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321 lines
7.7 KiB
C
321 lines
7.7 KiB
C
/*
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* Copyright 1998-2018 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 "internal/cryptlib.h"
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#include "bn_local.h"
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int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
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{
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/*
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* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
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* always holds)
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*/
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if (!(BN_mod(r, m, d, ctx)))
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return 0;
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if (!r->neg)
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return 1;
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/* now -|d| < r < 0, so we have to set r := r + |d| */
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return (d->neg ? BN_sub : BN_add) (r, r, d);
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}
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int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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if (!BN_add(r, a, b))
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return 0;
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return BN_nnmod(r, r, m, ctx);
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}
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/*
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* BN_mod_add variant that may be used if both a and b are non-negative and
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* less than m. The original algorithm was
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*
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* if (!BN_uadd(r, a, b))
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* return 0;
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* if (BN_ucmp(r, m) >= 0)
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* return BN_usub(r, r, m);
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*
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* which is replaced with addition, subtracting modulus, and conditional
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* move depending on whether or not subtraction borrowed.
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*/
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int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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size_t i, ai, bi, mtop = m->top;
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BN_ULONG storage[1024 / BN_BITS2];
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BN_ULONG carry, temp, mask, *rp, *tp = storage;
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const BN_ULONG *ap, *bp;
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if (bn_wexpand(r, mtop) == NULL)
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return 0;
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if (mtop > sizeof(storage) / sizeof(storage[0])
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&& (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
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return 0;
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ap = a->d != NULL ? a->d : tp;
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bp = b->d != NULL ? b->d : tp;
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for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
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mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
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temp = ((ap[ai] & mask) + carry) & BN_MASK2;
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carry = (temp < carry);
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mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
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tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
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carry += (tp[i] < temp);
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i++;
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ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
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bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
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}
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rp = r->d;
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carry -= bn_sub_words(rp, tp, m->d, mtop);
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for (i = 0; i < mtop; i++) {
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rp[i] = (carry & tp[i]) | (~carry & rp[i]);
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((volatile BN_ULONG *)tp)[i] = 0;
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}
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r->top = mtop;
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r->flags |= BN_FLG_FIXED_TOP;
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r->neg = 0;
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if (tp != storage)
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OPENSSL_free(tp);
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return 1;
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}
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int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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int ret = bn_mod_add_fixed_top(r, a, b, m);
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if (ret)
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bn_correct_top(r);
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return ret;
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}
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int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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if (!BN_sub(r, a, b))
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return 0;
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return BN_nnmod(r, r, m, ctx);
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}
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/*
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* BN_mod_sub variant that may be used if both a and b are non-negative,
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* a is less than m, while b is of same bit width as m. It's implemented
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* as subtraction followed by two conditional additions.
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*
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* 0 <= a < m
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* 0 <= b < 2^w < 2*m
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*
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* after subtraction
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*
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* -2*m < r = a - b < m
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*
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* Thus it takes up to two conditional additions to make |r| positive.
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*/
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int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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size_t i, ai, bi, mtop = m->top;
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BN_ULONG borrow, carry, ta, tb, mask, *rp;
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const BN_ULONG *ap, *bp;
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if (bn_wexpand(r, mtop) == NULL)
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return 0;
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rp = r->d;
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ap = a->d != NULL ? a->d : rp;
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bp = b->d != NULL ? b->d : rp;
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for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
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mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
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ta = ap[ai] & mask;
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mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
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tb = bp[bi] & mask;
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rp[i] = ta - tb - borrow;
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if (ta != tb)
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borrow = (ta < tb);
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i++;
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ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
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bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
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}
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ap = m->d;
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for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
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ta = ((ap[i] & mask) + carry) & BN_MASK2;
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carry = (ta < carry);
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rp[i] = (rp[i] + ta) & BN_MASK2;
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carry += (rp[i] < ta);
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}
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borrow -= carry;
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for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
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ta = ((ap[i] & mask) + carry) & BN_MASK2;
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carry = (ta < carry);
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rp[i] = (rp[i] + ta) & BN_MASK2;
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carry += (rp[i] < ta);
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}
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r->top = mtop;
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r->flags |= BN_FLG_FIXED_TOP;
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r->neg = 0;
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return 1;
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}
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/*
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* BN_mod_sub variant that may be used if both a and b are non-negative and
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* less than m
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*/
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int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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const BIGNUM *m)
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{
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if (!BN_sub(r, a, b))
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return 0;
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if (r->neg)
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return BN_add(r, r, m);
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return 1;
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}
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/* slow but works */
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int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx)
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{
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BIGNUM *t;
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int ret = 0;
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bn_check_top(a);
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bn_check_top(b);
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bn_check_top(m);
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BN_CTX_start(ctx);
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if ((t = BN_CTX_get(ctx)) == NULL)
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goto err;
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if (a == b) {
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if (!BN_sqr(t, a, ctx))
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goto err;
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} else {
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if (!BN_mul(t, a, b, ctx))
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goto err;
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}
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if (!BN_nnmod(r, t, m, ctx))
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goto err;
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bn_check_top(r);
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
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{
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if (!BN_sqr(r, a, ctx))
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return 0;
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/* r->neg == 0, thus we don't need BN_nnmod */
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return BN_mod(r, r, m, ctx);
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}
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int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
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{
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if (!BN_lshift1(r, a))
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return 0;
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bn_check_top(r);
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return BN_nnmod(r, r, m, ctx);
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}
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/*
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* BN_mod_lshift1 variant that may be used if a is non-negative and less than
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* m
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*/
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int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
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{
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if (!BN_lshift1(r, a))
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return 0;
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bn_check_top(r);
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if (BN_cmp(r, m) >= 0)
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return BN_sub(r, r, m);
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return 1;
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}
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int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
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BN_CTX *ctx)
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{
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BIGNUM *abs_m = NULL;
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int ret;
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if (!BN_nnmod(r, a, m, ctx))
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return 0;
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if (m->neg) {
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abs_m = BN_dup(m);
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if (abs_m == NULL)
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return 0;
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abs_m->neg = 0;
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}
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ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
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bn_check_top(r);
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BN_free(abs_m);
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return ret;
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}
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/*
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* BN_mod_lshift variant that may be used if a is non-negative and less than
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* m
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*/
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int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
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{
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if (r != a) {
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if (BN_copy(r, a) == NULL)
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return 0;
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}
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while (n > 0) {
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int max_shift;
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/* 0 < r < m */
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max_shift = BN_num_bits(m) - BN_num_bits(r);
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/* max_shift >= 0 */
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if (max_shift < 0) {
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BNerr(BN_F_BN_MOD_LSHIFT_QUICK, BN_R_INPUT_NOT_REDUCED);
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return 0;
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}
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if (max_shift > n)
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max_shift = n;
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if (max_shift) {
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if (!BN_lshift(r, r, max_shift))
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return 0;
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n -= max_shift;
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} else {
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if (!BN_lshift1(r, r))
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return 0;
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--n;
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}
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/* BN_num_bits(r) <= BN_num_bits(m) */
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if (BN_cmp(r, m) >= 0) {
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if (!BN_sub(r, r, m))
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return 0;
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}
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}
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bn_check_top(r);
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return 1;
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}
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