linux/crypto/ecc.c
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   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
  36typedef struct {
  37        u64 m_low;
  38        u64 m_high;
  39} uint128_t;
  40
  41static 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
  54static 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
  64static void ecc_free_digits_space(u64 *space)
  65{
  66        kzfree(space);
  67}
  68
  69static 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
  88err_alloc_y:
  89        ecc_free_digits_space(p->x);
  90err_alloc_x:
  91        kfree(p);
  92        return NULL;
  93}
  94
  95static 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
 105static 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. */
 114static 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. */
 127static 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. */
 133static 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. */
 147static 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. */
 164static 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. */
 173static 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 */
 190static 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. */
 207static 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. */
 222static 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. */
 242static 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
 261static 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
 286static 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
 296static 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
 332static 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 */
 374static 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 */
 391static 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 */
 408static 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 */
 435static 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*/
 514static 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. */
 535static 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. */
 545static 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 */
 559static 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. */
 636static 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 */
 647static 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) */
 710static 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' */
 722static 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 */
 748static 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 */
 789static 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
 842static 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
 897static 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
 906int 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
 930int 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
 963err_free_point:
 964        ecc_free_point(pk);
 965out:
 966        return ret;
 967}
 968
 969int 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);
1014err_alloc_product:
1015        ecc_free_point(pk);
1016out:
1017        return ret;
1018}
1019