1/*
2 * Copyright 1995-2023 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/*
11 * Details about Montgomery multiplication algorithms can be found at
12 * http://security.ece.orst.edu/publications.html, e.g.
13 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
14 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
15 */
16
17#include "internal/cryptlib.h"
18#include "bn_local.h"
19
20#define MONT_WORD               /* use the faster word-based algorithm */
21
22#ifdef MONT_WORD
23static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
24#endif
25
26int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
27                          BN_MONT_CTX *mont, BN_CTX *ctx)
28{
29    int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
30
31    bn_correct_top(r);
32    bn_check_top(r);
33
34    return ret;
35}
36
37int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
38                          BN_MONT_CTX *mont, BN_CTX *ctx)
39{
40    BIGNUM *tmp;
41    int ret = 0;
42    int num = mont->N.top;
43
44#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
45    if (num > 1 && num <= BN_SOFT_LIMIT && a->top == num && b->top == num) {
46        if (bn_wexpand(r, num) == NULL)
47            return 0;
48        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
49            r->neg = a->neg ^ b->neg;
50            r->top = num;
51            r->flags |= BN_FLG_FIXED_TOP;
52            return 1;
53        }
54    }
55#endif
56
57    if ((a->top + b->top) > 2 * num)
58        return 0;
59
60    BN_CTX_start(ctx);
61    tmp = BN_CTX_get(ctx);
62    if (tmp == NULL)
63        goto err;
64
65    bn_check_top(tmp);
66    if (a == b) {
67        if (!bn_sqr_fixed_top(tmp, a, ctx))
68            goto err;
69    } else {
70        if (!bn_mul_fixed_top(tmp, a, b, ctx))
71            goto err;
72    }
73    /* reduce from aRR to aR */
74#ifdef MONT_WORD
75    if (!bn_from_montgomery_word(r, tmp, mont))
76        goto err;
77#else
78    if (!BN_from_montgomery(r, tmp, mont, ctx))
79        goto err;
80#endif
81    ret = 1;
82 err:
83    BN_CTX_end(ctx);
84    return ret;
85}
86
87#ifdef MONT_WORD
88static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
89{
90    BIGNUM *n;
91    BN_ULONG *ap, *np, *rp, n0, v, carry;
92    int nl, max, i;
93    unsigned int rtop;
94
95    n = &(mont->N);
96    nl = n->top;
97    if (nl == 0) {
98        ret->top = 0;
99        return 1;
100    }
101
102    max = (2 * nl);             /* carry is stored separately */
103    if (bn_wexpand(r, max) == NULL)
104        return 0;
105
106    r->neg ^= n->neg;
107    np = n->d;
108    rp = r->d;
109
110    /* clear the top words of T */
111    for (rtop = r->top, i = 0; i < max; i++) {
112        v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
113        rp[i] &= v;
114    }
115
116    r->top = max;
117    r->flags |= BN_FLG_FIXED_TOP;
118    n0 = mont->n0[0];
119
120    /*
121     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
122     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
123     * includes |carry| which is stored separately.
124     */
125    for (carry = 0, i = 0; i < nl; i++, rp++) {
126        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
127        v = (v + carry + rp[nl]) & BN_MASK2;
128        carry |= (v != rp[nl]);
129        carry &= (v <= rp[nl]);
130        rp[nl] = v;
131    }
132
133    if (bn_wexpand(ret, nl) == NULL)
134        return 0;
135    ret->top = nl;
136    ret->flags |= BN_FLG_FIXED_TOP;
137    ret->neg = r->neg;
138
139    rp = ret->d;
140
141    /*
142     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
143     * includes |carry| which is stored separately.
144     */
145    ap = &(r->d[nl]);
146
147    carry -= bn_sub_words(rp, ap, np, nl);
148    /*
149     * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
150     * |carry| cannot be 1. That would imply the subtraction did not fit in
151     * |nl| words, and we know at most one subtraction is needed.
152     */
153    for (i = 0; i < nl; i++) {
154        rp[i] = (carry & ap[i]) | (~carry & rp[i]);
155        ap[i] = 0;
156    }
157
158    return 1;
159}
160#endif                          /* MONT_WORD */
161
162int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
163                       BN_CTX *ctx)
164{
165    int retn;
166
167    retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
168    bn_correct_top(ret);
169    bn_check_top(ret);
170
171    return retn;
172}
173
174int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
175                           BN_CTX *ctx)
176{
177    int retn = 0;
178#ifdef MONT_WORD
179    BIGNUM *t;
180
181    BN_CTX_start(ctx);
182    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
183        retn = bn_from_montgomery_word(ret, t, mont);
184    }
185    BN_CTX_end(ctx);
186#else                           /* !MONT_WORD */
187    BIGNUM *t1, *t2;
188
189    BN_CTX_start(ctx);
190    t1 = BN_CTX_get(ctx);
191    t2 = BN_CTX_get(ctx);
192    if (t2 == NULL)
193        goto err;
194
195    if (!BN_copy(t1, a))
196        goto err;
197    BN_mask_bits(t1, mont->ri);
198
199    if (!BN_mul(t2, t1, &mont->Ni, ctx))
200        goto err;
201    BN_mask_bits(t2, mont->ri);
202
203    if (!BN_mul(t1, t2, &mont->N, ctx))
204        goto err;
205    if (!BN_add(t2, a, t1))
206        goto err;
207    if (!BN_rshift(ret, t2, mont->ri))
208        goto err;
209
210    if (BN_ucmp(ret, &(mont->N)) >= 0) {
211        if (!BN_usub(ret, ret, &(mont->N)))
212            goto err;
213    }
214    retn = 1;
215    bn_check_top(ret);
216 err:
217    BN_CTX_end(ctx);
218#endif                          /* MONT_WORD */
219    return retn;
220}
221
222int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
223                         BN_CTX *ctx)
224{
225    return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
226}
227
228BN_MONT_CTX *BN_MONT_CTX_new(void)
229{
230    BN_MONT_CTX *ret;
231
232    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
233        ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
234        return NULL;
235    }
236
237    BN_MONT_CTX_init(ret);
238    ret->flags = BN_FLG_MALLOCED;
239    return ret;
240}
241
242void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
243{
244    ctx->ri = 0;
245    bn_init(&ctx->RR);
246    bn_init(&ctx->N);
247    bn_init(&ctx->Ni);
248    ctx->n0[0] = ctx->n0[1] = 0;
249    ctx->flags = 0;
250}
251
252void BN_MONT_CTX_free(BN_MONT_CTX *mont)
253{
254    if (mont == NULL)
255        return;
256    BN_clear_free(&mont->RR);
257    BN_clear_free(&mont->N);
258    BN_clear_free(&mont->Ni);
259    if (mont->flags & BN_FLG_MALLOCED)
260        OPENSSL_free(mont);
261}
262
263int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
264{
265    int i, ret = 0;
266    BIGNUM *Ri, *R;
267
268    if (BN_is_zero(mod))
269        return 0;
270
271    BN_CTX_start(ctx);
272    if ((Ri = BN_CTX_get(ctx)) == NULL)
273        goto err;
274    R = &(mont->RR);            /* grab RR as a temp */
275    if (!BN_copy(&(mont->N), mod))
276        goto err;               /* Set N */
277    if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
278        BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
279    mont->N.neg = 0;
280
281#ifdef MONT_WORD
282    {
283        BIGNUM tmod;
284        BN_ULONG buf[2];
285
286        bn_init(&tmod);
287        tmod.d = buf;
288        tmod.dmax = 2;
289        tmod.neg = 0;
290
291        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
292            BN_set_flags(&tmod, BN_FLG_CONSTTIME);
293
294        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
295
296# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
297        /*
298         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
299         * and we could use the #else case (with a shorter R value) for the
300         * others.  However, currently only the assembler files do know which
301         * is which.
302         */
303
304        BN_zero(R);
305        if (!(BN_set_bit(R, 2 * BN_BITS2)))
306            goto err;
307
308        tmod.top = 0;
309        if ((buf[0] = mod->d[0]))
310            tmod.top = 1;
311        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
312            tmod.top = 2;
313
314        if (BN_is_one(&tmod))
315            BN_zero(Ri);
316        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
317            goto err;
318        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
319            goto err;           /* R*Ri */
320        if (!BN_is_zero(Ri)) {
321            if (!BN_sub_word(Ri, 1))
322                goto err;
323        } else {                /* if N mod word size == 1 */
324
325            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
326                goto err;
327            /* Ri-- (mod double word size) */
328            Ri->neg = 0;
329            Ri->d[0] = BN_MASK2;
330            Ri->d[1] = BN_MASK2;
331            Ri->top = 2;
332        }
333        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
334            goto err;
335        /*
336         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
337         */
338        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
339        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
340# else
341        BN_zero(R);
342        if (!(BN_set_bit(R, BN_BITS2)))
343            goto err;           /* R */
344
345        buf[0] = mod->d[0];     /* tmod = N mod word size */
346        buf[1] = 0;
347        tmod.top = buf[0] != 0 ? 1 : 0;
348        /* Ri = R^-1 mod N */
349        if (BN_is_one(&tmod))
350            BN_zero(Ri);
351        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
352            goto err;
353        if (!BN_lshift(Ri, Ri, BN_BITS2))
354            goto err;           /* R*Ri */
355        if (!BN_is_zero(Ri)) {
356            if (!BN_sub_word(Ri, 1))
357                goto err;
358        } else {                /* if N mod word size == 1 */
359
360            if (!BN_set_word(Ri, BN_MASK2))
361                goto err;       /* Ri-- (mod word size) */
362        }
363        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
364            goto err;
365        /*
366         * Ni = (R*Ri-1)/N, keep only least significant word:
367         */
368        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
369        mont->n0[1] = 0;
370# endif
371    }
372#else                           /* !MONT_WORD */
373    {                           /* bignum version */
374        mont->ri = BN_num_bits(&mont->N);
375        BN_zero(R);
376        if (!BN_set_bit(R, mont->ri))
377            goto err;           /* R = 2^ri */
378        /* Ri = R^-1 mod N */
379        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
380            goto err;
381        if (!BN_lshift(Ri, Ri, mont->ri))
382            goto err;           /* R*Ri */
383        if (!BN_sub_word(Ri, 1))
384            goto err;
385        /*
386         * Ni = (R*Ri-1) / N
387         */
388        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
389            goto err;
390    }
391#endif
392
393    /* setup RR for conversions */
394    BN_zero(&(mont->RR));
395    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
396        goto err;
397    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
398        goto err;
399
400    for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
401        mont->RR.d[i] = 0;
402    mont->RR.top = ret;
403    mont->RR.flags |= BN_FLG_FIXED_TOP;
404
405    ret = 1;
406 err:
407    BN_CTX_end(ctx);
408    return ret;
409}
410
411BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
412{
413    if (to == from)
414        return to;
415
416    if (!BN_copy(&(to->RR), &(from->RR)))
417        return NULL;
418    if (!BN_copy(&(to->N), &(from->N)))
419        return NULL;
420    if (!BN_copy(&(to->Ni), &(from->Ni)))
421        return NULL;
422    to->ri = from->ri;
423    to->n0[0] = from->n0[0];
424    to->n0[1] = from->n0[1];
425    return to;
426}
427
428BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
429                                    const BIGNUM *mod, BN_CTX *ctx)
430{
431    BN_MONT_CTX *ret;
432
433    if (!CRYPTO_THREAD_read_lock(lock))
434        return NULL;
435    ret = *pmont;
436    CRYPTO_THREAD_unlock(lock);
437    if (ret)
438        return ret;
439
440    /*
441     * We don't want to serialize globally while doing our lazy-init math in
442     * BN_MONT_CTX_set. That punishes threads that are doing independent
443     * things. Instead, punish the case where more than one thread tries to
444     * lazy-init the same 'pmont', by having each do the lazy-init math work
445     * independently and only use the one from the thread that wins the race
446     * (the losers throw away the work they've done).
447     */
448    ret = BN_MONT_CTX_new();
449    if (ret == NULL)
450        return NULL;
451    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
452        BN_MONT_CTX_free(ret);
453        return NULL;
454    }
455
456    /* The locked compare-and-set, after the local work is done. */
457    if (!CRYPTO_THREAD_write_lock(lock)) {
458        BN_MONT_CTX_free(ret);
459        return NULL;
460    }
461
462    if (*pmont) {
463        BN_MONT_CTX_free(ret);
464        ret = *pmont;
465    } else
466        *pmont = ret;
467    CRYPTO_THREAD_unlock(lock);
468    return ret;
469}
470