/src/openssl33/crypto/bn/bn_mod.c

Source
/*
 * Copyright 1998-2021 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the Apache License 2.0 (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#include "internal/cryptlib.h"
#include "bn_local.h"

int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
{
    /*
     * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
     * always holds)
     */

    if (r == d) {
        ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
        return 0;
    }

    if (!(BN_mod(r, m, d, ctx)))
        return 0;
    if (!r->neg)
        return 1;
    /* now   -|d| < r < 0,  so we have to set  r := r + |d| */
    return (d->neg ? BN_sub : BN_add)(r, r, d);
}

int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
    BN_CTX *ctx)
{
    if (!BN_add(r, a, b))
        return 0;
    return BN_nnmod(r, r, m, ctx);
}

/*
 * BN_mod_add variant that may be used if both a and b are non-negative and
 * less than m. The original algorithm was
 *
 *    if (!BN_uadd(r, a, b))
 *       return 0;
 *    if (BN_ucmp(r, m) >= 0)
 *       return BN_usub(r, r, m);
 *
 * which is replaced with addition, subtracting modulus, and conditional
 * move depending on whether or not subtraction borrowed.
 */
int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
    const BIGNUM *m)
{
    size_t i, ai, bi, mtop = m->top;
    BN_ULONG storage[1024 / BN_BITS2];
    BN_ULONG carry, temp, mask, *rp, *tp = storage;
    const BN_ULONG *ap, *bp;

    if (bn_wexpand(r, mtop) == NULL)
        return 0;

    if (mtop > sizeof(storage) / sizeof(storage[0])) {
        tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
        if (tp == NULL)
            return 0;
    }

    ap = a->d != NULL ? a->d : tp;
    bp = b->d != NULL ? b->d : tp;

    for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
        temp = ((ap[ai] & mask) + carry) & BN_MASK2;
        carry = (temp < carry);

        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
        tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
        carry += (tp[i] < temp);

        i++;
        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
    }
    rp = r->d;
    carry -= bn_sub_words(rp, tp, m->d, mtop);
    for (i = 0; i < mtop; i++) {
        rp[i] = (carry & tp[i]) | (~carry & rp[i]);
        ((volatile BN_ULONG *)tp)[i] = 0;
    }
    r->top = mtop;
    r->flags |= BN_FLG_FIXED_TOP;
    r->neg = 0;

    if (tp != storage)
        OPENSSL_free(tp);

    return 1;
}

int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
    const BIGNUM *m)
{
    int ret = bn_mod_add_fixed_top(r, a, b, m);

    if (ret)
        bn_correct_top(r);

    return ret;
}

int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
    BN_CTX *ctx)
{
    if (!BN_sub(r, a, b))
        return 0;
    return BN_nnmod(r, r, m, ctx);
}

/*
 * BN_mod_sub variant that may be used if both a and b are non-negative,
 * a is less than m, while b is of same bit width as m. It's implemented
 * as subtraction followed by two conditional additions.
 *
 * 0 <= a < m
 * 0 <= b < 2^w < 2*m
 *
 * after subtraction
 *
 * -2*m < r = a - b < m
 *
 * Thus it takes up to two conditional additions to make |r| positive.
 */
int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
    const BIGNUM *m)
{
    size_t i, ai, bi, mtop = m->top;
    BN_ULONG borrow, carry, ta, tb, mask, *rp;
    const BN_ULONG *ap, *bp;

    if (bn_wexpand(r, mtop) == NULL)
        return 0;

    rp = r->d;
    ap = a->d != NULL ? a->d : rp;
    bp = b->d != NULL ? b->d : rp;

    for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
        ta = ap[ai] & mask;

        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
        tb = bp[bi] & mask;
        rp[i] = ta - tb - borrow;
        if (ta != tb)
            borrow = (ta < tb);

        i++;
        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
    }
    ap = m->d;
    for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
        ta = ((ap[i] & mask) + carry) & BN_MASK2;
        carry = (ta < carry);
        rp[i] = (rp[i] + ta) & BN_MASK2;
        carry += (rp[i] < ta);
    }
    borrow -= carry;
    for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
        ta = ((ap[i] & mask) + carry) & BN_MASK2;
        carry = (ta < carry);
        rp[i] = (rp[i] + ta) & BN_MASK2;
        carry += (rp[i] < ta);
    }

    r->top = mtop;
    r->flags |= BN_FLG_FIXED_TOP;
    r->neg = 0;

    return 1;
}

/*
 * BN_mod_sub variant that may be used if both a and b are non-negative and
 * less than m
 */
int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
    const BIGNUM *m)
{
    if (r == m) {
        ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
        return 0;
    }

    if (!BN_sub(r, a, b))
        return 0;
    if (r->neg)
        return BN_add(r, r, m);
    return 1;
}

/* slow but works */
int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
    BN_CTX *ctx)
{
    BIGNUM *t;
    int ret = 0;

    bn_check_top(a);
    bn_check_top(b);
    bn_check_top(m);

    BN_CTX_start(ctx);
    if ((t = BN_CTX_get(ctx)) == NULL)
        goto err;
    if (a == b) {
        if (!BN_sqr(t, a, ctx))
            goto err;
    } else {
        if (!BN_mul(t, a, b, ctx))
            goto err;
    }
    if (!BN_nnmod(r, t, m, ctx))
        goto err;
    bn_check_top(r);
    ret = 1;
err:
    BN_CTX_end(ctx);
    return ret;
}

int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
{
    if (!BN_sqr(r, a, ctx))
        return 0;
    /* r->neg == 0,  thus we don't need BN_nnmod */
    return BN_mod(r, r, m, ctx);
}

int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
{
    if (!BN_lshift1(r, a))
        return 0;
    bn_check_top(r);
    return BN_nnmod(r, r, m, ctx);
}

/*
 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
 * m
 */
int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
{
    if (!BN_lshift1(r, a))
        return 0;
    bn_check_top(r);
    if (BN_cmp(r, m) >= 0)
        return BN_sub(r, r, m);
    return 1;
}

int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
    BN_CTX *ctx)
{
    BIGNUM *abs_m = NULL;
    int ret;

    if (!BN_nnmod(r, a, m, ctx))
        return 0;

    if (m->neg) {
        abs_m = BN_dup(m);
        if (abs_m == NULL)
            return 0;
        abs_m->neg = 0;
    }

    ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
    bn_check_top(r);

    BN_free(abs_m);
    return ret;
}

/*
 * BN_mod_lshift variant that may be used if a is non-negative and less than
 * m
 */
int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
{
    if (r != a) {
        if (BN_copy(r, a) == NULL)
            return 0;
    }

    while (n > 0) {
        int max_shift;

        /* 0 < r < m */
        max_shift = BN_num_bits(m) - BN_num_bits(r);
        /* max_shift >= 0 */

        if (max_shift < 0) {
            ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
            return 0;
        }

        if (max_shift > n)
            max_shift = n;

        if (max_shift) {
            if (!BN_lshift(r, r, max_shift))
                return 0;
            n -= max_shift;
        } else {
            if (!BN_lshift1(r, r))
                return 0;
            --n;
        }

        /* BN_num_bits(r) <= BN_num_bits(m) */

        if (BN_cmp(r, m) >= 0) {
            if (!BN_sub(r, r, m))
                return 0;
        }
    }
    bn_check_top(r);

    return 1;
}

Coverage Report

Created: 2026-02-14 07:20

Line	Count	Source
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
13		int BN_nnmod(BIGNUM r, const BIGNUM m, const BIGNUM d, BN_CTX ctx)
14	104M	{
15		/*
16		* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < \|d\|
17		* always holds)
18		*/
19
20	104M	if (r == d) {
21	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
22	0	return 0;
23	0	}
24
25	104M	if (!(BN_mod(r, m, d, ctx)))
26	34	return 0;
27	104M	if (!r->neg)
28	104M	return 1;
29		/* now -\|d\| < r < 0, so we have to set r := r + \|d\| */
30	812k	return (d->neg ? BN_sub : BN_add)(r, r, d);
31	104M	}
32
33		int BN_mod_add(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
34		BN_CTX *ctx)
35	2.89k	{
36	2.89k	if (!BN_add(r, a, b))
37	0	return 0;
38	2.89k	return BN_nnmod(r, r, m, ctx);
39	2.89k	}
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		*/
53		int bn_mod_add_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
54		const BIGNUM *m)
55	18.7M	{
56	18.7M	size_t i, ai, bi, mtop = m->top;
57	18.7M	BN_ULONG storage[1024 / BN_BITS2];
58	18.7M	BN_ULONG carry, temp, mask, rp, tp = storage;
59	18.7M	const BN_ULONG ap, bp;
60
61	18.7M	if (bn_wexpand(r, mtop) == NULL)
62	0	return 0;
63
64	18.7M	if (mtop > sizeof(storage) / sizeof(storage[0])) {
65	16.3k	tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
66	16.3k	if (tp == NULL)
67	0	return 0;
68	16.3k	}
69
70	18.7M	ap = a->d != NULL ? a->d : tp;
71	18.7M	bp = b->d != NULL ? b->d : tp;
72
73	94.6M	for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
74	75.9M	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
75	75.9M	temp = ((ap[ai] & mask) + carry) & BN_MASK2;
76	75.9M	carry = (temp < carry);
77
78	75.9M	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
79	75.9M	tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
80	75.9M	carry += (tp[i] < temp);
81
82	75.9M	i++;
83	75.9M	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
84	75.9M	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
85	75.9M	}
86	18.7M	rp = r->d;
87	18.7M	carry -= bn_sub_words(rp, tp, m->d, mtop);
88	94.6M	for (i = 0; i < mtop; i++) {
89	75.9M	rp[i] = (carry & tp[i]) \| (~carry & rp[i]);
90	75.9M	((volatile BN_ULONG *)tp)[i] = 0;
91	75.9M	}
92	18.7M	r->top = mtop;
93	18.7M	r->flags \|= BN_FLG_FIXED_TOP;
94	18.7M	r->neg = 0;
95
96	18.7M	if (tp != storage)
97	16.3k	OPENSSL_free(tp);
98
99	18.7M	return 1;
100	18.7M	}
101
102		int BN_mod_add_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
103		const BIGNUM *m)
104	18.6M	{
105	18.6M	int ret = bn_mod_add_fixed_top(r, a, b, m);
106
107	18.6M	if (ret)
108	18.6M	bn_correct_top(r);
109
110	18.6M	return ret;
111	18.6M	}
112
113		int BN_mod_sub(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
114		BN_CTX *ctx)
115	0	{
116	0	if (!BN_sub(r, a, b))
117	0	return 0;
118	0	return BN_nnmod(r, r, m, ctx);
119	0	}
120
121		/*
122		* BN_mod_sub variant that may be used if both a and b are non-negative,
123		* a is less than m, while b is of same bit width as m. It's implemented
124		* as subtraction followed by two conditional additions.
125		*
126		* 0 <= a < m
127		* 0 <= b < 2^w < 2*m
128		*
129		* after subtraction
130		*
131		* -2*m < r = a - b < m
132		*
133		* Thus it takes up to two conditional additions to make \|r\| positive.
134		*/
135		int bn_mod_sub_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
136		const BIGNUM *m)
137	16.3k	{
138	16.3k	size_t i, ai, bi, mtop = m->top;
139	16.3k	BN_ULONG borrow, carry, ta, tb, mask, *rp;
140	16.3k	const BN_ULONG ap, bp;
141
142	16.3k	if (bn_wexpand(r, mtop) == NULL)
143	0	return 0;
144
145	16.3k	rp = r->d;
146	16.3k	ap = a->d != NULL ? a->d : rp;
147	16.3k	bp = b->d != NULL ? b->d : rp;
148
149	277k	for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
150	261k	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
151	261k	ta = ap[ai] & mask;
152
153	261k	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
154	261k	tb = bp[bi] & mask;
155	261k	rp[i] = ta - tb - borrow;
156	261k	if (ta != tb)
157	246k	borrow = (ta < tb);
158
159	261k	i++;
160	261k	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
161	261k	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
162	261k	}
163	16.3k	ap = m->d;
164	277k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
165	261k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
166	261k	carry = (ta < carry);
167	261k	rp[i] = (rp[i] + ta) & BN_MASK2;
168	261k	carry += (rp[i] < ta);
169	261k	}
170	16.3k	borrow -= carry;
171	277k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
172	261k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
173	261k	carry = (ta < carry);
174	261k	rp[i] = (rp[i] + ta) & BN_MASK2;
175	261k	carry += (rp[i] < ta);
176	261k	}
177
178	16.3k	r->top = mtop;
179	16.3k	r->flags \|= BN_FLG_FIXED_TOP;
180	16.3k	r->neg = 0;
181
182	16.3k	return 1;
183	16.3k	}
184
185		/*
186		* BN_mod_sub variant that may be used if both a and b are non-negative and
187		* less than m
188		*/
189		int BN_mod_sub_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
190		const BIGNUM *m)
191	18.1M	{
192	18.1M	if (r == m) {
193	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
194	0	return 0;
195	0	}
196
197	18.1M	if (!BN_sub(r, a, b))
198	0	return 0;
199	18.1M	if (r->neg)
200	8.75M	return BN_add(r, r, m);
201	9.39M	return 1;
202	18.1M	}
203
204		/* slow but works */
205		int BN_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
206		BN_CTX *ctx)
207	95.9M	{
208	95.9M	BIGNUM *t;
209	95.9M	int ret = 0;
210
211	95.9M	bn_check_top(a);
212	95.9M	bn_check_top(b);
213	95.9M	bn_check_top(m);
214
215	95.9M	BN_CTX_start(ctx);
216	95.9M	if ((t = BN_CTX_get(ctx)) == NULL)
217	0	goto err;
218	95.9M	if (a == b) {
219	91.8M	if (!BN_sqr(t, a, ctx))
220	0	goto err;
221	91.8M	} else {
222	4.11M	if (!BN_mul(t, a, b, ctx))
223	0	goto err;
224	4.11M	}
225	95.9M	if (!BN_nnmod(r, t, m, ctx))
226	34	goto err;
227	95.9M	bn_check_top(r);
228	95.9M	ret = 1;
229	95.9M	err:
230	95.9M	BN_CTX_end(ctx);
231	95.9M	return ret;
232	95.9M	}
233
234		int BN_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
235	3.96M	{
236	3.96M	if (!BN_sqr(r, a, ctx))
237	0	return 0;
238		/* r->neg == 0, thus we don't need BN_nnmod */
239	3.96M	return BN_mod(r, r, m, ctx);
240	3.96M	}
241
242		int BN_mod_lshift1(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
243	0	{
244	0	if (!BN_lshift1(r, a))
245	0	return 0;
246	0	bn_check_top(r);
247	0	return BN_nnmod(r, r, m, ctx);
248	0	}
249
250		/*
251		* BN_mod_lshift1 variant that may be used if a is non-negative and less than
252		* m
253		*/
254		int BN_mod_lshift1_quick(BIGNUM r, const BIGNUM a, const BIGNUM *m)
255	7.51M	{
256	7.51M	if (!BN_lshift1(r, a))
257	0	return 0;
258	7.51M	bn_check_top(r);
259	7.51M	if (BN_cmp(r, m) >= 0)
260	3.62M	return BN_sub(r, r, m);
261	3.89M	return 1;
262	7.51M	}
263
264		int BN_mod_lshift(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m,
265		BN_CTX *ctx)
266	0	{
267	0	BIGNUM *abs_m = NULL;
268	0	int ret;
269
270	0	if (!BN_nnmod(r, a, m, ctx))
271	0	return 0;
272
273	0	if (m->neg) {
274	0	abs_m = BN_dup(m);
275	0	if (abs_m == NULL)
276	0	return 0;
277	0	abs_m->neg = 0;
278	0	}
279
280	0	ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
281	0	bn_check_top(r);
282
283	0	BN_free(abs_m);
284	0	return ret;
285	0	}
286
287		/*
288		* BN_mod_lshift variant that may be used if a is non-negative and less than
289		* m
290		*/
291		int BN_mod_lshift_quick(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m)
292	4.02M	{
293	4.02M	if (r != a) {
294	3.24M	if (BN_copy(r, a) == NULL)
295	0	return 0;
296	3.24M	}
297
298	10.5M	while (n > 0) {
299	6.54M	int max_shift;
300
301		/* 0 < r < m */
302	6.54M	max_shift = BN_num_bits(m) - BN_num_bits(r);
303		/* max_shift >= 0 */
304
305	6.54M	if (max_shift < 0) {
306	0	ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
307	0	return 0;
308	0	}
309
310	6.54M	if (max_shift > n)
311	1.97M	max_shift = n;
312
313	6.54M	if (max_shift) {
314	3.88M	if (!BN_lshift(r, r, max_shift))
315	0	return 0;
316	3.88M	n -= max_shift;
317	3.88M	} else {
318	2.65M	if (!BN_lshift1(r, r))
319	0	return 0;
320	2.65M	--n;
321	2.65M	}
322
323		/* BN_num_bits(r) <= BN_num_bits(m) */
324
325	6.54M	if (BN_cmp(r, m) >= 0) {
326	3.30M	if (!BN_sub(r, r, m))
327	0	return 0;
328	3.30M	}
329	6.54M	}
330	4.02M	bn_check_top(r);
331
332	4.02M	return 1;
333	4.02M	}