alloc_product;
1487 
1488         ecc_swap_digits(private_key, priv, ndigits);
1489 
1490         product = ecc_alloc_point(ndigits);
1491         if (!product) {
1492                 ret = -ENOMEM;
1493                 goto err_alloc_product;
1494         }
1495 
1496         ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1497 
1498         ecc_swap_digits(product->x, secret, ndigits);
1499 
1500         if (ecc_point_is_zero(product))
1501                 ret = -EFAULT;
1502 
1503         ecc_free_point(product);
1504 err_alloc_product:
1505         ecc_free_point(pk);
1506 out:
1507         return ret;
1508 }
1509 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
1510 
1511 MODULE_LICENSE("Dual BSD/GPL");
/* [<][>][^][v][top][bottom][index][help] */
root/crypto/ecc.c

DEFINITIONS
