/src/openssl30/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 (!(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 (!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: 2023-06-08 06:41

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	233k	{
15		/*
16		* like BN_mod, but returns non-negative remainder (i.e., 0 <= r < \|d\|
17		* always holds)
18		*/
19
20	233k	if (!(BN_mod(r, m, d, ctx)))
21	0	return 0;
22	233k	if (!r->neg)
23	211k	return 1;
24		/* now -\|d\| < r < 0, so we have to set r := r + \|d\| */
25	21.9k	return (d->neg ? BN_sub : BN_add) (r, r, d);
26	233k	}
27
28		int BN_mod_add(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
29		BN_CTX *ctx)
30	0	{
31	0	if (!BN_add(r, a, b))
32	0	return 0;
33	0	return BN_nnmod(r, r, m, ctx);
34	0	}
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		*/
48		int bn_mod_add_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
49		const BIGNUM *m)
50	389k	{
51	389k	size_t i, ai, bi, mtop = m->top;
52	389k	BN_ULONG storage[1024 / BN_BITS2];
53	389k	BN_ULONG carry, temp, mask, rp, tp = storage;
54	389k	const BN_ULONG ap, bp;
55
56	389k	if (bn_wexpand(r, mtop) == NULL)
57	0	return 0;
58
59	389k	if (mtop > sizeof(storage) / sizeof(storage[0])) {
60	1.26k	tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
61	1.26k	if (tp == NULL) {
62	0	ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
63	0	return 0;
64	0	}
65	1.26k	}
66
67	389k	ap = a->d != NULL ? a->d : tp;
68	389k	bp = b->d != NULL ? b->d : tp;
69
70	2.59M	for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
71	2.20M	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
72	2.20M	temp = ((ap[ai] & mask) + carry) & BN_MASK2;
73	2.20M	carry = (temp < carry);
74
75	2.20M	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
76	2.20M	tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
77	2.20M	carry += (tp[i] < temp);
78
79	2.20M	i++;
80	2.20M	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
81	2.20M	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
82	2.20M	}
83	389k	rp = r->d;
84	389k	carry -= bn_sub_words(rp, tp, m->d, mtop);
85	2.59M	for (i = 0; i < mtop; i++) {
86	2.20M	rp[i] = (carry & tp[i]) \| (~carry & rp[i]);
87	2.20M	((volatile BN_ULONG *)tp)[i] = 0;
88	2.20M	}
89	389k	r->top = mtop;
90	389k	r->flags \|= BN_FLG_FIXED_TOP;
91	389k	r->neg = 0;
92
93	389k	if (tp != storage)
94	1.26k	OPENSSL_free(tp);
95
96	389k	return 1;
97	389k	}
98
99		int BN_mod_add_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
100		const BIGNUM *m)
101	387k	{
102	387k	int ret = bn_mod_add_fixed_top(r, a, b, m);
103
104	387k	if (ret)
105	387k	bn_correct_top(r);
106
107	387k	return ret;
108	387k	}
109
110		int BN_mod_sub(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
111		BN_CTX *ctx)
112	0	{
113	0	if (!BN_sub(r, a, b))
114	0	return 0;
115	0	return BN_nnmod(r, r, m, ctx);
116	0	}
117
118		/*
119		* BN_mod_sub variant that may be used if both a and b are non-negative,
120		* a is less than m, while b is of same bit width as m. It's implemented
121		* as subtraction followed by two conditional additions.
122		*
123		* 0 <= a < m
124		* 0 <= b < 2^w < 2*m
125		*
126		* after subtraction
127		*
128		* -2*m < r = a - b < m
129		*
130		* Thus it takes up to two conditional additions to make \|r\| positive.
131		*/
132		int bn_mod_sub_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM *b,
133		const BIGNUM *m)
134	1.26k	{
135	1.26k	size_t i, ai, bi, mtop = m->top;
136	1.26k	BN_ULONG borrow, carry, ta, tb, mask, *rp;
137	1.26k	const BN_ULONG ap, bp;
138
139	1.26k	if (bn_wexpand(r, mtop) == NULL)
140	0	return 0;
141
142	1.26k	rp = r->d;
143	1.26k	ap = a->d != NULL ? a->d : rp;
144	1.26k	bp = b->d != NULL ? b->d : rp;
145
146	21.4k	for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
147	20.1k	mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
148	20.1k	ta = ap[ai] & mask;
149
150	20.1k	mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
151	20.1k	tb = bp[bi] & mask;
152	20.1k	rp[i] = ta - tb - borrow;
153	20.1k	if (ta != tb)
154	17.0k	borrow = (ta < tb);
155
156	20.1k	i++;
157	20.1k	ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
158	20.1k	bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
159	20.1k	}
160	1.26k	ap = m->d;
161	21.4k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
162	20.1k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
163	20.1k	carry = (ta < carry);
164	20.1k	rp[i] = (rp[i] + ta) & BN_MASK2;
165	20.1k	carry += (rp[i] < ta);
166	20.1k	}
167	1.26k	borrow -= carry;
168	21.4k	for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
169	20.1k	ta = ((ap[i] & mask) + carry) & BN_MASK2;
170	20.1k	carry = (ta < carry);
171	20.1k	rp[i] = (rp[i] + ta) & BN_MASK2;
172	20.1k	carry += (rp[i] < ta);
173	20.1k	}
174
175	1.26k	r->top = mtop;
176	1.26k	r->flags \|= BN_FLG_FIXED_TOP;
177	1.26k	r->neg = 0;
178
179	1.26k	return 1;
180	1.26k	}
181
182		/*
183		* BN_mod_sub variant that may be used if both a and b are non-negative and
184		* less than m
185		*/
186		int BN_mod_sub_quick(BIGNUM r, const BIGNUM a, const BIGNUM *b,
187		const BIGNUM *m)
188	325k	{
189	325k	if (!BN_sub(r, a, b))
190	0	return 0;
191	325k	if (r->neg)
192	163k	return BN_add(r, r, m);
193	162k	return 1;
194	325k	}
195
196		/* slow but works */
197		int BN_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m,
198		BN_CTX *ctx)
199	210	{
200	210	BIGNUM *t;
201	210	int ret = 0;
202
203	210	bn_check_top(a);
204	210	bn_check_top(b);
205	210	bn_check_top(m);
206
207	210	BN_CTX_start(ctx);
208	210	if ((t = BN_CTX_get(ctx)) == NULL)
209	0	goto err;
210	210	if (a == b) {
211	0	if (!BN_sqr(t, a, ctx))
212	0	goto err;
213	210	} else {
214	210	if (!BN_mul(t, a, b, ctx))
215	0	goto err;
216	210	}
217	210	if (!BN_nnmod(r, t, m, ctx))
218	0	goto err;
219	210	bn_check_top(r);
220	210	ret = 1;
221	210	err:
222	210	BN_CTX_end(ctx);
223	210	return ret;
224	210	}
225
226		int BN_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
227	420	{
228	420	if (!BN_sqr(r, a, ctx))
229	0	return 0;
230		/* r->neg == 0, thus we don't need BN_nnmod */
231	420	return BN_mod(r, r, m, ctx);
232	420	}
233
234		int BN_mod_lshift1(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx)
235	0	{
236	0	if (!BN_lshift1(r, a))
237	0	return 0;
238	0	bn_check_top(r);
239	0	return BN_nnmod(r, r, m, ctx);
240	0	}
241
242		/*
243		* BN_mod_lshift1 variant that may be used if a is non-negative and less than
244		* m
245		*/
246		int BN_mod_lshift1_quick(BIGNUM r, const BIGNUM a, const BIGNUM *m)
247	123k	{
248	123k	if (!BN_lshift1(r, a))
249	0	return 0;
250	123k	bn_check_top(r);
251	123k	if (BN_cmp(r, m) >= 0)
252	63.3k	return BN_sub(r, r, m);
253	60.2k	return 1;
254	123k	}
255
256		int BN_mod_lshift(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m,
257		BN_CTX *ctx)
258	0	{
259	0	BIGNUM *abs_m = NULL;
260	0	int ret;
261
262	0	if (!BN_nnmod(r, a, m, ctx))
263	0	return 0;
264
265	0	if (m->neg) {
266	0	abs_m = BN_dup(m);
267	0	if (abs_m == NULL)
268	0	return 0;
269	0	abs_m->neg = 0;
270	0	}
271
272	0	ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
273	0	bn_check_top(r);
274
275	0	BN_free(abs_m);
276	0	return ret;
277	0	}
278
279		/*
280		* BN_mod_lshift variant that may be used if a is non-negative and less than
281		* m
282		*/
283		int BN_mod_lshift_quick(BIGNUM r, const BIGNUM a, int n, const BIGNUM *m)
284	65.9k	{
285	65.9k	if (r != a) {
286	56.4k	if (BN_copy(r, a) == NULL)
287	0	return 0;
288	56.4k	}
289
290	200k	while (n > 0) {
291	134k	int max_shift;
292
293		/* 0 < r < m */
294	134k	max_shift = BN_num_bits(m) - BN_num_bits(r);
295		/* max_shift >= 0 */
296
297	134k	if (max_shift < 0) {
298	0	ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
299	0	return 0;
300	0	}
301
302	134k	if (max_shift > n)
303	4.71k	max_shift = n;
304
305	134k	if (max_shift) {
306	16.4k	if (!BN_lshift(r, r, max_shift))
307	0	return 0;
308	16.4k	n -= max_shift;
309	117k	} else {
310	117k	if (!BN_lshift1(r, r))
311	0	return 0;
312	117k	--n;
313	117k	}
314
315		/* BN_num_bits(r) <= BN_num_bits(m) */
316
317	134k	if (BN_cmp(r, m) >= 0) {
318	117k	if (!BN_sub(r, r, m))
319	0	return 0;
320	117k	}
321	134k	}
322	65.9k	bn_check_top(r);
323
324	65.9k	return 1;
325	65.9k	}