1/*
2 * Copyright 1998-2018 The OpenSSL Project Authors. All Rights Reserved.
3 *
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
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 (!(BN_mod(r, m, d, ctx)))
21        return 0;
22    if (!r->neg)
23        return 1;
24    /* now   -|d| < r < 0,  so we have to set  r := r + |d| */
25    return (d->neg ? BN_sub : BN_add) (r, r, d);
26}
27
28int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
29               BN_CTX *ctx)
30{
31    if (!BN_add(r, a, b))
32        return 0;
33    return BN_nnmod(r, r, m, ctx);
34}
35
36/*
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
39 *
40 *    if (!BN_uadd(r, a, b))
41 *       return 0;
42 *    if (BN_ucmp(r, m) >= 0)
43 *       return BN_usub(r, r, m);
44 *
45 * which is replaced with addition, subtracting modulus, and conditional
46 * move depending on whether or not subtraction borrowed.
47 */
48int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
49                         const BIGNUM *m)
50{
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;
55
56    if (bn_wexpand(r, mtop) == NULL)
57        return 0;
58
59    if (mtop > sizeof(storage) / sizeof(storage[0])
60        && (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
61        return 0;
62
63    ap = a->d != NULL ? a->d : tp;
64    bp = b->d != NULL ? b->d : tp;
65
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);
70
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);
74
75        i++;
76        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
77        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
78    }
79    rp = r->d;
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;
84    }
85    r->top = mtop;
86    r->flags |= BN_FLG_FIXED_TOP;
87    r->neg = 0;
88
89    if (tp != storage)
90        OPENSSL_free(tp);
91
92    return 1;
93}
94
95int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
96                     const BIGNUM *m)
97{
98    int ret = bn_mod_add_fixed_top(r, a, b, m);
99
100    if (ret)
101        bn_correct_top(r);
102
103    return ret;
104}
105
106int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
107               BN_CTX *ctx)
108{
109    if (!BN_sub(r, a, b))
110        return 0;
111    return BN_nnmod(r, r, m, ctx);
112}
113
114/*
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.
118 *
119 * 0 <= a < m
120 * 0 <= b < 2^w < 2*m
121 *
122 * after subtraction
123 *
124 * -2*m < r = a - b < m
125 *
126 * Thus it takes up to two conditional additions to make |r| positive.
127 */
128int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
129                         const BIGNUM *m)
130{
131    size_t i, ai, bi, mtop = m->top;
132    BN_ULONG borrow, carry, ta, tb, mask, *rp;
133    const BN_ULONG *ap, *bp;
134
135    if (bn_wexpand(r, mtop) == NULL)
136        return 0;
137
138    rp = r->d;
139    ap = a->d != NULL ? a->d : rp;
140    bp = b->d != NULL ? b->d : rp;
141
142    for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
143        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
144        ta = ap[ai] & mask;
145
146        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
147        tb = bp[bi] & mask;
148        rp[i] = ta - tb - borrow;
149        if (ta != tb)
150            borrow = (ta < tb);
151
152        i++;
153        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
154        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
155    }
156    ap = m->d;
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);
162    }
163    borrow -= carry;
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);
169    }
170
171    r->top = mtop;
172    r->flags |= BN_FLG_FIXED_TOP;
173    r->neg = 0;
174
175    return 1;
176}
177
178/*
179 * BN_mod_sub variant that may be used if both a and b are non-negative and
180 * less than m
181 */
182int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
183                     const BIGNUM *m)
184{
185    if (!BN_sub(r, a, b))
186        return 0;
187    if (r->neg)
188        return BN_add(r, r, m);
189    return 1;
190}
191
192/* slow but works */
193int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
194               BN_CTX *ctx)
195{
196    BIGNUM *t;
197    int ret = 0;
198
199    bn_check_top(a);
200    bn_check_top(b);
201    bn_check_top(m);
202
203    BN_CTX_start(ctx);
204    if ((t = BN_CTX_get(ctx)) == NULL)
205        goto err;
206    if (a == b) {
207        if (!BN_sqr(t, a, ctx))
208            goto err;
209    } else {
210        if (!BN_mul(t, a, b, ctx))
211            goto err;
212    }
213    if (!BN_nnmod(r, t, m, ctx))
214        goto err;
215    bn_check_top(r);
216    ret = 1;
217 err:
218    BN_CTX_end(ctx);
219    return ret;
220}
221
222int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
223{
224    if (!BN_sqr(r, a, ctx))
225        return 0;
226    /* r->neg == 0,  thus we don't need BN_nnmod */
227    return BN_mod(r, r, m, ctx);
228}
229
230int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
231{
232    if (!BN_lshift1(r, a))
233        return 0;
234    bn_check_top(r);
235    return BN_nnmod(r, r, m, ctx);
236}
237
238/*
239 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
240 * m
241 */
242int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
243{
244    if (!BN_lshift1(r, a))
245        return 0;
246    bn_check_top(r);
247    if (BN_cmp(r, m) >= 0)
248        return BN_sub(r, r, m);
249    return 1;
250}
251
252int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
253                  BN_CTX *ctx)
254{
255    BIGNUM *abs_m = NULL;
256    int ret;
257
258    if (!BN_nnmod(r, a, m, ctx))
259        return 0;
260
261    if (m->neg) {
262        abs_m = BN_dup(m);
263        if (abs_m == NULL)
264            return 0;
265        abs_m->neg = 0;
266    }
267
268    ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
269    bn_check_top(r);
270
271    BN_free(abs_m);
272    return ret;
273}
274
275/*
276 * BN_mod_lshift variant that may be used if a is non-negative and less than
277 * m
278 */
279int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
280{
281    if (r != a) {
282        if (BN_copy(r, a) == NULL)
283            return 0;
284    }
285
286    while (n > 0) {
287        int max_shift;
288
289        /* 0 < r < m */
290        max_shift = BN_num_bits(m) - BN_num_bits(r);
291        /* max_shift >= 0 */
292
293        if (max_shift < 0) {
294            BNerr(BN_F_BN_MOD_LSHIFT_QUICK, BN_R_INPUT_NOT_REDUCED);
295            return 0;
296        }
297
298        if (max_shift > n)
299            max_shift = n;
300
301        if (max_shift) {
302            if (!BN_lshift(r, r, max_shift))
303                return 0;
304            n -= max_shift;
305        } else {
306            if (!BN_lshift1(r, r))
307                return 0;
308            --n;
309        }
310
311        /* BN_num_bits(r) <= BN_num_bits(m) */
312
313        if (BN_cmp(r, m) >= 0) {
314            if (!BN_sub(r, r, m))
315                return 0;
316        }
317    }
318    bn_check_top(r);
319
320    return 1;
321}
322