/src/openssl31/crypto/bn/bn_mod.c

Source (jump to first uncovered line)
/*
 * 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) {
            ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
            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: 2025-06-13 06:58

Line	Count	Source (jump to first uncovered line)
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	68.9M	{
15		/*
16		* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < \|d\|
17		* always holds)
18		*/
19
20	68.9M	if (r == d) {
21	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
22	0	return 0;
23	0	}
24
25	68.9M	if (!(BN_mod(r, m, d, ctx)))
26	14	return 0;
27	68.9M	if (!r->neg)
28	68.3M	return 1;
29		/* now -\|d\| < r < 0, so we have to set r := r + \|d\| */
30	542k	return (d->neg ? BN_sub : BN_add) (r, r, d);
31	68.9M	}
32
33		int BN_mod_add(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
34		BN_CTX *ctx)
35	962	{
36	962	if (!BN_add(r, a, b))
37	0	return 0;
38	962	return BN_nnmod(r, r, m, ctx);
39	962	}
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	12.8M	{
56	12.8M	size_t i, ai, bi, mtop = m->top;
57	12.8M	BN_ULONG storage[1024 / BN_BITS2];
58	12.8M	BN_ULONG carry, temp, mask, rp, tp = storage;
59	12.8M	const BN_ULONG ap, bp;
60
61	12.8M	if (bn_wexpand(r, mtop) == NULL)
62	0	return 0;
63
64	12.8M	if (mtop > sizeof(storage) / sizeof(storage[0])) {
65	8.87k	tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
66	8.87k	if (tp == NULL) {
67	0	ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
68	0	return 0;
69	0	}
70	8.87k	}
71
72	12.8M	ap = a->d != NULL ? a->d : tp;
73	12.8M	bp = b->d != NULL ? b->d : tp;
74
75	70.2M	for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
76	57.4M	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
77	57.4M	temp = ((ap[ai] & mask) + carry) & BN_MASK2;
78	57.4M	carry = (temp < carry);
79
80	57.4M	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
81	57.4M	tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
82	57.4M	carry += (tp[i] < temp);
83
84	57.4M	i++;
85	57.4M	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
86	57.4M	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
87	57.4M	}
88	12.8M	rp = r->d;
89	12.8M	carry -= bn_sub_words(rp, tp, m->d, mtop);
90	70.2M	for (i = 0; i < mtop; i++) {
91	57.4M	rp[i] = (carry & tp[i]) \| (~carry & rp[i]);
92	57.4M	((volatile BN_ULONG *)tp)[i] = 0;
93	57.4M	}
94	12.8M	r->top = mtop;
95	12.8M	r->flags \|= BN_FLG_FIXED_TOP;
96	12.8M	r->neg = 0;
97
98	12.8M	if (tp != storage)
99	8.87k	OPENSSL_free(tp);
100
101	12.8M	return 1;
102	12.8M	}
103
104		int BN_mod_add_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
105		const BIGNUM *m)
106	12.8M	{
107	12.8M	int ret = bn_mod_add_fixed_top(r, a, b, m);
108
109	12.8M	if (ret)
110	12.8M	bn_correct_top(r);
111
112	12.8M	return ret;
113	12.8M	}
114
115		int BN_mod_sub(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
116		BN_CTX *ctx)
117	0	{
118	0	if (!BN_sub(r, a, b))
119	0	return 0;
120	0	return BN_nnmod(r, r, m, ctx);
121	0	}
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		*/
137		int bn_mod_sub_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
138		const BIGNUM *m)
139	8.87k	{
140	8.87k	size_t i, ai, bi, mtop = m->top;
141	8.87k	BN_ULONG borrow, carry, ta, tb, mask, *rp;
142	8.87k	const BN_ULONG ap, bp;
143
144	8.87k	if (bn_wexpand(r, mtop) == NULL)
145	0	return 0;
146
147	8.87k	rp = r->d;
148	8.87k	ap = a->d != NULL ? a->d : rp;
149	8.87k	bp = b->d != NULL ? b->d : rp;
150
151	150k	for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
152	142k	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
153	142k	ta = ap[ai] & mask;
154
155	142k	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
156	142k	tb = bp[bi] & mask;
157	142k	rp[i] = ta - tb - borrow;
158	142k	if (ta != tb)
159	129k	borrow = (ta < tb);
160
161	142k	i++;
162	142k	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
163	142k	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
164	142k	}
165	8.87k	ap = m->d;
166	150k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
167	142k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
168	142k	carry = (ta < carry);
169	142k	rp[i] = (rp[i] + ta) & BN_MASK2;
170	142k	carry += (rp[i] < ta);
171	142k	}
172	8.87k	borrow -= carry;
173	150k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
174	142k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
175	142k	carry = (ta < carry);
176	142k	rp[i] = (rp[i] + ta) & BN_MASK2;
177	142k	carry += (rp[i] < ta);
178	142k	}
179
180	8.87k	r->top = mtop;
181	8.87k	r->flags \|= BN_FLG_FIXED_TOP;
182	8.87k	r->neg = 0;
183
184	8.87k	return 1;
185	8.87k	}
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		*/
191		int BN_mod_sub_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
192		const BIGNUM *m)
193	12.9M	{
194	12.9M	if (r == m) {
195	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
196	0	return 0;
197	0	}
198
199	12.9M	if (!BN_sub(r, a, b))
200	0	return 0;
201	12.9M	if (r->neg)
202	6.30M	return BN_add(r, r, m);
203	6.63M	return 1;
204	12.9M	}
205
206		/* slow but works */
207		int BN_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
208		BN_CTX *ctx)
209	63.3M	{
210	63.3M	BIGNUM *t;
211	63.3M	int ret = 0;
212
213	63.3M	bn_check_top(a);
214	63.3M	bn_check_top(b);
215	63.3M	bn_check_top(m);
216
217	63.3M	BN_CTX_start(ctx);
218	63.3M	if ((t = BN_CTX_get(ctx)) == NULL)
219	0	goto err;
220	63.3M	if (a == b) {
221	60.6M	if (!BN_sqr(t, a, ctx))
222	0	goto err;
223	60.6M	} else {
224	2.75M	if (!BN_mul(t, a, b, ctx))
225	0	goto err;
226	2.75M	}
227	63.3M	if (!BN_nnmod(r, t, m, ctx))
228	14	goto err;
229	63.3M	bn_check_top(r);
230	63.3M	ret = 1;
231	63.3M	err:
232	63.3M	BN_CTX_end(ctx);
233	63.3M	return ret;
234	63.3M	}
235
236		int BN_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
237	2.71M	{
238	2.71M	if (!BN_sqr(r, a, ctx))
239	0	return 0;
240		/* r->neg == 0, thus we don't need BN_nnmod */
241	2.71M	return BN_mod(r, r, m, ctx);
242	2.71M	}
243
244		int BN_mod_lshift1(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
245	0	{
246	0	if (!BN_lshift1(r, a))
247	0	return 0;
248	0	bn_check_top(r);
249	0	return BN_nnmod(r, r, m, ctx);
250	0	}
251
252		/*
253		* BN_mod_lshift1 variant that may be used if a is non-negative and less than
254		* m
255		*/
256		int BN_mod_lshift1_quick(BIGNUM r, const BIGNUM a, const BIGNUM *m)
257	5.38M	{
258	5.38M	if (!BN_lshift1(r, a))
259	0	return 0;
260	5.38M	bn_check_top(r);
261	5.38M	if (BN_cmp(r, m) >= 0)
262	2.64M	return BN_sub(r, r, m);
263	2.73M	return 1;
264	5.38M	}
265
266		int BN_mod_lshift(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m,
267		BN_CTX *ctx)
268	0	{
269	0	BIGNUM *abs_m = NULL;
270	0	int ret;
271
272	0	if (!BN_nnmod(r, a, m, ctx))
273	0	return 0;
274
275	0	if (m->neg) {
276	0	abs_m = BN_dup(m);
277	0	if (abs_m == NULL)
278	0	return 0;
279	0	abs_m->neg = 0;
280	0	}
281
282	0	ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
283	0	bn_check_top(r);
284
285	0	BN_free(abs_m);
286	0	return ret;
287	0	}
288
289		/*
290		* BN_mod_lshift variant that may be used if a is non-negative and less than
291		* m
292		*/
293		int BN_mod_lshift_quick(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m)
294	2.90M	{
295	2.90M	if (r != a) {
296	2.30M	if (BN_copy(r, a) == NULL)
297	0	return 0;
298	2.30M	}
299
300	8.06M	while (n > 0) {
301	5.16M	int max_shift;
302
303		/* 0 < r < m */
304	5.16M	max_shift = BN_num_bits(m) - BN_num_bits(r);
305		/* max_shift >= 0 */
306
307	5.16M	if (max_shift < 0) {
308	0	ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
309	0	return 0;
310	0	}
311
312	5.16M	if (max_shift > n)
313	1.27M	max_shift = n;
314
315	5.16M	if (max_shift) {
316	2.63M	if (!BN_lshift(r, r, max_shift))
317	0	return 0;
318	2.63M	n -= max_shift;
319	2.63M	} else {
320	2.52M	if (!BN_lshift1(r, r))
321	0	return 0;
322	2.52M	--n;
323	2.52M	}
324
325		/* BN_num_bits(r) <= BN_num_bits(m) */
326
327	5.16M	if (BN_cmp(r, m) >= 0) {
328	3.03M	if (!BN_sub(r, r, m))
329	0	return 0;
330	3.03M	}
331	5.16M	}
332	2.90M	bn_check_top(r);
333
334	2.90M	return 1;
335	2.90M	}