1/*
2 * Copyright 1998-2021 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (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
8 */
9
10#include "internal/cryptlib.h"
11#include "bn_local.h"
12
13int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
14{
15    /*
16     * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
17     * always holds)
18     */
19
20    if (r == d) {
21        ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
22        return 0;
23    }
24
25    if (!(BN_mod(r, m, d, ctx)))
26        return 0;
27    if (!r->neg)
28        return 1;
29    /* now   -|d| < r < 0,  so we have to set  r := r + |d| */
30    return (d->neg ? BN_sub : BN_add) (r, r, d);
31}
32
33int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
34               BN_CTX *ctx)
35{
36    if (!BN_add(r, a, b))
37        return 0;
38    return BN_nnmod(r, r, m, ctx);
39}
40
41/*
42 * BN_mod_add variant that may be used if both a and b are non-negative and
43 * less than m. The original algorithm was
44 *
45 *    if (!BN_uadd(r, a, b))
46 *       return 0;
47 *    if (BN_ucmp(r, m) >= 0)
48 *       return BN_usub(r, r, m);
49 *
50 * which is replaced with addition, subtracting modulus, and conditional
51 * move depending on whether or not subtraction borrowed.
52 */
53int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
54                         const BIGNUM *m)
55{
56    size_t i, ai, bi, mtop = m->top;
57    BN_ULONG storage[1024 / BN_BITS2];
58    BN_ULONG carry, temp, mask, *rp, *tp = storage;
59    const BN_ULONG *ap, *bp;
60
61    if (bn_wexpand(r, mtop) == NULL)
62        return 0;
63
64    if (mtop > sizeof(storage) / sizeof(storage[0])) {
65        tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
66        if (tp == NULL) {
67            ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
68            return 0;
69        }
70    }
71
72    ap = a->d != NULL ? a->d : tp;
73    bp = b->d != NULL ? b->d : tp;
74
75    for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
76        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
77        temp = ((ap[ai] & mask) + carry) & BN_MASK2;
78        carry = (temp < carry);
79
80        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
81        tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
82        carry += (tp[i] < temp);
83
84        i++;
85        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
86        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
87    }
88    rp = r->d;
89    carry -= bn_sub_words(rp, tp, m->d, mtop);
90    for (i = 0; i < mtop; i++) {
91        rp[i] = (carry & tp[i]) | (~carry & rp[i]);
92        ((volatile BN_ULONG *)tp)[i] = 0;
93    }
94    r->top = mtop;
95    r->flags |= BN_FLG_FIXED_TOP;
96    r->neg = 0;
97
98    if (tp != storage)
99        OPENSSL_free(tp);
100
101    return 1;
102}
103
104int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
105                     const BIGNUM *m)
106{
107    int ret = bn_mod_add_fixed_top(r, a, b, m);
108
109    if (ret)
110        bn_correct_top(r);
111
112    return ret;
113}
114
115int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
116               BN_CTX *ctx)
117{
118    if (!BN_sub(r, a, b))
119        return 0;
120    return BN_nnmod(r, r, m, ctx);
121}
122
123/*
124 * BN_mod_sub variant that may be used if both a and b are non-negative,
125 * a is less than m, while b is of same bit width as m. It's implemented
126 * as subtraction followed by two conditional additions.
127 *
128 * 0 <= a < m
129 * 0 <= b < 2^w < 2*m
130 *
131 * after subtraction
132 *
133 * -2*m < r = a - b < m
134 *
135 * Thus it takes up to two conditional additions to make |r| positive.
136 */
137int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
138                         const BIGNUM *m)
139{
140    size_t i, ai, bi, mtop = m->top;
141    BN_ULONG borrow, carry, ta, tb, mask, *rp;
142    const BN_ULONG *ap, *bp;
143
144    if (bn_wexpand(r, mtop) == NULL)
145        return 0;
146
147    rp = r->d;
148    ap = a->d != NULL ? a->d : rp;
149    bp = b->d != NULL ? b->d : rp;
150
151    for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
152        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
153        ta = ap[ai] & mask;
154
155        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
156        tb = bp[bi] & mask;
157        rp[i] = ta - tb - borrow;
158        if (ta != tb)
159            borrow = (ta < tb);
160
161        i++;
162        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
163        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
164    }
165    ap = m->d;
166    for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
167        ta = ((ap[i] & mask) + carry) & BN_MASK2;
168        carry = (ta < carry);
169        rp[i] = (rp[i] + ta) & BN_MASK2;
170        carry += (rp[i] < ta);
171    }
172    borrow -= carry;
173    for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
174        ta = ((ap[i] & mask) + carry) & BN_MASK2;
175        carry = (ta < carry);
176        rp[i] = (rp[i] + ta) & BN_MASK2;
177        carry += (rp[i] < ta);
178    }
179
180    r->top = mtop;
181    r->flags |= BN_FLG_FIXED_TOP;
182    r->neg = 0;
183
184    return 1;
185}
186
187/*
188 * BN_mod_sub variant that may be used if both a and b are non-negative and
189 * less than m
190 */
191int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
192                     const BIGNUM *m)
193{
194    if (r == m) {
195        ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
196        return 0;
197    }
198
199    if (!BN_sub(r, a, b))
200        return 0;
201    if (r->neg)
202        return BN_add(r, r, m);
203    return 1;
204}
205
206/* slow but works */
207int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
208               BN_CTX *ctx)
209{
210    BIGNUM *t;
211    int ret = 0;
212
213    bn_check_top(a);
214    bn_check_top(b);
215    bn_check_top(m);
216
217    BN_CTX_start(ctx);
218    if ((t = BN_CTX_get(ctx)) == NULL)
219        goto err;
220    if (a == b) {
221        if (!BN_sqr(t, a, ctx))
222            goto err;
223    } else {
224        if (!BN_mul(t, a, b, ctx))
225            goto err;
226    }
227    if (!BN_nnmod(r, t, m, ctx))
228        goto err;
229    bn_check_top(r);
230    ret = 1;
231 err:
232    BN_CTX_end(ctx);
233    return ret;
234}
235
236int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
237{
238    if (!BN_sqr(r, a, ctx))
239        return 0;
240    /* r->neg == 0,  thus we don't need BN_nnmod */
241    return BN_mod(r, r, m, ctx);
242}
243
244int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
245{
246    if (!BN_lshift1(r, a))
247        return 0;
248    bn_check_top(r);
249    return BN_nnmod(r, r, m, ctx);
250}
251
252/*
253 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
254 * m
255 */
256int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
257{
258    if (!BN_lshift1(r, a))
259        return 0;
260    bn_check_top(r);
261    if (BN_cmp(r, m) >= 0)
262        return BN_sub(r, r, m);
263    return 1;
264}
265
266int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
267                  BN_CTX *ctx)
268{
269    BIGNUM *abs_m = NULL;
270    int ret;
271
272    if (!BN_nnmod(r, a, m, ctx))
273        return 0;
274
275    if (m->neg) {
276        abs_m = BN_dup(m);
277        if (abs_m == NULL)
278            return 0;
279        abs_m->neg = 0;
280    }
281
282    ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
283    bn_check_top(r);
284
285    BN_free(abs_m);
286    return ret;
287}
288
289/*
290 * BN_mod_lshift variant that may be used if a is non-negative and less than
291 * m
292 */
293int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
294{
295    if (r != a) {
296        if (BN_copy(r, a) == NULL)
297            return 0;
298    }
299
300    while (n > 0) {
301        int max_shift;
302
303        /* 0 < r < m */
304        max_shift = BN_num_bits(m) - BN_num_bits(r);
305        /* max_shift >= 0 */
306
307        if (max_shift < 0) {
308            ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
309            return 0;
310        }
311
312        if (max_shift > n)
313            max_shift = n;
314
315        if (max_shift) {
316            if (!BN_lshift(r, r, max_shift))
317                return 0;
318            n -= max_shift;
319        } else {
320            if (!BN_lshift1(r, r))
321                return 0;
322            --n;
323        }
324
325        /* BN_num_bits(r) <= BN_num_bits(m) */
326
327        if (BN_cmp(r, m) >= 0) {
328            if (!BN_sub(r, r, m))
329                return 0;
330        }
331    }
332    bn_check_top(r);
333
334    return 1;
335}
336