/*

 * Copyright 1995-2026 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

 */

/*

 * Details about Montgomery multiplication algorithms can be found in

 * https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf

 * and https://cetinkayakoc.net/docs/r01.pdf

 */

#include "internal/cryptlib.h"

#include "bn_local.h"

#define MONT_WORD /* use the faster word-based algorithm */

#ifdef MONT_WORD

static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);

#endif

int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,

    BN_MONT_CTX *mont, BN_CTX *ctx)

{

    int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);

    bn_correct_top(r);

    bn_check_top(r);

    return ret;

}

int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,

    BN_MONT_CTX *mont, BN_CTX *ctx)

{

    BIGNUM *tmp;

    int ret = 0;

    int num = mont->N.top;

#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)

    if (num > 1 && num <= BN_SOFT_LIMIT && a->top == num && b->top == num) {

        if (bn_wexpand(r, num) == NULL)

            return 0;

        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {

            r->neg = a->neg ^ b->neg;

            r->top = num;

            r->flags |= BN_FLG_FIXED_TOP;

            return 1;

        }

    }

#endif

    if ((a->top + b->top) > 2 * num)

        return 0;

    BN_CTX_start(ctx);

    tmp = BN_CTX_get(ctx);

    if (tmp == NULL)

        goto err;

    bn_check_top(tmp);

    if (a == b) {

        if (!bn_sqr_fixed_top(tmp, a, ctx))

            goto err;

    } else {

        if (!bn_mul_fixed_top(tmp, a, b, ctx))

            goto err;

    }

    /* reduce from aRR to aR */

#ifdef MONT_WORD

    if (!bn_from_montgomery_word(r, tmp, mont))

        goto err;

#else

    if (!BN_from_montgomery(r, tmp, mont, ctx))

        goto err;

#endif

    ret = 1;

err:

    BN_CTX_end(ctx);

    return ret;

}

#ifdef MONT_WORD

static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)

{

    BIGNUM *n;

    BN_ULONG *ap, *np, *rp, n0, v, carry;

    int nl, max, i;

    unsigned int rtop;

    n = &(mont->N);

    nl = n->top;

    if (nl == 0) {

        ret->top = 0;

        return 1;

    }

    max = (2 * nl); /* carry is stored separately */

    if (bn_wexpand(r, max) == NULL)

        return 0;

    r->neg ^= n->neg;

    np = n->d;

    rp = r->d;

    /* clear the top words of T */

    for (rtop = r->top, i = 0; i < max; i++) {

        v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));

        rp[i] &= v;

    }

    r->top = max;

    r->flags |= BN_FLG_FIXED_TOP;

    n0 = mont->n0[0];

    /*

     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On

     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|

     * includes |carry| which is stored separately.

     */

    for (carry = 0, i = 0; i < nl; i++, rp++) {

        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);

        v = (v + carry + rp[nl]) & BN_MASK2;

        carry |= (v != rp[nl]);

        carry &= (v <= rp[nl]);

        rp[nl] = v;

    }

    if (bn_wexpand(ret, nl) == NULL)

        return 0;

    ret->top = nl;

    ret->flags |= BN_FLG_FIXED_TOP;

    ret->neg = r->neg;

    rp = ret->d;

    /*

     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|

     * includes |carry| which is stored separately.

     */

    ap = &(r->d[nl]);

    carry -= bn_sub_words(rp, ap, np, nl);

    /*

     * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note

     * |carry| cannot be 1. That would imply the subtraction did not fit in

     * |nl| words, and we know at most one subtraction is needed.

     */

    for (i = 0; i < nl; i++) {

        rp[i] = (carry & ap[i]) | (~carry & rp[i]);

        ap[i] = 0;

    }

    return 1;

}

#endif /* MONT_WORD */

int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,

    BN_CTX *ctx)

{

    int retn;

    retn = bn_from_mont_fixed_top(ret, a, mont, ctx);

    bn_correct_top(ret);

    bn_check_top(ret);

    return retn;

}

int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,

    BN_CTX *ctx)

{

    int retn = 0;

#ifdef MONT_WORD

    BIGNUM *t;

    BN_CTX_start(ctx);

    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {

        retn = bn_from_montgomery_word(ret, t, mont);

    }

    BN_CTX_end(ctx);

#else /* !MONT_WORD */

    BIGNUM *t1, *t2;

    BN_CTX_start(ctx);

    t1 = BN_CTX_get(ctx);

    t2 = BN_CTX_get(ctx);

    if (t2 == NULL)

        goto err;

    if (!BN_copy(t1, a))

        goto err;

    BN_mask_bits(t1, mont->ri);

    if (!BN_mul(t2, t1, &mont->Ni, ctx))

        goto err;

    BN_mask_bits(t2, mont->ri);

    if (!BN_mul(t1, t2, &mont->N, ctx))

        goto err;

    if (!BN_add(t2, a, t1))

        goto err;

    if (!BN_rshift(ret, t2, mont->ri))

        goto err;

    if (BN_ucmp(ret, &(mont->N)) >= 0) {

        if (!BN_usub(ret, ret, &(mont->N)))

            goto err;

    }

    retn = 1;

    bn_check_top(ret);

err:

    BN_CTX_end(ctx);

#endif /* MONT_WORD */

    return retn;

}

int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,

    BN_CTX *ctx)

{

    return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);

}

BN_MONT_CTX *BN_MONT_CTX_new(void)

{

    BN_MONT_CTX *ret;

    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)

        return NULL;

    BN_MONT_CTX_init(ret);

    ret->flags = BN_FLG_MALLOCED;

    return ret;

}

void BN_MONT_CTX_init(BN_MONT_CTX *ctx)

{

    ctx->ri = 0;

    bn_init(&ctx->RR);

    bn_init(&ctx->N);

    bn_init(&ctx->Ni);

    ctx->n0[0] = ctx->n0[1] = 0;

    ctx->flags = 0;

}

void BN_MONT_CTX_free(BN_MONT_CTX *mont)

{

    if (mont == NULL)

        return;

    BN_clear_free(&mont->RR);

    BN_clear_free(&mont->N);

    BN_clear_free(&mont->Ni);

    if (mont->flags & BN_FLG_MALLOCED)

        OPENSSL_free(mont);

}

int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)

{

    int i, ret = 0;

    BIGNUM *Ri, *R;

    if (BN_is_zero(mod))

        return 0;

    BN_CTX_start(ctx);

    if ((Ri = BN_CTX_get(ctx)) == NULL)

        goto err;

    R = &(mont->RR); /* grab RR as a temp */

    if (!BN_copy(&(mont->N), mod))

        goto err; /* Set N */

    if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)

        BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);

    mont->N.neg = 0;

#ifdef MONT_WORD

    {

        BIGNUM tmod;

        BN_ULONG buf[2];

        bn_init(&tmod);

        tmod.d = buf;

        tmod.dmax = 2;

        tmod.neg = 0;

        if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)

            BN_set_flags(&tmod, BN_FLG_CONSTTIME);

        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;

#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32)

        /*

         * Only certain BN_BITS2<=32 platforms actually make use of n0[1],

         * and we could use the #else case (with a shorter R value) for the

         * others.  However, currently only the assembler files do know which

         * is which.

         */

        BN_zero(R);

        if (!(BN_set_bit(R, 2 * BN_BITS2)))

            goto err;

        tmod.top = 0;

        if ((buf[0] = mod->d[0]))

            tmod.top = 1;

        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))

            tmod.top = 2;

        if (BN_is_one(&tmod))

            BN_zero(Ri);

        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)

            goto err;

        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))

            goto err; /* R*Ri */

        if (!BN_is_zero(Ri)) {

            if (!BN_sub_word(Ri, 1))

                goto err;

        } else { /* if N mod word size == 1 */

            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)

                goto err;

            /* Ri-- (mod double word size) */

            Ri->neg = 0;

            Ri->d[0] = BN_MASK2;

            Ri->d[1] = BN_MASK2;

            Ri->top = 2;

        }

        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))

            goto err;

        /*

         * Ni = (R*Ri-1)/N, keep only couple of least significant words:

         */

        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;

        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;

#else

        BN_zero(R);

        if (!(BN_set_bit(R, BN_BITS2)))

            goto err; /* R */

        buf[0] = mod->d[0]; /* tmod = N mod word size */

        buf[1] = 0;

        tmod.top = buf[0] != 0 ? 1 : 0;

        /* Ri = R^-1 mod N */

        if (BN_is_one(&tmod))

            BN_zero(Ri);

        else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)

            goto err;

        if (!BN_lshift(Ri, Ri, BN_BITS2))

            goto err; /* R*Ri */

        if (!BN_is_zero(Ri)) {

            if (!BN_sub_word(Ri, 1))

                goto err;

        } else { /* if N mod word size == 1 */

            if (!BN_set_word(Ri, BN_MASK2))

                goto err; /* Ri-- (mod word size) */

        }

        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))

            goto err;

        /*

         * Ni = (R*Ri-1)/N, keep only least significant word:

         */

        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;

        mont->n0[1] = 0;

#endif

    }

#else /* !MONT_WORD */

    { /* bignum version */

        mont->ri = BN_num_bits(&mont->N);

        BN_zero(R);

        if (!BN_set_bit(R, mont->ri))

            goto err; /* R = 2^ri */

        /* Ri = R^-1 mod N */

        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)

            goto err;

        if (!BN_lshift(Ri, Ri, mont->ri))

            goto err; /* R*Ri */

        if (!BN_sub_word(Ri, 1))

            goto err;

        /*

         * Ni = (R*Ri-1) / N

         */

        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))

            goto err;

    }

#endif

    /* setup RR for conversions */

    BN_zero(&(mont->RR));

    if (!BN_set_bit(&(mont->RR), mont->ri * 2))

        goto err;

    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))

        goto err;

    for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)

        mont->RR.d[i] = 0;

    mont->RR.top = ret;

    mont->RR.flags |= BN_FLG_FIXED_TOP;

    ret = 1;

err:

    BN_CTX_end(ctx);

    return ret;

}

BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)

{

    if (to == from)

        return to;

    if (!BN_copy(&(to->RR), &(from->RR)))

        return NULL;

    if (!BN_copy(&(to->N), &(from->N)))

        return NULL;

    if (!BN_copy(&(to->Ni), &(from->Ni)))

        return NULL;

    to->ri = from->ri;

    to->n0[0] = from->n0[0];

    to->n0[1] = from->n0[1];

    return to;

}

BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,

    const BIGNUM *mod, BN_CTX *ctx)

{

    BN_MONT_CTX *ret;

    if (!CRYPTO_THREAD_read_lock(lock))

        return NULL;

    ret = *pmont;

    CRYPTO_THREAD_unlock(lock);

    if (ret)

        return ret;

    /*

     * We don't want to serialize globally while doing our lazy-init math in

     * BN_MONT_CTX_set. That punishes threads that are doing independent

     * things. Instead, punish the case where more than one thread tries to

     * lazy-init the same 'pmont', by having each do the lazy-init math work

     * independently and only use the one from the thread that wins the race

     * (the losers throw away the work they've done).

     */

    ret = BN_MONT_CTX_new();

    if (ret == NULL)

        return NULL;

    if (!BN_MONT_CTX_set(ret, mod, ctx)) {

        BN_MONT_CTX_free(ret);

        return NULL;

    }

    /* The locked compare-and-set, after the local work is done. */

    if (!CRYPTO_THREAD_write_lock(lock)) {

        BN_MONT_CTX_free(ret);

        return NULL;

    }

    if (*pmont) {

        BN_MONT_CTX_free(ret);

        ret = *pmont;

    } else

        *pmont = ret;

    CRYPTO_THREAD_unlock(lock);

    return ret;

}

int ossl_bn_mont_ctx_set(BN_MONT_CTX *ctx, const BIGNUM *modulus, int ri, const unsigned char *rr,

    int rrlen, uint32_t nlo, uint32_t nhi)

{

    if (BN_copy(&ctx->N, modulus) == NULL)

        return 0;

    if (BN_bin2bn(rr, rrlen, &ctx->RR) == NULL)

        return 0;

    ctx->ri = ri;

#if (BN_BITS2 <= 32) && defined(OPENSSL_BN_ASM_MONT)

    ctx->n0[0] = nlo;

    ctx->n0[1] = nhi;

#elif BN_BITS2 <= 32

    ctx->n0[0] = nlo;

    ctx->n0[1] = 0;

#else

    ctx->n0[0] = ((BN_ULONG)nhi << 32) | nlo;

    ctx->n0[1] = 0;

#endif

    return 1;

}

int ossl_bn_mont_ctx_eq(const BN_MONT_CTX *m1, const BN_MONT_CTX *m2)

{

    if (m1->ri != m2->ri)

        return 0;

    if (BN_cmp(&m1->RR, &m2->RR) != 0)

        return 0;

    if (m1->flags != m2->flags)

        return 0;

#ifdef MONT_WORD

    if (m1->n0[0] != m2->n0[0])

        return 0;

    if (m1->n0[1] != m2->n0[1])

        return 0;

#else

    if (BN_cmp(&m1->Ni, &m2->Ni) != 0)

        return 0;

#endif

    return 1;

}