404 lines
12 KiB
C
404 lines
12 KiB
C
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/* $OpenBSD: bn_div.c,v 1.25 2017/01/29 17:49:22 beck Exp $ */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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#include <stdio.h>
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#include <openssl/opensslconf.h>
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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include "bn_lcl.h"
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#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
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&& !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), "g"(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(_LP64)
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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), "g"(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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/* 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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static int
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BN_div_internal(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
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BN_CTX *ctx, int ct)
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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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/* Invalid zero-padding would have particularly bad consequences
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* in the case of 'num', so don't just rely on bn_check_top() for this one
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* (bn_check_top() works only for BN_DEBUG builds) */
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if (num->top > 0 && num->d[num->top - 1] == 0) {
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BNerror(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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if (ct)
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no_branch = 1;
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bn_check_top(dv);
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bn_check_top(rm);
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/* bn_check_top(num); */ /* 'num' has been checked already */
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bn_check_top(divisor);
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if (BN_is_zero(divisor)) {
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BNerror(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 (tmp == NULL || snum == NULL || sdiv == NULL || res == 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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/* Since we don't know whether snum is larger than sdiv,
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* we pad snum with enough zeroes without changing its
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* 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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/* Lets setup a 'window' into snum
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* This is the part that corresponds to the current
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* 'area' being divided */
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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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/* only needed when BN_ucmp messes up the values between top and max */
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wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
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wnum.flags = snum->flags | BN_FLG_STATIC_DATA;
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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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/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
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* bn_pollute) the const bignum arguments =>
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* clean the values between top and max again */
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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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/* if res->top == 0 then clear the neg value otherwise decrease
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* the resp pointer */
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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--, resp--) {
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BN_ULONG q, l0;
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/* the first part of the loop uses the top two words of
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* snum and sdiv to calculate a BN_ULONG q such that
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* | wnum - sdiv * q | < sdiv */
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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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{
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#ifdef BN_LLONG
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BN_ULLONG t2;
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#if 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) |
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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) 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) ||
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((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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/* ingore top values of the bignums just sub the two
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* BN_ULONG arrays with bn_sub_words */
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if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
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/* Note: As we have considered only the leading
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* two BN_ULONGs in the calculation of q, sdiv * q
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* might be greater than wnum (but then (q-1) * sdiv
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* 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))
|
||
|
|
/* we can't have an overflow here (assuming
|
||
|
|
* that q != 0, but if q == 0 then tmp is
|
||
|
|
* zero anyway) */
|
||
|
|
(*wnump)++;
|
||
|
|
}
|
||
|
|
/* store part of the result */
|
||
|
|
*resp = q;
|
||
|
|
}
|
||
|
|
bn_correct_top(snum);
|
||
|
|
if (rm != NULL) {
|
||
|
|
/* Keep a copy of the neg flag in num because if rm==num
|
||
|
|
* BN_rshift() will overwrite it.
|
||
|
|
*/
|
||
|
|
int neg = num->neg;
|
||
|
|
BN_rshift(rm, snum, norm_shift);
|
||
|
|
if (!BN_is_zero(rm))
|
||
|
|
rm->neg = neg;
|
||
|
|
bn_check_top(rm);
|
||
|
|
}
|
||
|
|
if (no_branch)
|
||
|
|
bn_correct_top(res);
|
||
|
|
BN_CTX_end(ctx);
|
||
|
|
return (1);
|
||
|
|
|
||
|
|
err:
|
||
|
|
bn_check_top(rm);
|
||
|
|
BN_CTX_end(ctx);
|
||
|
|
return (0);
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
|
||
|
|
BN_CTX *ctx)
|
||
|
|
{
|
||
|
|
int ct = ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) ||
|
||
|
|
(BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0));
|
||
|
|
|
||
|
|
return BN_div_internal(dv, rm, num, divisor, ctx, ct);
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
BN_div_nonct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
|
||
|
|
BN_CTX *ctx)
|
||
|
|
{
|
||
|
|
return BN_div_internal(dv, rm, num, divisor, ctx, 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
BN_div_ct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
|
||
|
|
BN_CTX *ctx)
|
||
|
|
{
|
||
|
|
return BN_div_internal(dv, rm, num, divisor, ctx, 1);
|
||
|
|
}
|