423 lines
12 KiB
C
423 lines
12 KiB
C
/*
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* Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <openssl/bn.h>
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#include "internal/cryptlib.h"
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#include "bn_lcl.h"
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/* The old slow way */
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#if 0
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int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
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BN_CTX *ctx)
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{
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int i, nm, nd;
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int ret = 0;
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BIGNUM *D;
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bn_check_top(m);
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bn_check_top(d);
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if (BN_is_zero(d)) {
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BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
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return (0);
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}
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if (BN_ucmp(m, d) < 0) {
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if (rem != NULL) {
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if (BN_copy(rem, m) == NULL)
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return (0);
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}
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if (dv != NULL)
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BN_zero(dv);
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return (1);
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}
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BN_CTX_start(ctx);
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D = BN_CTX_get(ctx);
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if (dv == NULL)
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dv = BN_CTX_get(ctx);
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if (rem == NULL)
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rem = BN_CTX_get(ctx);
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if (D == NULL || dv == NULL || rem == NULL)
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goto end;
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nd = BN_num_bits(d);
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nm = BN_num_bits(m);
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if (BN_copy(D, d) == NULL)
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goto end;
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if (BN_copy(rem, m) == NULL)
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goto end;
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/*
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* The next 2 are needed so we can do a dv->d[0]|=1 later since
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* BN_lshift1 will only work once there is a value :-)
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*/
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BN_zero(dv);
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if (bn_wexpand(dv, 1) == NULL)
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goto end;
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dv->top = 1;
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if (!BN_lshift(D, D, nm - nd))
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goto end;
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for (i = nm - nd; i >= 0; i--) {
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if (!BN_lshift1(dv, dv))
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goto end;
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if (BN_ucmp(rem, D) >= 0) {
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dv->d[0] |= 1;
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if (!BN_usub(rem, rem, D))
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goto end;
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}
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/* CAN IMPROVE (and have now :=) */
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if (!BN_rshift1(D, D))
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goto end;
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}
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rem->neg = BN_is_zero(rem) ? 0 : m->neg;
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dv->neg = m->neg ^ d->neg;
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ret = 1;
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end:
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BN_CTX_end(ctx);
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return (ret);
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}
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#else
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# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
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&& !defined(PEDANTIC) && !defined(BN_DIV3W)
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# if defined(__GNUC__) && __GNUC__>=2
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# if defined(__i386) || defined (__i386__)
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/*-
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* There were two reasons for implementing this template:
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* - GNU C generates a call to a function (__udivdi3 to be exact)
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* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
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* understand why...);
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* - divl doesn't only calculate quotient, but also leaves
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* remainder in %edx which we can definitely use here:-)
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*
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* <appro@fy.chalmers.se>
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*/
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# undef bn_div_words
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# define bn_div_words(n0,n1,d0) \
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({ asm volatile ( \
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"divl %4" \
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: "=a"(q), "=d"(rem) \
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: "a"(n1), "d"(n0), "r"(d0) \
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: "cc"); \
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q; \
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})
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# define REMAINDER_IS_ALREADY_CALCULATED
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# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
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/*
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* Same story here, but it's 128-bit by 64-bit division. Wow!
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* <appro@fy.chalmers.se>
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*/
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# undef bn_div_words
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# define bn_div_words(n0,n1,d0) \
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({ asm volatile ( \
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"divq %4" \
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: "=a"(q), "=d"(rem) \
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: "a"(n1), "d"(n0), "r"(d0) \
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: "cc"); \
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q; \
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})
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# define REMAINDER_IS_ALREADY_CALCULATED
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# endif /* __<cpu> */
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# endif /* __GNUC__ */
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# endif /* OPENSSL_NO_ASM */
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/*-
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* BN_div computes dv := num / divisor, rounding towards
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* zero, and sets up rm such that dv*divisor + rm = num holds.
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* Thus:
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* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
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* rm->neg == num->neg (unless the remainder is zero)
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* If 'dv' or 'rm' is NULL, the respective value is not returned.
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*/
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int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
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BN_CTX *ctx)
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{
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int norm_shift, i, loop;
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BIGNUM *tmp, wnum, *snum, *sdiv, *res;
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BN_ULONG *resp, *wnump;
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BN_ULONG d0, d1;
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int num_n, div_n;
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int no_branch = 0;
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/*
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* Invalid zero-padding would have particularly bad consequences so don't
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* just rely on bn_check_top() here (bn_check_top() works only for
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* BN_DEBUG builds)
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*/
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if ((num->top > 0 && num->d[num->top - 1] == 0) ||
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(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
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BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
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return 0;
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}
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bn_check_top(num);
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bn_check_top(divisor);
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if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
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|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
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no_branch = 1;
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}
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bn_check_top(dv);
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bn_check_top(rm);
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/*- bn_check_top(num); *//*
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* 'num' has been checked already
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*/
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/*- bn_check_top(divisor); *//*
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* 'divisor' has been checked already
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*/
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if (BN_is_zero(divisor)) {
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BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
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return (0);
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}
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if (!no_branch && BN_ucmp(num, divisor) < 0) {
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if (rm != NULL) {
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if (BN_copy(rm, num) == NULL)
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return (0);
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}
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if (dv != NULL)
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BN_zero(dv);
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return (1);
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}
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BN_CTX_start(ctx);
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tmp = BN_CTX_get(ctx);
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snum = BN_CTX_get(ctx);
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sdiv = BN_CTX_get(ctx);
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if (dv == NULL)
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res = BN_CTX_get(ctx);
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else
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res = dv;
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if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
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goto err;
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/* First we normalise the numbers */
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norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
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if (!(BN_lshift(sdiv, divisor, norm_shift)))
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goto err;
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sdiv->neg = 0;
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norm_shift += BN_BITS2;
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if (!(BN_lshift(snum, num, norm_shift)))
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goto err;
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snum->neg = 0;
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if (no_branch) {
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/*
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* Since we don't know whether snum is larger than sdiv, we pad snum
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* with enough zeroes without changing its value.
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*/
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if (snum->top <= sdiv->top + 1) {
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if (bn_wexpand(snum, sdiv->top + 2) == NULL)
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goto err;
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for (i = snum->top; i < sdiv->top + 2; i++)
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snum->d[i] = 0;
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snum->top = sdiv->top + 2;
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} else {
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if (bn_wexpand(snum, snum->top + 1) == NULL)
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goto err;
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snum->d[snum->top] = 0;
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snum->top++;
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}
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}
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div_n = sdiv->top;
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num_n = snum->top;
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loop = num_n - div_n;
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/*
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* Lets setup a 'window' into snum This is the part that corresponds to
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* the current 'area' being divided
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*/
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wnum.neg = 0;
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wnum.d = &(snum->d[loop]);
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wnum.top = div_n;
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/*
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* only needed when BN_ucmp messes up the values between top and max
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*/
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wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
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/* Get the top 2 words of sdiv */
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/* div_n=sdiv->top; */
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d0 = sdiv->d[div_n - 1];
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d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
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/* pointer to the 'top' of snum */
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wnump = &(snum->d[num_n - 1]);
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/* Setup to 'res' */
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res->neg = (num->neg ^ divisor->neg);
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if (!bn_wexpand(res, (loop + 1)))
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goto err;
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res->top = loop - no_branch;
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resp = &(res->d[loop - 1]);
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/* space for temp */
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if (!bn_wexpand(tmp, (div_n + 1)))
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goto err;
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if (!no_branch) {
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if (BN_ucmp(&wnum, sdiv) >= 0) {
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/*
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* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
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* the const bignum arguments => clean the values between top and
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* max again
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*/
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bn_clear_top2max(&wnum);
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bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
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*resp = 1;
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} else
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res->top--;
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}
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/* Increase the resp pointer so that we never create an invalid pointer. */
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resp++;
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/*
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* if res->top == 0 then clear the neg value otherwise decrease the resp
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* pointer
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*/
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if (res->top == 0)
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res->neg = 0;
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else
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resp--;
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for (i = 0; i < loop - 1; i++, wnump--) {
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BN_ULONG q, l0;
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/*
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* the first part of the loop uses the top two words of snum and sdiv
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* to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
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*/
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# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
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BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
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q = bn_div_3_words(wnump, d1, d0);
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# else
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BN_ULONG n0, n1, rem = 0;
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n0 = wnump[0];
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n1 = wnump[-1];
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if (n0 == d0)
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q = BN_MASK2;
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else { /* n0 < d0 */
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# ifdef BN_LLONG
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BN_ULLONG t2;
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# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
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q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
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# else
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q = bn_div_words(n0, n1, d0);
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# endif
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# ifndef REMAINDER_IS_ALREADY_CALCULATED
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/*
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* rem doesn't have to be BN_ULLONG. The least we
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* know it's less that d0, isn't it?
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*/
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rem = (n1 - q * d0) & BN_MASK2;
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# endif
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t2 = (BN_ULLONG) d1 *q;
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for (;;) {
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if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
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break;
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q--;
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rem += d0;
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if (rem < d0)
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break; /* don't let rem overflow */
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t2 -= d1;
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}
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# else /* !BN_LLONG */
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BN_ULONG t2l, t2h;
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q = bn_div_words(n0, n1, d0);
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# ifndef REMAINDER_IS_ALREADY_CALCULATED
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rem = (n1 - q * d0) & BN_MASK2;
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# endif
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# if defined(BN_UMULT_LOHI)
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BN_UMULT_LOHI(t2l, t2h, d1, q);
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# elif defined(BN_UMULT_HIGH)
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t2l = d1 * q;
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t2h = BN_UMULT_HIGH(d1, q);
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# else
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{
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BN_ULONG ql, qh;
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t2l = LBITS(d1);
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t2h = HBITS(d1);
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ql = LBITS(q);
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qh = HBITS(q);
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mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
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}
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# endif
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for (;;) {
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if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
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break;
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q--;
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rem += d0;
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if (rem < d0)
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break; /* don't let rem overflow */
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if (t2l < d1)
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t2h--;
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t2l -= d1;
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}
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# endif /* !BN_LLONG */
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}
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# endif /* !BN_DIV3W */
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l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
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tmp->d[div_n] = l0;
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wnum.d--;
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/*
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* ingore top values of the bignums just sub the two BN_ULONG arrays
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* with bn_sub_words
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*/
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if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
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/*
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* Note: As we have considered only the leading two BN_ULONGs in
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* the calculation of q, sdiv * q might be greater than wnum (but
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* then (q-1) * sdiv is less or equal than wnum)
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*/
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q--;
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if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
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/*
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* we can't have an overflow here (assuming that q != 0, but
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* if q == 0 then tmp is zero anyway)
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*/
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(*wnump)++;
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}
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/* store part of the result */
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resp--;
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*resp = q;
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}
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bn_correct_top(snum);
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if (rm != NULL) {
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/*
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* Keep a copy of the neg flag in num because if rm==num BN_rshift()
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* will overwrite it.
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*/
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int neg = num->neg;
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BN_rshift(rm, snum, norm_shift);
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if (!BN_is_zero(rm))
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rm->neg = neg;
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bn_check_top(rm);
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}
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if (no_branch)
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bn_correct_top(res);
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BN_CTX_end(ctx);
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return (1);
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err:
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bn_check_top(rm);
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BN_CTX_end(ctx);
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return (0);
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}
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#endif
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