2 * Copyright 1998-2018 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 #include "internal/cryptlib.h"
13 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
16 * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
20 if (!(BN_mod(r, m, d, ctx)))
24 /* now -|d| < r < 0, so we have to set r := r + |d| */
25 return (d->neg ? BN_sub : BN_add) (r, r, d);
28 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
33 return BN_nnmod(r, r, m, ctx);
37 * BN_mod_add variant that may be used if both a and b are non-negative and
38 * less than m. The original algorithm was
40 * if (!BN_uadd(r, a, b))
42 * if (BN_ucmp(r, m) >= 0)
43 * return BN_usub(r, r, m);
45 * which is replaced with addition, subtracting modulus, and conditional
46 * move depending on whether or not subtraction borrowed.
48 int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
51 size_t i, ai, bi, mtop = m->top;
52 BN_ULONG storage[1024 / BN_BITS2];
53 BN_ULONG carry, temp, mask, *rp, *tp = storage;
54 const BN_ULONG *ap, *bp;
56 if (bn_wexpand(r, mtop) == NULL)
59 if (mtop > sizeof(storage) / sizeof(storage[0])
60 && (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
63 ap = a->d != NULL ? a->d : tp;
64 bp = b->d != NULL ? b->d : tp;
66 for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
67 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
68 temp = ((ap[ai] & mask) + carry) & BN_MASK2;
69 carry = (temp < carry);
71 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
72 tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
73 carry += (tp[i] < temp);
76 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
77 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
80 carry -= bn_sub_words(rp, tp, m->d, mtop);
81 for (i = 0; i < mtop; i++) {
82 rp[i] = (carry & tp[i]) | (~carry & rp[i]);
83 ((volatile BN_ULONG *)tp)[i] = 0;
86 r->flags |= BN_FLG_FIXED_TOP;
95 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
98 int ret = bn_mod_add_fixed_top(r, a, b, m);
106 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
109 if (!BN_sub(r, a, b))
111 return BN_nnmod(r, r, m, ctx);
115 * BN_mod_sub variant that may be used if both a and b are non-negative,
116 * a is less than m, while b is of same bit width as m. It's implemented
117 * as subtraction followed by two conditional additions.
124 * -2*m < r = a - b < m
126 * Thus it takes up to two conditional additions to make |r| positive.
128 int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
131 size_t i, ai, bi, mtop = m->top;
132 BN_ULONG borrow, carry, ta, tb, mask, *rp;
133 const BN_ULONG *ap, *bp;
135 if (bn_wexpand(r, mtop) == NULL)
139 ap = a->d != NULL ? a->d : rp;
140 bp = b->d != NULL ? b->d : rp;
142 for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
143 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
146 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
148 rp[i] = ta - tb - borrow;
153 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
154 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
157 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
158 ta = ((ap[i] & mask) + carry) & BN_MASK2;
159 carry = (ta < carry);
160 rp[i] = (rp[i] + ta) & BN_MASK2;
161 carry += (rp[i] < ta);
164 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
165 ta = ((ap[i] & mask) + carry) & BN_MASK2;
166 carry = (ta < carry);
167 rp[i] = (rp[i] + ta) & BN_MASK2;
168 carry += (rp[i] < ta);
172 r->flags |= BN_FLG_FIXED_TOP;
179 * BN_mod_sub variant that may be used if both a and b are non-negative and
182 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
185 if (!BN_sub(r, a, b))
188 return BN_add(r, r, m);
193 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
204 if ((t = BN_CTX_get(ctx)) == NULL)
207 if (!BN_sqr(t, a, ctx))
210 if (!BN_mul(t, a, b, ctx))
213 if (!BN_nnmod(r, t, m, ctx))
222 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
224 if (!BN_sqr(r, a, ctx))
226 /* r->neg == 0, thus we don't need BN_nnmod */
227 return BN_mod(r, r, m, ctx);
230 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
232 if (!BN_lshift1(r, a))
235 return BN_nnmod(r, r, m, ctx);
239 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
242 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
244 if (!BN_lshift1(r, a))
247 if (BN_cmp(r, m) >= 0)
248 return BN_sub(r, r, m);
252 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
255 BIGNUM *abs_m = NULL;
258 if (!BN_nnmod(r, a, m, ctx))
268 ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
276 * BN_mod_lshift variant that may be used if a is non-negative and less than
279 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
282 if (BN_copy(r, a) == NULL)
290 max_shift = BN_num_bits(m) - BN_num_bits(r);
294 BNerr(BN_F_BN_MOD_LSHIFT_QUICK, BN_R_INPUT_NOT_REDUCED);
302 if (!BN_lshift(r, r, max_shift))
306 if (!BN_lshift1(r, r))
311 /* BN_num_bits(r) <= BN_num_bits(m) */
313 if (BN_cmp(r, m) >= 0) {
314 if (!BN_sub(r, r, m))