bn_lib.c 21.7 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984
/*
 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the OpenSSL license (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#include <assert.h>
#include <limits.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
#include <openssl/opensslconf.h>
#include "internal/constant_time_locl.h"

/* This stuff appears to be completely unused, so is deprecated */
#if OPENSSL_API_COMPAT < 0x00908000L
/*-
 * For a 32 bit machine
 * 2 -   4 ==  128
 * 3 -   8 ==  256
 * 4 -  16 ==  512
 * 5 -  32 == 1024
 * 6 -  64 == 2048
 * 7 - 128 == 4096
 * 8 - 256 == 8192
 */
static int bn_limit_bits = 0;
static int bn_limit_num = 8;    /* (1<<bn_limit_bits) */
static int bn_limit_bits_low = 0;
static int bn_limit_num_low = 8; /* (1<<bn_limit_bits_low) */
static int bn_limit_bits_high = 0;
static int bn_limit_num_high = 8; /* (1<<bn_limit_bits_high) */
static int bn_limit_bits_mont = 0;
static int bn_limit_num_mont = 8; /* (1<<bn_limit_bits_mont) */

void BN_set_params(int mult, int high, int low, int mont)
{
    if (mult >= 0) {
        if (mult > (int)(sizeof(int) * 8) - 1)
            mult = sizeof(int) * 8 - 1;
        bn_limit_bits = mult;
        bn_limit_num = 1 << mult;
    }
    if (high >= 0) {
        if (high > (int)(sizeof(int) * 8) - 1)
            high = sizeof(int) * 8 - 1;
        bn_limit_bits_high = high;
        bn_limit_num_high = 1 << high;
    }
    if (low >= 0) {
        if (low > (int)(sizeof(int) * 8) - 1)
            low = sizeof(int) * 8 - 1;
        bn_limit_bits_low = low;
        bn_limit_num_low = 1 << low;
    }
    if (mont >= 0) {
        if (mont > (int)(sizeof(int) * 8) - 1)
            mont = sizeof(int) * 8 - 1;
        bn_limit_bits_mont = mont;
        bn_limit_num_mont = 1 << mont;
    }
}

int BN_get_params(int which)
{
    if (which == 0)
        return bn_limit_bits;
    else if (which == 1)
        return bn_limit_bits_high;
    else if (which == 2)
        return bn_limit_bits_low;
    else if (which == 3)
        return bn_limit_bits_mont;
    else
        return 0;
}
#endif

const BIGNUM *BN_value_one(void)
{
    static const BN_ULONG data_one = 1L;
    static const BIGNUM const_one =
        { (BN_ULONG *)&data_one, 1, 1, 0, BN_FLG_STATIC_DATA };

    return &const_one;
}

int BN_num_bits_word(BN_ULONG l)
{
    BN_ULONG x, mask;
    int bits = (l != 0);

#if BN_BITS2 > 32
    x = l >> 32;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 32 & mask;
    l ^= (x ^ l) & mask;
#endif

    x = l >> 16;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 16 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 8;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 8 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 4;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 4 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 2;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 2 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 1;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 1 & mask;

    return bits;
}

int BN_num_bits(const BIGNUM *a)
{
    int i = a->top - 1;
    bn_check_top(a);

    if (BN_is_zero(a))
        return 0;
    return ((i * BN_BITS2) + BN_num_bits_word(a->d[i]));
}

static void bn_free_d(BIGNUM *a)
{
    if (BN_get_flags(a, BN_FLG_SECURE))
        OPENSSL_secure_free(a->d);
    else
        OPENSSL_free(a->d);
}


void BN_clear_free(BIGNUM *a)
{
    if (a == NULL)
        return;
    if (a->d != NULL && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
        OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0]));
        bn_free_d(a);
    }
    if (BN_get_flags(a, BN_FLG_MALLOCED)) {
        OPENSSL_cleanse(a, sizeof(*a));
        OPENSSL_free(a);
    }
}

void BN_free(BIGNUM *a)
{
    if (a == NULL)
        return;
    if (!BN_get_flags(a, BN_FLG_STATIC_DATA))
        bn_free_d(a);
    if (a->flags & BN_FLG_MALLOCED)
        OPENSSL_free(a);
}

void bn_init(BIGNUM *a)
{
    static BIGNUM nilbn;

    *a = nilbn;
    bn_check_top(a);
}

BIGNUM *BN_new(void)
{
    BIGNUM *ret;

    if ((ret = OPENSSL_zalloc(sizeof(*ret))) == NULL) {
        BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE);
        return NULL;
    }
    ret->flags = BN_FLG_MALLOCED;
    bn_check_top(ret);
    return ret;
}

 BIGNUM *BN_secure_new(void)
 {
     BIGNUM *ret = BN_new();
     if (ret != NULL)
         ret->flags |= BN_FLG_SECURE;
     return ret;
 }

/* This is used by bn_expand2() */
/* The caller MUST check that words > b->dmax before calling this */
static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
{
    BN_ULONG *a = NULL;

    if (words > (INT_MAX / (4 * BN_BITS2))) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_BIGNUM_TOO_LONG);
        return NULL;
    }
    if (BN_get_flags(b, BN_FLG_STATIC_DATA)) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
        return NULL;
    }
    if (BN_get_flags(b, BN_FLG_SECURE))
        a = OPENSSL_secure_zalloc(words * sizeof(*a));
    else
        a = OPENSSL_zalloc(words * sizeof(*a));
    if (a == NULL) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE);
        return NULL;
    }

    assert(b->top <= words);
    if (b->top > 0)
        memcpy(a, b->d, sizeof(*a) * b->top);

    return a;
}

/*
 * This is an internal function that should not be used in applications. It
 * ensures that 'b' has enough room for a 'words' word number and initialises
 * any unused part of b->d with leading zeros. It is mostly used by the
 * various BIGNUM routines. If there is an error, NULL is returned. If not,
 * 'b' is returned.
 */

BIGNUM *bn_expand2(BIGNUM *b, int words)
{
    if (words > b->dmax) {
        BN_ULONG *a = bn_expand_internal(b, words);
        if (!a)
            return NULL;
        if (b->d) {
            OPENSSL_cleanse(b->d, b->dmax * sizeof(b->d[0]));
            bn_free_d(b);
        }
        b->d = a;
        b->dmax = words;
    }

    return b;
}

BIGNUM *BN_dup(const BIGNUM *a)
{
    BIGNUM *t;

    if (a == NULL)
        return NULL;
    bn_check_top(a);

    t = BN_get_flags(a, BN_FLG_SECURE) ? BN_secure_new() : BN_new();
    if (t == NULL)
        return NULL;
    if (!BN_copy(t, a)) {
        BN_free(t);
        return NULL;
    }
    bn_check_top(t);
    return t;
}

BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
{
    bn_check_top(b);

    if (a == b)
        return a;
    if (bn_wexpand(a, b->top) == NULL)
        return NULL;

    if (b->top > 0)
        memcpy(a->d, b->d, sizeof(b->d[0]) * b->top);

    a->neg = b->neg;
    a->top = b->top;
    a->flags |= b->flags & BN_FLG_FIXED_TOP;
    bn_check_top(a);
    return a;
}

#define FLAGS_DATA(flags) ((flags) & (BN_FLG_STATIC_DATA \
                                    | BN_FLG_CONSTTIME   \
                                    | BN_FLG_SECURE      \
                                    | BN_FLG_FIXED_TOP))
#define FLAGS_STRUCT(flags) ((flags) & (BN_FLG_MALLOCED))

void BN_swap(BIGNUM *a, BIGNUM *b)
{
    int flags_old_a, flags_old_b;
    BN_ULONG *tmp_d;
    int tmp_top, tmp_dmax, tmp_neg;

    bn_check_top(a);
    bn_check_top(b);

    flags_old_a = a->flags;
    flags_old_b = b->flags;

    tmp_d = a->d;
    tmp_top = a->top;
    tmp_dmax = a->dmax;
    tmp_neg = a->neg;

    a->d = b->d;
    a->top = b->top;
    a->dmax = b->dmax;
    a->neg = b->neg;

    b->d = tmp_d;
    b->top = tmp_top;
    b->dmax = tmp_dmax;
    b->neg = tmp_neg;

    a->flags = FLAGS_STRUCT(flags_old_a) | FLAGS_DATA(flags_old_b);
    b->flags = FLAGS_STRUCT(flags_old_b) | FLAGS_DATA(flags_old_a);
    bn_check_top(a);
    bn_check_top(b);
}

void BN_clear(BIGNUM *a)
{
    bn_check_top(a);
    if (a->d != NULL)
        OPENSSL_cleanse(a->d, sizeof(*a->d) * a->dmax);
    a->neg = 0;
    a->top = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
}

BN_ULONG BN_get_word(const BIGNUM *a)
{
    if (a->top > 1)
        return BN_MASK2;
    else if (a->top == 1)
        return a->d[0];
    /* a->top == 0 */
    return 0;
}

int BN_set_word(BIGNUM *a, BN_ULONG w)
{
    bn_check_top(a);
    if (bn_expand(a, (int)sizeof(BN_ULONG) * 8) == NULL)
        return 0;
    a->neg = 0;
    a->d[0] = w;
    a->top = (w ? 1 : 0);
    a->flags &= ~BN_FLG_FIXED_TOP;
    bn_check_top(a);
    return 1;
}

BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
    unsigned int i, m;
    unsigned int n;
    BN_ULONG l;
    BIGNUM *bn = NULL;

    if (ret == NULL)
        ret = bn = BN_new();
    if (ret == NULL)
        return NULL;
    bn_check_top(ret);
    /* Skip leading zero's. */
    for ( ; len > 0 && *s == 0; s++, len--)
        continue;
    n = len;
    if (n == 0) {
        ret->top = 0;
        return ret;
    }
    i = ((n - 1) / BN_BYTES) + 1;
    m = ((n - 1) % (BN_BYTES));
    if (bn_wexpand(ret, (int)i) == NULL) {
        BN_free(bn);
        return NULL;
    }
    ret->top = i;
    ret->neg = 0;
    l = 0;
    while (n--) {
        l = (l << 8L) | *(s++);
        if (m-- == 0) {
            ret->d[--i] = l;
            l = 0;
            m = BN_BYTES - 1;
        }
    }
    /*
     * need to call this due to clear byte at top if avoiding having the top
     * bit set (-ve number)
     */
    bn_correct_top(ret);
    return ret;
}

/* ignore negative */
static int bn2binpad(const BIGNUM *a, unsigned char *to, int tolen)
{
    int n;
    size_t i, lasti, j, atop, mask;
    BN_ULONG l;

    /*
     * In case |a| is fixed-top, BN_num_bytes can return bogus length,
     * but it's assumed that fixed-top inputs ought to be "nominated"
     * even for padded output, so it works out...
     */
    n = BN_num_bytes(a);
    if (tolen == -1) {
        tolen = n;
    } else if (tolen < n) {     /* uncommon/unlike case */
        BIGNUM temp = *a;

        bn_correct_top(&temp);
        n = BN_num_bytes(&temp);
        if (tolen < n)
            return -1;
    }

    /* Swipe through whole available data and don't give away padded zero. */
    atop = a->dmax * BN_BYTES;
    if (atop == 0) {
        OPENSSL_cleanse(to, tolen);
        return tolen;
    }

    lasti = atop - 1;
    atop = a->top * BN_BYTES;
    for (i = 0, j = 0, to += tolen; j < (size_t)tolen; j++) {
        l = a->d[i / BN_BYTES];
        mask = 0 - ((j - atop) >> (8 * sizeof(i) - 1));
        *--to = (unsigned char)(l >> (8 * (i % BN_BYTES)) & mask);
        i += (i - lasti) >> (8 * sizeof(i) - 1); /* stay on last limb */
    }

    return tolen;
}

int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen)
{
    if (tolen < 0)
        return -1;
    return bn2binpad(a, to, tolen);
}

int BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
    return bn2binpad(a, to, -1);
}

BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
    unsigned int i, m;
    unsigned int n;
    BN_ULONG l;
    BIGNUM *bn = NULL;

    if (ret == NULL)
        ret = bn = BN_new();
    if (ret == NULL)
        return NULL;
    bn_check_top(ret);
    s += len;
    /* Skip trailing zeroes. */
    for ( ; len > 0 && s[-1] == 0; s--, len--)
        continue;
    n = len;
    if (n == 0) {
        ret->top = 0;
        return ret;
    }
    i = ((n - 1) / BN_BYTES) + 1;
    m = ((n - 1) % (BN_BYTES));
    if (bn_wexpand(ret, (int)i) == NULL) {
        BN_free(bn);
        return NULL;
    }
    ret->top = i;
    ret->neg = 0;
    l = 0;
    while (n--) {
        s--;
        l = (l << 8L) | *s;
        if (m-- == 0) {
            ret->d[--i] = l;
            l = 0;
            m = BN_BYTES - 1;
        }
    }
    /*
     * need to call this due to clear byte at top if avoiding having the top
     * bit set (-ve number)
     */
    bn_correct_top(ret);
    return ret;
}

int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen)
{
    int i;
    BN_ULONG l;
    bn_check_top(a);
    i = BN_num_bytes(a);
    if (tolen < i)
        return -1;
    /* Add trailing zeroes if necessary */
    if (tolen > i)
        memset(to + i, 0, tolen - i);
    to += i;
    while (i--) {
        l = a->d[i / BN_BYTES];
        to--;
        *to = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
    }
    return tolen;
}

int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
{
    int i;
    BN_ULONG t1, t2, *ap, *bp;

    bn_check_top(a);
    bn_check_top(b);

    i = a->top - b->top;
    if (i != 0)
        return i;
    ap = a->d;
    bp = b->d;
    for (i = a->top - 1; i >= 0; i--) {
        t1 = ap[i];
        t2 = bp[i];
        if (t1 != t2)
            return ((t1 > t2) ? 1 : -1);
    }
    return 0;
}

int BN_cmp(const BIGNUM *a, const BIGNUM *b)
{
    int i;
    int gt, lt;
    BN_ULONG t1, t2;

    if ((a == NULL) || (b == NULL)) {
        if (a != NULL)
            return -1;
        else if (b != NULL)
            return 1;
        else
            return 0;
    }

    bn_check_top(a);
    bn_check_top(b);

    if (a->neg != b->neg) {
        if (a->neg)
            return -1;
        else
            return 1;
    }
    if (a->neg == 0) {
        gt = 1;
        lt = -1;
    } else {
        gt = -1;
        lt = 1;
    }

    if (a->top > b->top)
        return gt;
    if (a->top < b->top)
        return lt;
    for (i = a->top - 1; i >= 0; i--) {
        t1 = a->d[i];
        t2 = b->d[i];
        if (t1 > t2)
            return gt;
        if (t1 < t2)
            return lt;
    }
    return 0;
}

int BN_set_bit(BIGNUM *a, int n)
{
    int i, j, k;

    if (n < 0)
        return 0;

    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i) {
        if (bn_wexpand(a, i + 1) == NULL)
            return 0;
        for (k = a->top; k < i + 1; k++)
            a->d[k] = 0;
        a->top = i + 1;
        a->flags &= ~BN_FLG_FIXED_TOP;
    }

    a->d[i] |= (((BN_ULONG)1) << j);
    bn_check_top(a);
    return 1;
}

int BN_clear_bit(BIGNUM *a, int n)
{
    int i, j;

    bn_check_top(a);
    if (n < 0)
        return 0;

    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i)
        return 0;

    a->d[i] &= (~(((BN_ULONG)1) << j));
    bn_correct_top(a);
    return 1;
}

int BN_is_bit_set(const BIGNUM *a, int n)
{
    int i, j;

    bn_check_top(a);
    if (n < 0)
        return 0;
    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i)
        return 0;
    return (int)(((a->d[i]) >> j) & ((BN_ULONG)1));
}

int BN_mask_bits(BIGNUM *a, int n)
{
    int b, w;

    bn_check_top(a);
    if (n < 0)
        return 0;

    w = n / BN_BITS2;
    b = n % BN_BITS2;
    if (w >= a->top)
        return 0;
    if (b == 0)
        a->top = w;
    else {
        a->top = w + 1;
        a->d[w] &= ~(BN_MASK2 << b);
    }
    bn_correct_top(a);
    return 1;
}

void BN_set_negative(BIGNUM *a, int b)
{
    if (b && !BN_is_zero(a))
        a->neg = 1;
    else
        a->neg = 0;
}

int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
{
    int i;
    BN_ULONG aa, bb;

    aa = a[n - 1];
    bb = b[n - 1];
    if (aa != bb)
        return ((aa > bb) ? 1 : -1);
    for (i = n - 2; i >= 0; i--) {
        aa = a[i];
        bb = b[i];
        if (aa != bb)
            return ((aa > bb) ? 1 : -1);
    }
    return 0;
}

/*
 * Here follows a specialised variants of bn_cmp_words().  It has the
 * capability of performing the operation on arrays of different sizes. The
 * sizes of those arrays is expressed through cl, which is the common length
 * ( basically, min(len(a),len(b)) ), and dl, which is the delta between the
 * two lengths, calculated as len(a)-len(b). All lengths are the number of
 * BN_ULONGs...
 */

int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl)
{
    int n, i;
    n = cl - 1;

    if (dl < 0) {
        for (i = dl; i < 0; i++) {
            if (b[n - i] != 0)
                return -1;      /* a < b */
        }
    }
    if (dl > 0) {
        for (i = dl; i > 0; i--) {
            if (a[n + i] != 0)
                return 1;       /* a > b */
        }
    }
    return bn_cmp_words(a, b, cl);
}

/*
 * Constant-time conditional swap of a and b.
 * a and b are swapped if condition is not 0.  The code assumes that at most one bit of condition is set.
 * nwords is the number of words to swap.  The code assumes that at least nwords are allocated in both a and b,
 * and that no more than nwords are used by either a or b.
 * a and b cannot be the same number
 */
void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
{
    BN_ULONG t;
    int i;

    bn_wcheck_size(a, nwords);
    bn_wcheck_size(b, nwords);

    assert(a != b);
    assert((condition & (condition - 1)) == 0);
    assert(sizeof(BN_ULONG) >= sizeof(int));

    condition = ((condition - 1) >> (BN_BITS2 - 1)) - 1;

    t = (a->top ^ b->top) & condition;
    a->top ^= t;
    b->top ^= t;

    t = (a->neg ^ b->neg) & condition;
    a->neg ^= t;
    b->neg ^= t;

    /*-
     * Idea behind BN_FLG_STATIC_DATA is actually to
     * indicate that data may not be written to.
     * Intention is actually to treat it as it's
     * read-only data, and some (if not most) of it does
     * reside in read-only segment. In other words
     * observation of BN_FLG_STATIC_DATA in
     * BN_consttime_swap should be treated as fatal
     * condition. It would either cause SEGV or
     * effectively cause data corruption.
     * BN_FLG_MALLOCED refers to BN structure itself,
     * and hence must be preserved. Remaining flags are
     * BN_FLG_CONSTIME and BN_FLG_SECURE. Latter must be
     * preserved, because it determines how x->d was
     * allocated and hence how to free it. This leaves
     * BN_FLG_CONSTTIME that one can do something about.
     * To summarize it's sufficient to mask and swap
     * BN_FLG_CONSTTIME alone. BN_FLG_STATIC_DATA should
     * be treated as fatal.
     */
    t = ((a->flags ^ b->flags) & BN_FLG_CONSTTIME) & condition;
    a->flags ^= t;
    b->flags ^= t;

#define BN_CONSTTIME_SWAP(ind) \
        do { \
                t = (a->d[ind] ^ b->d[ind]) & condition; \
                a->d[ind] ^= t; \
                b->d[ind] ^= t; \
        } while (0)

    switch (nwords) {
    default:
        for (i = 10; i < nwords; i++)
            BN_CONSTTIME_SWAP(i);
        /* Fallthrough */
    case 10:
        BN_CONSTTIME_SWAP(9);   /* Fallthrough */
    case 9:
        BN_CONSTTIME_SWAP(8);   /* Fallthrough */
    case 8:
        BN_CONSTTIME_SWAP(7);   /* Fallthrough */
    case 7:
        BN_CONSTTIME_SWAP(6);   /* Fallthrough */
    case 6:
        BN_CONSTTIME_SWAP(5);   /* Fallthrough */
    case 5:
        BN_CONSTTIME_SWAP(4);   /* Fallthrough */
    case 4:
        BN_CONSTTIME_SWAP(3);   /* Fallthrough */
    case 3:
        BN_CONSTTIME_SWAP(2);   /* Fallthrough */
    case 2:
        BN_CONSTTIME_SWAP(1);   /* Fallthrough */
    case 1:
        BN_CONSTTIME_SWAP(0);
    }
#undef BN_CONSTTIME_SWAP
}

/* Bits of security, see SP800-57 */

int BN_security_bits(int L, int N)
{
    int secbits, bits;
    if (L >= 15360)
        secbits = 256;
    else if (L >= 7680)
        secbits = 192;
    else if (L >= 3072)
        secbits = 128;
    else if (L >= 2048)
        secbits = 112;
    else if (L >= 1024)
        secbits = 80;
    else
        return 0;
    if (N == -1)
        return secbits;
    bits = N / 2;
    if (bits < 80)
        return 0;
    return bits >= secbits ? secbits : bits;
}

void BN_zero_ex(BIGNUM *a)
{
    a->neg = 0;
    a->top = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
}

int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w)
{
    return ((a->top == 1) && (a->d[0] == w)) || ((w == 0) && (a->top == 0));
}

int BN_is_zero(const BIGNUM *a)
{
    return a->top == 0;
}

int BN_is_one(const BIGNUM *a)
{
    return BN_abs_is_word(a, 1) && !a->neg;
}

int BN_is_word(const BIGNUM *a, const BN_ULONG w)
{
    return BN_abs_is_word(a, w) && (!w || !a->neg);
}

int BN_is_odd(const BIGNUM *a)
{
    return (a->top > 0) && (a->d[0] & 1);
}

int BN_is_negative(const BIGNUM *a)
{
    return (a->neg != 0);
}

int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
                     BN_CTX *ctx)
{
    return BN_mod_mul_montgomery(r, a, &(mont->RR), mont, ctx);
}

void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags)
{
    dest->d = b->d;
    dest->top = b->top;
    dest->dmax = b->dmax;
    dest->neg = b->neg;
    dest->flags = ((dest->flags & BN_FLG_MALLOCED)
                   | (b->flags & ~BN_FLG_MALLOCED)
                   | BN_FLG_STATIC_DATA | flags);
}

BN_GENCB *BN_GENCB_new(void)
{
    BN_GENCB *ret;

    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
        BNerr(BN_F_BN_GENCB_NEW, ERR_R_MALLOC_FAILURE);
        return NULL;
    }

    return ret;
}

void BN_GENCB_free(BN_GENCB *cb)
{
    if (cb == NULL)
        return;
    OPENSSL_free(cb);
}

void BN_set_flags(BIGNUM *b, int n)
{
    b->flags |= n;
}

int BN_get_flags(const BIGNUM *b, int n)
{
    return b->flags & n;
}

/* Populate a BN_GENCB structure with an "old"-style callback */
void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
                      void *cb_arg)
{
    BN_GENCB *tmp_gencb = gencb;
    tmp_gencb->ver = 1;
    tmp_gencb->arg = cb_arg;
    tmp_gencb->cb.cb_1 = callback;
}

/* Populate a BN_GENCB structure with a "new"-style callback */
void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
                  void *cb_arg)
{
    BN_GENCB *tmp_gencb = gencb;
    tmp_gencb->ver = 2;
    tmp_gencb->arg = cb_arg;
    tmp_gencb->cb.cb_2 = callback;
}

void *BN_GENCB_get_arg(BN_GENCB *cb)
{
    return cb->arg;
}

BIGNUM *bn_wexpand(BIGNUM *a, int words)
{
    return (words <= a->dmax) ? a : bn_expand2(a, words);
}

void bn_correct_top(BIGNUM *a)
{
    BN_ULONG *ftl;
    int tmp_top = a->top;

    if (tmp_top > 0) {
        for (ftl = &(a->d[tmp_top]); tmp_top > 0; tmp_top--) {
            ftl--;
            if (*ftl != 0)
                break;
        }
        a->top = tmp_top;
    }
    if (a->top == 0)
        a->neg = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
    bn_pollute(a);
}