/src/openssl/crypto/bn/bn_mod.c

Source
/*
 * Copyright 1998-2025 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 "internal/nelem.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, (int)mtop) == NULL)
        return 0;

    if (mtop > OSSL_NELEM(storage)) {
        tp = OPENSSL_malloc_array(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, (int)mtop);
    for (i = 0; i < mtop; i++) {
        rp[i] = (carry & tp[i]) | (~carry & rp[i]);
        ((volatile BN_ULONG *)tp)[i] = 0;
    }
    r->top = (int)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, (int)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 = (int)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: 2025-10-28 06:56

Line	Count	Source
1		/*
2		* Copyright 1998-2025 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 "internal/nelem.h"
12		#include "bn_local.h"
13
14		int BN_nnmod(BIGNUM r, const BIGNUM m, const BIGNUM d, BN_CTX ctx)
15	0	{
16		/*
17		* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < \|d\|
18		* always holds)
19		*/
20
21	0	if (r == d) {
22	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
23	0	return 0;
24	0	}
25
26	0	if (!(BN_mod(r, m, d, ctx)))
27	0	return 0;
28	0	if (!r->neg)
29	0	return 1;
30		/* now -\|d\| < r < 0, so we have to set r := r + \|d\| */
31	0	return (d->neg ? BN_sub : BN_add) (r, r, d);
32	0	}
33
34		int BN_mod_add(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
35		BN_CTX *ctx)
36	0	{
37	0	if (!BN_add(r, a, b))
38	0	return 0;
39	0	return BN_nnmod(r, r, m, ctx);
40	0	}
41
42		/*
43		* BN_mod_add variant that may be used if both a and b are non-negative and
44		* less than m. The original algorithm was
45		*
46		* if (!BN_uadd(r, a, b))
47		* return 0;
48		* if (BN_ucmp(r, m) >= 0)
49		* return BN_usub(r, r, m);
50		*
51		* which is replaced with addition, subtracting modulus, and conditional
52		* move depending on whether or not subtraction borrowed.
53		*/
54		int bn_mod_add_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
55		const BIGNUM *m)
56	0	{
57	0	size_t i, ai, bi, mtop = m->top;
58	0	BN_ULONG storage[1024 / BN_BITS2];
59	0	BN_ULONG carry, temp, mask, rp, tp = storage;
60	0	const BN_ULONG ap, bp;
61
62	0	if (bn_wexpand(r, (int)mtop) == NULL)
63	0	return 0;
64
65	0	if (mtop > OSSL_NELEM(storage)) {
66	0	tp = OPENSSL_malloc_array(mtop, sizeof(BN_ULONG));
67	0	if (tp == NULL)
68	0	return 0;
69	0	}
70
71	0	ap = a->d != NULL ? a->d : tp;
72	0	bp = b->d != NULL ? b->d : tp;
73
74	0	for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
75	0	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
76	0	temp = ((ap[ai] & mask) + carry) & BN_MASK2;
77	0	carry = (temp < carry);
78
79	0	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
80	0	tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
81	0	carry += (tp[i] < temp);
82
83	0	i++;
84	0	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
85	0	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
86	0	}
87	0	rp = r->d;
88	0	carry -= bn_sub_words(rp, tp, m->d, (int)mtop);
89	0	for (i = 0; i < mtop; i++) {
90	0	rp[i] = (carry & tp[i]) \| (~carry & rp[i]);
91	0	((volatile BN_ULONG *)tp)[i] = 0;
92	0	}
93	0	r->top = (int)mtop;
94	0	r->flags \|= BN_FLG_FIXED_TOP;
95	0	r->neg = 0;
96
97	0	if (tp != storage)
98	0	OPENSSL_free(tp);
99
100	0	return 1;
101	0	}
102
103		int BN_mod_add_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
104		const BIGNUM *m)
105	0	{
106	0	int ret = bn_mod_add_fixed_top(r, a, b, m);
107
108	0	if (ret)
109	0	bn_correct_top(r);
110
111	0	return ret;
112	0	}
113
114		int BN_mod_sub(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
115		BN_CTX *ctx)
116	0	{
117	0	if (!BN_sub(r, a, b))
118	0	return 0;
119	0	return BN_nnmod(r, r, m, ctx);
120	0	}
121
122		/*
123		* BN_mod_sub variant that may be used if both a and b are non-negative,
124		* a is less than m, while b is of same bit width as m. It's implemented
125		* as subtraction followed by two conditional additions.
126		*
127		* 0 <= a < m
128		* 0 <= b < 2^w < 2*m
129		*
130		* after subtraction
131		*
132		* -2*m < r = a - b < m
133		*
134		* Thus it takes up to two conditional additions to make \|r\| positive.
135		*/
136		int bn_mod_sub_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
137		const BIGNUM *m)
138	0	{
139	0	size_t i, ai, bi, mtop = m->top;
140	0	BN_ULONG borrow, carry, ta, tb, mask, *rp;
141	0	const BN_ULONG ap, bp;
142
143	0	if (bn_wexpand(r, (int)mtop) == NULL)
144	0	return 0;
145
146	0	rp = r->d;
147	0	ap = a->d != NULL ? a->d : rp;
148	0	bp = b->d != NULL ? b->d : rp;
149
150	0	for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
151	0	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
152	0	ta = ap[ai] & mask;
153
154	0	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
155	0	tb = bp[bi] & mask;
156	0	rp[i] = ta - tb - borrow;
157	0	if (ta != tb)
158	0	borrow = (ta < tb);
159
160	0	i++;
161	0	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
162	0	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
163	0	}
164	0	ap = m->d;
165	0	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
166	0	ta = ((ap[i] & mask) + carry) & BN_MASK2;
167	0	carry = (ta < carry);
168	0	rp[i] = (rp[i] + ta) & BN_MASK2;
169	0	carry += (rp[i] < ta);
170	0	}
171	0	borrow -= carry;
172	0	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
173	0	ta = ((ap[i] & mask) + carry) & BN_MASK2;
174	0	carry = (ta < carry);
175	0	rp[i] = (rp[i] + ta) & BN_MASK2;
176	0	carry += (rp[i] < ta);
177	0	}
178
179	0	r->top = (int)mtop;
180	0	r->flags \|= BN_FLG_FIXED_TOP;
181	0	r->neg = 0;
182
183	0	return 1;
184	0	}
185
186		/*
187		* BN_mod_sub variant that may be used if both a and b are non-negative and
188		* less than m
189		*/
190		int BN_mod_sub_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
191		const BIGNUM *m)
192	0	{
193	0	if (r == m) {
194	0	ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
195	0	return 0;
196	0	}
197
198	0	if (!BN_sub(r, a, b))
199	0	return 0;
200	0	if (r->neg)
201	0	return BN_add(r, r, m);
202	0	return 1;
203	0	}
204
205		/* slow but works */
206		int BN_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
207		BN_CTX *ctx)
208	0	{
209	0	BIGNUM *t;
210	0	int ret = 0;
211
212	0	bn_check_top(a);
213	0	bn_check_top(b);
214	0	bn_check_top(m);
215
216	0	BN_CTX_start(ctx);
217	0	if ((t = BN_CTX_get(ctx)) == NULL)
218	0	goto err;
219	0	if (a == b) {
220	0	if (!BN_sqr(t, a, ctx))
221	0	goto err;
222	0	} else {
223	0	if (!BN_mul(t, a, b, ctx))
224	0	goto err;
225	0	}
226	0	if (!BN_nnmod(r, t, m, ctx))
227	0	goto err;
228	0	bn_check_top(r);
229	0	ret = 1;
230	0	err:
231	0	BN_CTX_end(ctx);
232	0	return ret;
233	0	}
234
235		int BN_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
236	0	{
237	0	if (!BN_sqr(r, a, ctx))
238	0	return 0;
239		/* r->neg == 0, thus we don't need BN_nnmod */
240	0	return BN_mod(r, r, m, ctx);
241	0	}
242
243		int BN_mod_lshift1(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
244	0	{
245	0	if (!BN_lshift1(r, a))
246	0	return 0;
247	0	bn_check_top(r);
248	0	return BN_nnmod(r, r, m, ctx);
249	0	}
250
251		/*
252		* BN_mod_lshift1 variant that may be used if a is non-negative and less than
253		* m
254		*/
255		int BN_mod_lshift1_quick(BIGNUM r, const BIGNUM a, const BIGNUM *m)
256	0	{
257	0	if (!BN_lshift1(r, a))
258	0	return 0;
259	0	bn_check_top(r);
260	0	if (BN_cmp(r, m) >= 0)
261	0	return BN_sub(r, r, m);
262	0	return 1;
263	0	}
264
265		int BN_mod_lshift(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m,
266		BN_CTX *ctx)
267	0	{
268	0	BIGNUM *abs_m = NULL;
269	0	int ret;
270
271	0	if (!BN_nnmod(r, a, m, ctx))
272	0	return 0;
273
274	0	if (m->neg) {
275	0	abs_m = BN_dup(m);
276	0	if (abs_m == NULL)
277	0	return 0;
278	0	abs_m->neg = 0;
279	0	}
280
281	0	ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
282	0	bn_check_top(r);
283
284	0	BN_free(abs_m);
285	0	return ret;
286	0	}
287
288		/*
289		* BN_mod_lshift variant that may be used if a is non-negative and less than
290		* m
291		*/
292		int BN_mod_lshift_quick(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m)
293	0	{
294	0	if (r != a) {
295	0	if (BN_copy(r, a) == NULL)
296	0	return 0;
297	0	}
298
299	0	while (n > 0) {
300	0	int max_shift;
301
302		/* 0 < r < m */
303	0	max_shift = BN_num_bits(m) - BN_num_bits(r);
304		/* max_shift >= 0 */
305
306	0	if (max_shift < 0) {
307	0	ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
308	0	return 0;
309	0	}
310
311	0	if (max_shift > n)
312	0	max_shift = n;
313
314	0	if (max_shift) {
315	0	if (!BN_lshift(r, r, max_shift))
316	0	return 0;
317	0	n -= max_shift;
318	0	} else {
319	0	if (!BN_lshift1(r, r))
320	0	return 0;
321	0	--n;
322	0	}
323
324		/* BN_num_bits(r) <= BN_num_bits(m) */
325
326	0	if (BN_cmp(r, m) >= 0) {
327	0	if (!BN_sub(r, r, m))
328	0	return 0;
329	0	}
330	0	}
331	0	bn_check_top(r);
332
333	0	return 1;
334	0	}