461 lines
14 KiB
C
461 lines
14 KiB
C
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/*
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* Copyright 1995-2022 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 <assert.h>
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#include <openssl/bn.h>
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#include "internal/cryptlib.h"
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#include "bn_local.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(BN_DIV3W)
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BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0);
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# elif 0
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/*
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* This is #if-ed away, because it's a reference for assembly implementations,
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* where it can and should be made constant-time. But if you want to test it,
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* just replace 0 with 1.
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*/
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# if BN_BITS2 == 64 && defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16
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# undef BN_ULLONG
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# define BN_ULLONG __uint128_t
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# define BN_LLONG
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# endif
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# ifdef BN_LLONG
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# define BN_DIV3W
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/*
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* Interface is somewhat quirky, |m| is pointer to most significant limb,
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* and less significant limb is referred at |m[-1]|. This means that caller
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* is responsible for ensuring that |m[-1]| is valid. Second condition that
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* has to be met is that |d0|'s most significant bit has to be set. Or in
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* other words divisor has to be "bit-aligned to the left." bn_div_fixed_top
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* does all this. The subroutine considers four limbs, two of which are
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* "overlapping," hence the name...
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*/
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static BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0)
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{
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BN_ULLONG R = ((BN_ULLONG)m[0] << BN_BITS2) | m[-1];
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BN_ULLONG D = ((BN_ULLONG)d0 << BN_BITS2) | d1;
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BN_ULONG Q = 0, mask;
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int i;
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for (i = 0; i < BN_BITS2; i++) {
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Q <<= 1;
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if (R >= D) {
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Q |= 1;
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R -= D;
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}
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D >>= 1;
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}
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mask = 0 - (Q >> (BN_BITS2 - 1)); /* does it overflow? */
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Q <<= 1;
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Q |= (R >= D);
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return (Q | mask) & BN_MASK2;
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}
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# endif
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# endif
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static int bn_left_align(BIGNUM *num)
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{
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BN_ULONG *d = num->d, n, m, rmask;
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int top = num->top;
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int rshift = BN_num_bits_word(d[top - 1]), lshift, i;
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lshift = BN_BITS2 - rshift;
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rshift %= BN_BITS2; /* say no to undefined behaviour */
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rmask = (BN_ULONG)0 - rshift; /* rmask = 0 - (rshift != 0) */
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rmask |= rmask >> 8;
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for (i = 0, m = 0; i < top; i++) {
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n = d[i];
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d[i] = ((n << lshift) | m) & BN_MASK2;
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m = (n >> rshift) & rmask;
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}
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return lshift;
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}
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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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# 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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*/
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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 ret;
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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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/*
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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 (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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ret = bn_div_fixed_top(dv, rm, num, divisor, ctx);
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if (ret) {
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if (dv != NULL)
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bn_correct_top(dv);
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if (rm != NULL)
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bn_correct_top(rm);
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}
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return ret;
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}
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/*
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* It's argued that *length* of *significant* part of divisor is public.
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* Even if it's private modulus that is. Again, *length* is assumed
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* public, but not *value*. Former is likely to be pre-defined by
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* algorithm with bit granularity, though below subroutine is invariant
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* of limb length. Thanks to this assumption we can require that |divisor|
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* may not be zero-padded, yet claim this subroutine "constant-time"(*).
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* This is because zero-padded dividend, |num|, is tolerated, so that
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* caller can pass dividend of public length(*), but with smaller amount
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* of significant limbs. This naturally means that quotient, |dv|, would
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* contain correspongly less significant limbs as well, and will be zero-
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* padded accordingly. Returned remainder, |rm|, will have same bit length
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* as divisor, also zero-padded if needed. These actually leave sign bits
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* in ambiguous state. In sense that we try to avoid negative zeros, while
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* zero-padded zeros would retain sign.
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*
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* (*) "Constant-time-ness" has two pre-conditions:
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*
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* - availability of constant-time bn_div_3_words;
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* - dividend is at least as "wide" as divisor, limb-wise, zero-padded
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* if so required, which shouldn't be a privacy problem, because
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* divisor's length is considered public;
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*/
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int bn_div_fixed_top(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
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const BIGNUM *divisor, BN_CTX *ctx)
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{
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int norm_shift, i, j, loop;
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BIGNUM *tmp, *snum, *sdiv, *res;
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BN_ULONG *resp, *wnum, *wnumtop;
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BN_ULONG d0, d1;
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int num_n, div_n, num_neg;
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assert(divisor->top > 0 && divisor->d[divisor->top - 1] != 0);
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bn_check_top(num);
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bn_check_top(divisor);
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bn_check_top(dv);
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bn_check_top(rm);
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BN_CTX_start(ctx);
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res = (dv == NULL) ? BN_CTX_get(ctx) : dv;
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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 (sdiv == NULL)
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goto err;
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/* First we normalise the numbers */
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if (!BN_copy(sdiv, divisor))
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goto err;
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norm_shift = bn_left_align(sdiv);
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sdiv->neg = 0;
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/*
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* Note that bn_lshift_fixed_top's output is always one limb longer
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* than input, even when norm_shift is zero. This means that amount of
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* inner loop iterations is invariant of dividend value, and that one
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* doesn't need to compare dividend and divisor if they were originally
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* of the same bit length.
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*/
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if (!(bn_lshift_fixed_top(snum, num, norm_shift)))
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goto err;
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div_n = sdiv->top;
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num_n = snum->top;
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if (num_n <= div_n) {
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/* caller didn't pad dividend -> no constant-time guarantee... */
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if (bn_wexpand(snum, div_n + 1) == NULL)
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goto err;
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memset(&(snum->d[num_n]), 0, (div_n - num_n + 1) * sizeof(BN_ULONG));
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snum->top = num_n = div_n + 1;
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}
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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 = &(snum->d[loop]);
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wnumtop = &(snum->d[num_n - 1]);
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/* Get the top 2 words of sdiv */
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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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/* Setup quotient */
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if (!bn_wexpand(res, loop))
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goto err;
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num_neg = num->neg;
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res->neg = (num_neg ^ divisor->neg);
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res->top = loop;
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res->flags |= BN_FLG_FIXED_TOP;
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resp = &(res->d[loop]);
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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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for (i = 0; i < loop; i++, wnumtop--) {
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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)
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q = bn_div_3_words(wnumtop, d1, d0);
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# else
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BN_ULONG n0, n1, rem = 0;
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n0 = wnumtop[0];
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n1 = wnumtop[-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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BN_ULONG n2 = (wnumtop == wnum) ? 0 : wnumtop[-2];
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# ifdef BN_LLONG
|
||
|
|
BN_ULLONG t2;
|
||
|
|
|
||
|
|
# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
|
||
|
|
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
|
||
|
|
# else
|
||
|
|
q = bn_div_words(n0, n1, d0);
|
||
|
|
# endif
|
||
|
|
|
||
|
|
# ifndef REMAINDER_IS_ALREADY_CALCULATED
|
||
|
|
/*
|
||
|
|
* rem doesn't have to be BN_ULLONG. The least we
|
||
|
|
* know it's less that d0, isn't it?
|
||
|
|
*/
|
||
|
|
rem = (n1 - q * d0) & BN_MASK2;
|
||
|
|
# endif
|
||
|
|
t2 = (BN_ULLONG) d1 *q;
|
||
|
|
|
||
|
|
for (;;) {
|
||
|
|
if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | n2))
|
||
|
|
break;
|
||
|
|
q--;
|
||
|
|
rem += d0;
|
||
|
|
if (rem < d0)
|
||
|
|
break; /* don't let rem overflow */
|
||
|
|
t2 -= d1;
|
||
|
|
}
|
||
|
|
# else /* !BN_LLONG */
|
||
|
|
BN_ULONG t2l, t2h;
|
||
|
|
|
||
|
|
q = bn_div_words(n0, n1, d0);
|
||
|
|
# ifndef REMAINDER_IS_ALREADY_CALCULATED
|
||
|
|
rem = (n1 - q * d0) & BN_MASK2;
|
||
|
|
# endif
|
||
|
|
|
||
|
|
# if defined(BN_UMULT_LOHI)
|
||
|
|
BN_UMULT_LOHI(t2l, t2h, d1, q);
|
||
|
|
# elif defined(BN_UMULT_HIGH)
|
||
|
|
t2l = d1 * q;
|
||
|
|
t2h = BN_UMULT_HIGH(d1, q);
|
||
|
|
# else
|
||
|
|
{
|
||
|
|
BN_ULONG ql, qh;
|
||
|
|
t2l = LBITS(d1);
|
||
|
|
t2h = HBITS(d1);
|
||
|
|
ql = LBITS(q);
|
||
|
|
qh = HBITS(q);
|
||
|
|
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
|
||
|
|
}
|
||
|
|
# endif
|
||
|
|
|
||
|
|
for (;;) {
|
||
|
|
if ((t2h < rem) || ((t2h == rem) && (t2l <= n2)))
|
||
|
|
break;
|
||
|
|
q--;
|
||
|
|
rem += d0;
|
||
|
|
if (rem < d0)
|
||
|
|
break; /* don't let rem overflow */
|
||
|
|
if (t2l < d1)
|
||
|
|
t2h--;
|
||
|
|
t2l -= d1;
|
||
|
|
}
|
||
|
|
# endif /* !BN_LLONG */
|
||
|
|
}
|
||
|
|
# endif /* !BN_DIV3W */
|
||
|
|
|
||
|
|
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
|
||
|
|
tmp->d[div_n] = l0;
|
||
|
|
wnum--;
|
||
|
|
/*
|
||
|
|
* ignore top values of the bignums just sub the two BN_ULONG arrays
|
||
|
|
* with bn_sub_words
|
||
|
|
*/
|
||
|
|
l0 = bn_sub_words(wnum, wnum, tmp->d, div_n + 1);
|
||
|
|
q -= l0;
|
||
|
|
/*
|
||
|
|
* Note: As we have considered only the leading two BN_ULONGs in
|
||
|
|
* the calculation of q, sdiv * q might be greater than wnum (but
|
||
|
|
* then (q-1) * sdiv is less or equal than wnum)
|
||
|
|
*/
|
||
|
|
for (l0 = 0 - l0, j = 0; j < div_n; j++)
|
||
|
|
tmp->d[j] = sdiv->d[j] & l0;
|
||
|
|
l0 = bn_add_words(wnum, wnum, tmp->d, div_n);
|
||
|
|
(*wnumtop) += l0;
|
||
|
|
assert((*wnumtop) == 0);
|
||
|
|
|
||
|
|
/* store part of the result */
|
||
|
|
*--resp = q;
|
||
|
|
}
|
||
|
|
/* snum holds remainder, it's as wide as divisor */
|
||
|
|
snum->neg = num_neg;
|
||
|
|
snum->top = div_n;
|
||
|
|
snum->flags |= BN_FLG_FIXED_TOP;
|
||
|
|
|
||
|
|
if (rm != NULL && bn_rshift_fixed_top(rm, snum, norm_shift) == 0)
|
||
|
|
goto err;
|
||
|
|
|
||
|
|
BN_CTX_end(ctx);
|
||
|
|
return 1;
|
||
|
|
err:
|
||
|
|
bn_check_top(rm);
|
||
|
|
BN_CTX_end(ctx);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
#endif
|