/* $OpenBSD: rsa_eay.c,v 1.66 2025/05/10 05:54:38 tb Exp $ */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <stdio.h>
#include <string.h>

#include <openssl/opensslconf.h>

#include <openssl/bn.h>
#include <openssl/rsa.h>

#include "bn_local.h"
#include "err_local.h"
#include "rsa_local.h"

static int
rsa_public_encrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        BIGNUM *f, *ret;
        int i, j, k, num = 0, r = -1;
        unsigned char *buf = NULL;
        BN_CTX *ctx = NULL;

        if (BN_num_bits(rsa->n) > OPENSSL_RSA_MAX_MODULUS_BITS) {
                RSAerror(RSA_R_MODULUS_TOO_LARGE);
                return -1;
        }

        if (BN_ucmp(rsa->n, rsa->e) <= 0) {
                RSAerror(RSA_R_BAD_E_VALUE);
                return -1;
        }

        /* for large moduli, enforce exponent limit */
        if (BN_num_bits(rsa->n) > OPENSSL_RSA_SMALL_MODULUS_BITS) {
                if (BN_num_bits(rsa->e) > OPENSSL_RSA_MAX_PUBEXP_BITS) {
                        RSAerror(RSA_R_BAD_E_VALUE);
                        return -1;
                }
        }

        if ((ctx = BN_CTX_new()) == NULL)
                goto err;

        BN_CTX_start(ctx);
        f = BN_CTX_get(ctx);
        ret = BN_CTX_get(ctx);
        num = BN_num_bytes(rsa->n);
        buf = malloc(num);

        if (f == NULL || ret == NULL || buf == NULL) {
                RSAerror(ERR_R_MALLOC_FAILURE);
                goto err;
        }

        switch (padding) {
        case RSA_PKCS1_PADDING:
                i = RSA_padding_add_PKCS1_type_2(buf, num, from, flen);
                break;
#ifndef OPENSSL_NO_SHA
        case RSA_PKCS1_OAEP_PADDING:
                i = RSA_padding_add_PKCS1_OAEP(buf, num, from, flen, NULL, 0);
                break;
#endif
        case RSA_NO_PADDING:
                i = RSA_padding_add_none(buf, num, from, flen);
                break;
        default:
                RSAerror(RSA_R_UNKNOWN_PADDING_TYPE);
                goto err;
        }
        if (i <= 0)
                goto err;

        if (BN_bin2bn(buf, num, f) == NULL)
                goto err;

        if (BN_ucmp(f, rsa->n) >= 0) {
                /* usually the padding functions would catch this */
                RSAerror(RSA_R_DATA_TOO_LARGE_FOR_MODULUS);
                goto err;
        }

        if (rsa->flags & RSA_FLAG_CACHE_PUBLIC) {
                if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n,
                    CRYPTO_LOCK_RSA, rsa->n, ctx))
                        goto err;
        }

        if (!rsa->meth->bn_mod_exp(ret, f, rsa->e, rsa->n, ctx,
            rsa->_method_mod_n))
                goto err;

        /* put in leading 0 bytes if the number is less than the
         * length of the modulus */
        j = BN_num_bytes(ret);
        i = BN_bn2bin(ret, &(to[num - j]));
        for (k = 0; k < num - i; k++)
                to[k] = 0;

        r = num;
err:
        if (ctx != NULL) {
                BN_CTX_end(ctx);
                BN_CTX_free(ctx);
        }
        freezero(buf, num);
        return r;
}

static BN_BLINDING *
rsa_get_blinding(RSA *rsa, int *local, BN_CTX *ctx)
{
        BN_BLINDING *ret;
        int got_write_lock = 0;

        CRYPTO_r_lock(CRYPTO_LOCK_RSA);

        if (rsa->blinding == NULL) {
                CRYPTO_r_unlock(CRYPTO_LOCK_RSA);
                CRYPTO_w_lock(CRYPTO_LOCK_RSA);
                got_write_lock = 1;

                if (rsa->blinding == NULL)
                        rsa->blinding = RSA_setup_blinding(rsa, ctx);
        }

        if ((ret = rsa->blinding) == NULL)
                goto err;

        /*
         * We need a shared blinding. Accesses require locks and a copy of the
         * blinding factor needs to be retained on use.
         */
        if ((*local = BN_BLINDING_is_local(ret)) == 0) {
                if (rsa->mt_blinding == NULL) {
                        if (!got_write_lock) {
                                CRYPTO_r_unlock(CRYPTO_LOCK_RSA);
                                CRYPTO_w_lock(CRYPTO_LOCK_RSA);
                                got_write_lock = 1;
                        }

                        if (rsa->mt_blinding == NULL)
                                rsa->mt_blinding = RSA_setup_blinding(rsa, ctx);
                }
                ret = rsa->mt_blinding;
        }

 err:
        if (got_write_lock)
                CRYPTO_w_unlock(CRYPTO_LOCK_RSA);
        else
                CRYPTO_r_unlock(CRYPTO_LOCK_RSA);

        return ret;
}

static int
rsa_blinding_convert(BN_BLINDING *b, BIGNUM *f, BIGNUM *unblind, BN_CTX *ctx)
{
        if (unblind == NULL)
                /*
                 * Local blinding: store the unblinding factor
                 * in BN_BLINDING.
                 */
                return BN_BLINDING_convert(f, NULL, b, ctx);
        else {
                /*
                 * Shared blinding: store the unblinding factor
                 * outside BN_BLINDING.
                 */
                int ret;
                CRYPTO_w_lock(CRYPTO_LOCK_RSA_BLINDING);
                ret = BN_BLINDING_convert(f, unblind, b, ctx);
                CRYPTO_w_unlock(CRYPTO_LOCK_RSA_BLINDING);
                return ret;
        }
}

static int
rsa_blinding_invert(BN_BLINDING *b, BIGNUM *f, BIGNUM *unblind, BN_CTX *ctx)
{
        /*
         * For local blinding, unblind is set to NULL, and BN_BLINDING_invert()
         * will use the unblinding factor stored in BN_BLINDING.
         * If BN_BLINDING is shared between threads, unblind must be non-null:
         * BN_BLINDING_invert() will then use the local unblinding factor,
         * and will only read the modulus from BN_BLINDING.
         * In both cases it's safe to access the blinding without a lock.
         */
        return BN_BLINDING_invert(f, unblind, b, ctx);
}

/* signing */
static int
rsa_private_encrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        BIGNUM *f, *ret, *res;
        int i, j, k, num = 0, r = -1;
        unsigned char *buf = NULL;
        BN_CTX *ctx = NULL;
        int local_blinding = 0;
        /*
         * Used only if the blinding structure is shared. A non-NULL unblind
         * instructs rsa_blinding_convert() and rsa_blinding_invert() to store
         * the unblinding factor outside the blinding structure.
         */
        BIGNUM *unblind = NULL;
        BN_BLINDING *blinding = NULL;

        if ((ctx = BN_CTX_new()) == NULL)
                goto err;

        BN_CTX_start(ctx);
        f = BN_CTX_get(ctx);
        ret = BN_CTX_get(ctx);
        num = BN_num_bytes(rsa->n);
        buf = malloc(num);

        if (f == NULL || ret == NULL || buf == NULL) {
                RSAerror(ERR_R_MALLOC_FAILURE);
                goto err;
        }

        switch (padding) {
        case RSA_PKCS1_PADDING:
                i = RSA_padding_add_PKCS1_type_1(buf, num, from, flen);
                break;
        case RSA_X931_PADDING:
                i = RSA_padding_add_X931(buf, num, from, flen);
                break;
        case RSA_NO_PADDING:
                i = RSA_padding_add_none(buf, num, from, flen);
                break;
        default:
                RSAerror(RSA_R_UNKNOWN_PADDING_TYPE);
                goto err;
        }
        if (i <= 0)
                goto err;

        if (BN_bin2bn(buf, num, f) == NULL)
                goto err;

        if (BN_ucmp(f, rsa->n) >= 0) {
                /* usually the padding functions would catch this */
                RSAerror(RSA_R_DATA_TOO_LARGE_FOR_MODULUS);
                goto err;
        }

        if (rsa->flags & RSA_FLAG_CACHE_PUBLIC) {
                if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n,
                    CRYPTO_LOCK_RSA, rsa->n, ctx))
                        goto err;
        }

        if (!(rsa->flags & RSA_FLAG_NO_BLINDING)) {
                blinding = rsa_get_blinding(rsa, &local_blinding, ctx);
                if (blinding == NULL) {
                        RSAerror(ERR_R_INTERNAL_ERROR);
                        goto err;
                }
        }

        if (blinding != NULL) {
                if (!local_blinding && ((unblind = BN_CTX_get(ctx)) == NULL)) {
                        RSAerror(ERR_R_MALLOC_FAILURE);
                        goto err;
                }
                if (!rsa_blinding_convert(blinding, f, unblind, ctx))
                        goto err;
        }

        if ((rsa->flags & RSA_FLAG_EXT_PKEY) ||
            (rsa->p != NULL && rsa->q != NULL && rsa->dmp1 != NULL &&
            rsa->dmq1 != NULL && rsa->iqmp != NULL)) {
                if (!rsa->meth->rsa_mod_exp(ret, f, rsa, ctx))
                        goto err;
        } else {
                BIGNUM d;

                BN_init(&d);
                BN_with_flags(&d, rsa->d, BN_FLG_CONSTTIME);

                if (!rsa->meth->bn_mod_exp(ret, f, &d, rsa->n, ctx,
                    rsa->_method_mod_n)) {
                        goto err;
                }
        }

        if (blinding)
                if (!rsa_blinding_invert(blinding, ret, unblind, ctx))
                        goto err;

        if (padding == RSA_X931_PADDING) {
                if (!BN_sub(f, rsa->n, ret))
                        goto err;
                if (BN_cmp(ret, f) > 0)
                        res = f;
                else
                        res = ret;
        } else
                res = ret;

        /* put in leading 0 bytes if the number is less than the
         * length of the modulus */
        j = BN_num_bytes(res);
        i = BN_bn2bin(res, &(to[num - j]));
        for (k = 0; k < num - i; k++)
                to[k] = 0;

        r = num;
err:
        if (ctx != NULL) {
                BN_CTX_end(ctx);
                BN_CTX_free(ctx);
        }
        freezero(buf, num);
        return r;
}

static int
rsa_private_decrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        BIGNUM *f, *ret;
        int j, num = 0, r = -1;
        unsigned char *p;
        unsigned char *buf = NULL;
        BN_CTX *ctx = NULL;
        int local_blinding = 0;
        /*
         * Used only if the blinding structure is shared. A non-NULL unblind
         * instructs rsa_blinding_convert() and rsa_blinding_invert() to store
         * the unblinding factor outside the blinding structure.
         */
        BIGNUM *unblind = NULL;
        BN_BLINDING *blinding = NULL;

        if ((ctx = BN_CTX_new()) == NULL)
                goto err;

        BN_CTX_start(ctx);
        f = BN_CTX_get(ctx);
        ret = BN_CTX_get(ctx);
        num = BN_num_bytes(rsa->n);
        buf = malloc(num);

        if (!f || !ret || !buf) {
                RSAerror(ERR_R_MALLOC_FAILURE);
                goto err;
        }

        /* This check was for equality but PGP does evil things
         * and chops off the top '0' bytes */
        if (flen > num) {
                RSAerror(RSA_R_DATA_GREATER_THAN_MOD_LEN);
                goto err;
        }

        /* make data into a big number */
        if (BN_bin2bn(from, (int)flen, f) == NULL)
                goto err;

        if (BN_ucmp(f, rsa->n) >= 0) {
                RSAerror(RSA_R_DATA_TOO_LARGE_FOR_MODULUS);
                goto err;
        }

        if (rsa->flags & RSA_FLAG_CACHE_PUBLIC) {
                if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n,
                    CRYPTO_LOCK_RSA, rsa->n, ctx))
                        goto err;
        }

        if (!(rsa->flags & RSA_FLAG_NO_BLINDING)) {
                blinding = rsa_get_blinding(rsa, &local_blinding, ctx);
                if (blinding == NULL) {
                        RSAerror(ERR_R_INTERNAL_ERROR);
                        goto err;
                }
        }

        if (blinding != NULL) {
                if (!local_blinding && ((unblind = BN_CTX_get(ctx)) == NULL)) {
                        RSAerror(ERR_R_MALLOC_FAILURE);
                        goto err;
                }
                if (!rsa_blinding_convert(blinding, f, unblind, ctx))
                        goto err;
        }

        /* do the decrypt */
        if ((rsa->flags & RSA_FLAG_EXT_PKEY) ||
            (rsa->p != NULL && rsa->q != NULL && rsa->dmp1 != NULL &&
            rsa->dmq1 != NULL && rsa->iqmp != NULL)) {
                if (!rsa->meth->rsa_mod_exp(ret, f, rsa, ctx))
                        goto err;
        } else {
                BIGNUM d;

                BN_init(&d);
                BN_with_flags(&d, rsa->d, BN_FLG_CONSTTIME);

                if (!rsa->meth->bn_mod_exp(ret, f, &d, rsa->n, ctx,
                    rsa->_method_mod_n)) {
                        goto err;
                }
        }

        if (blinding)
                if (!rsa_blinding_invert(blinding, ret, unblind, ctx))
                        goto err;

        p = buf;
        j = BN_bn2bin(ret, p); /* j is only used with no-padding mode */

        switch (padding) {
        case RSA_PKCS1_PADDING:
                r = RSA_padding_check_PKCS1_type_2(to, num, buf, j, num);
                break;
#ifndef OPENSSL_NO_SHA
        case RSA_PKCS1_OAEP_PADDING:
                r = RSA_padding_check_PKCS1_OAEP(to, num, buf, j, num, NULL, 0);
                break;
#endif
        case RSA_NO_PADDING:
                r = RSA_padding_check_none(to, num, buf, j, num);
                break;
        default:
                RSAerror(RSA_R_UNKNOWN_PADDING_TYPE);
                goto err;
        }
        if (r < 0)
                RSAerror(RSA_R_PADDING_CHECK_FAILED);

err:
        if (ctx != NULL) {
                BN_CTX_end(ctx);
                BN_CTX_free(ctx);
        }
        freezero(buf, num);
        return r;
}

/* signature verification */
static int
rsa_public_decrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        BIGNUM *f, *ret;
        int i, num = 0, r = -1;
        unsigned char *p;
        unsigned char *buf = NULL;
        BN_CTX *ctx = NULL;

        if (BN_num_bits(rsa->n) > OPENSSL_RSA_MAX_MODULUS_BITS) {
                RSAerror(RSA_R_MODULUS_TOO_LARGE);
                return -1;
        }

        if (BN_ucmp(rsa->n, rsa->e) <= 0) {
                RSAerror(RSA_R_BAD_E_VALUE);
                return -1;
        }

        /* for large moduli, enforce exponent limit */
        if (BN_num_bits(rsa->n) > OPENSSL_RSA_SMALL_MODULUS_BITS) {
                if (BN_num_bits(rsa->e) > OPENSSL_RSA_MAX_PUBEXP_BITS) {
                        RSAerror(RSA_R_BAD_E_VALUE);
                        return -1;
                }
        }

        if ((ctx = BN_CTX_new()) == NULL)
                goto err;

        BN_CTX_start(ctx);
        f = BN_CTX_get(ctx);
        ret = BN_CTX_get(ctx);
        num = BN_num_bytes(rsa->n);
        buf = malloc(num);

        if (!f || !ret || !buf) {
                RSAerror(ERR_R_MALLOC_FAILURE);
                goto err;
        }

        /* This check was for equality but PGP does evil things
         * and chops off the top '0' bytes */
        if (flen > num) {
                RSAerror(RSA_R_DATA_GREATER_THAN_MOD_LEN);
                goto err;
        }

        if (BN_bin2bn(from, flen, f) == NULL)
                goto err;

        if (BN_ucmp(f, rsa->n) >= 0) {
                RSAerror(RSA_R_DATA_TOO_LARGE_FOR_MODULUS);
                goto err;
        }

        if (rsa->flags & RSA_FLAG_CACHE_PUBLIC) {
                if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n,
                    CRYPTO_LOCK_RSA, rsa->n, ctx))
                        goto err;
        }

        if (!rsa->meth->bn_mod_exp(ret, f, rsa->e, rsa->n, ctx,
            rsa->_method_mod_n))
                goto err;

        if (padding == RSA_X931_PADDING && (ret->d[0] & 0xf) != 12)
                if (!BN_sub(ret, rsa->n, ret))
                        goto err;

        p = buf;
        i = BN_bn2bin(ret, p);

        switch (padding) {
        case RSA_PKCS1_PADDING:
                r = RSA_padding_check_PKCS1_type_1(to, num, buf, i, num);
                break;
        case RSA_X931_PADDING:
                r = RSA_padding_check_X931(to, num, buf, i, num);
                break;
        case RSA_NO_PADDING:
                r = RSA_padding_check_none(to, num, buf, i, num);
                break;
        default:
                RSAerror(RSA_R_UNKNOWN_PADDING_TYPE);
                goto err;
        }
        if (r < 0)
                RSAerror(RSA_R_PADDING_CHECK_FAILED);

err:
        if (ctx != NULL) {
                BN_CTX_end(ctx);
                BN_CTX_free(ctx);
        }
        freezero(buf, num);
        return r;
}

static int
rsa_mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx)
{
        BIGNUM *r1, *m1, *vrfy;
        BIGNUM dmp1, dmq1, c, pr1;
        int ret = 0;

        BN_CTX_start(ctx);
        r1 = BN_CTX_get(ctx);
        m1 = BN_CTX_get(ctx);
        vrfy = BN_CTX_get(ctx);
        if (r1 == NULL || m1 == NULL || vrfy == NULL) {
                RSAerror(ERR_R_MALLOC_FAILURE);
                goto err;
        }

        {
                BIGNUM p, q;

                /*
                 * Make sure BN_mod_inverse in Montgomery initialization uses the
                 * BN_FLG_CONSTTIME flag
                 */
                BN_init(&p);
                BN_init(&q);
                BN_with_flags(&p, rsa->p, BN_FLG_CONSTTIME);
                BN_with_flags(&q, rsa->q, BN_FLG_CONSTTIME);

                if (rsa->flags & RSA_FLAG_CACHE_PRIVATE) {
                        if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_p,
                             CRYPTO_LOCK_RSA, &p, ctx) ||
                            !BN_MONT_CTX_set_locked(&rsa->_method_mod_q,
                             CRYPTO_LOCK_RSA, &q, ctx)) {
                                goto err;
                        }
                }
        }

        if (rsa->flags & RSA_FLAG_CACHE_PUBLIC) {
                if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n,
                    CRYPTO_LOCK_RSA, rsa->n, ctx))
                        goto err;
        }

        /* compute I mod q */
        BN_init(&c);
        BN_with_flags(&c, I, BN_FLG_CONSTTIME);

        if (!BN_mod_ct(r1, &c, rsa->q, ctx))
                goto err;

        /* compute r1^dmq1 mod q */
        BN_init(&dmq1);
        BN_with_flags(&dmq1, rsa->dmq1, BN_FLG_CONSTTIME);

        if (!rsa->meth->bn_mod_exp(m1, r1, &dmq1, rsa->q, ctx,
            rsa->_method_mod_q))
                goto err;

        /* compute I mod p */
        BN_init(&c);
        BN_with_flags(&c, I, BN_FLG_CONSTTIME);

        if (!BN_mod_ct(r1, &c, rsa->p, ctx))
                goto err;

        /* compute r1^dmp1 mod p */
        BN_init(&dmp1);
        BN_with_flags(&dmp1, rsa->dmp1, BN_FLG_CONSTTIME);

        if (!rsa->meth->bn_mod_exp(r0, r1, &dmp1, rsa->p, ctx,
            rsa->_method_mod_p))
                goto err;

        if (!BN_sub(r0, r0, m1))
                goto err;

        /*
         * This will help stop the size of r0 increasing, which does
         * affect the multiply if it optimised for a power of 2 size
         */
        if (BN_is_negative(r0))
                if (!BN_add(r0, r0, rsa->p))
                        goto err;

        if (!BN_mul(r1, r0, rsa->iqmp, ctx))
                goto err;

        /* Turn BN_FLG_CONSTTIME flag on before division operation */
        BN_init(&pr1);
        BN_with_flags(&pr1, r1, BN_FLG_CONSTTIME);

        if (!BN_mod_ct(r0, &pr1, rsa->p, ctx))
                goto err;

        /*
         * If p < q it is occasionally possible for the correction of
         * adding 'p' if r0 is negative above to leave the result still
         * negative. This can break the private key operations: the following
         * second correction should *always* correct this rare occurrence.
         * This will *never* happen with OpenSSL generated keys because
         * they ensure p > q [steve]
         */
        if (BN_is_negative(r0))
                if (!BN_add(r0, r0, rsa->p))
                        goto err;
        if (!BN_mul(r1, r0, rsa->q, ctx))
                goto err;
        if (!BN_add(r0, r1, m1))
                goto err;

        if (rsa->e && rsa->n) {
                if (!rsa->meth->bn_mod_exp(vrfy, r0, rsa->e, rsa->n, ctx,
                    rsa->_method_mod_n))
                        goto err;
                /*
                 * If 'I' was greater than (or equal to) rsa->n, the operation
                 * will be equivalent to using 'I mod n'. However, the result of
                 * the verify will *always* be less than 'n' so we don't check
                 * for absolute equality, just congruency.
                 */
                if (!BN_sub(vrfy, vrfy, I))
                        goto err;
                if (!BN_mod_ct(vrfy, vrfy, rsa->n, ctx))
                        goto err;
                if (BN_is_negative(vrfy))
                        if (!BN_add(vrfy, vrfy, rsa->n))
                                goto err;
                if (!BN_is_zero(vrfy)) {
                        /*
                         * 'I' and 'vrfy' aren't congruent mod n. Don't leak
                         * miscalculated CRT output, just do a raw (slower)
                         * mod_exp and return that instead.
                         */
                        BIGNUM d;

                        BN_init(&d);
                        BN_with_flags(&d, rsa->d, BN_FLG_CONSTTIME);

                        if (!rsa->meth->bn_mod_exp(r0, I, &d, rsa->n, ctx,
                            rsa->_method_mod_n)) {
                                goto err;
                        }
                }
        }
        ret = 1;
err:
        BN_CTX_end(ctx);
        return ret;
}

static int
rsa_init(RSA *rsa)
{
        rsa->flags |= RSA_FLAG_CACHE_PUBLIC | RSA_FLAG_CACHE_PRIVATE;
        return 1;
}

static int
rsa_finish(RSA *rsa)
{
        BN_MONT_CTX_free(rsa->_method_mod_n);
        BN_MONT_CTX_free(rsa->_method_mod_p);
        BN_MONT_CTX_free(rsa->_method_mod_q);

        return 1;
}

static const RSA_METHOD rsa_pkcs1_meth = {
        .name = "OpenSSL PKCS#1 RSA",
        .rsa_pub_enc = rsa_public_encrypt,
        .rsa_pub_dec = rsa_public_decrypt, /* signature verification */
        .rsa_priv_enc = rsa_private_encrypt, /* signing */
        .rsa_priv_dec = rsa_private_decrypt,
        .rsa_mod_exp = rsa_mod_exp,
        .bn_mod_exp = BN_mod_exp_mont_ct, /* XXX probably we should not use Montgomery if  e == 3 */
        .init = rsa_init,
        .finish = rsa_finish,
};

const RSA_METHOD *
RSA_PKCS1_OpenSSL(void)
{
        return &rsa_pkcs1_meth;
}
LCRYPTO_ALIAS(RSA_PKCS1_OpenSSL);

const RSA_METHOD *
RSA_PKCS1_SSLeay(void)
{
        return RSA_PKCS1_OpenSSL();
}
LCRYPTO_ALIAS(RSA_PKCS1_SSLeay);

int
RSA_bits(const RSA *r)
{
        return BN_num_bits(r->n);
}
LCRYPTO_ALIAS(RSA_bits);

int
RSA_size(const RSA *r)
{
        return BN_num_bytes(r->n);
}
LCRYPTO_ALIAS(RSA_size);

int
RSA_public_encrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        return rsa->meth->rsa_pub_enc(flen, from, to, rsa, padding);
}
LCRYPTO_ALIAS(RSA_public_encrypt);

int
RSA_private_encrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        return rsa->meth->rsa_priv_enc(flen, from, to, rsa, padding);
}
LCRYPTO_ALIAS(RSA_private_encrypt);

int
RSA_private_decrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        return rsa->meth->rsa_priv_dec(flen, from, to, rsa, padding);
}
LCRYPTO_ALIAS(RSA_private_decrypt);

int
RSA_public_decrypt(int flen, const unsigned char *from, unsigned char *to,
    RSA *rsa, int padding)
{
        return rsa->meth->rsa_pub_dec(flen, from, to, rsa, padding);
}
LCRYPTO_ALIAS(RSA_public_decrypt);

int
RSA_flags(const RSA *r)
{
        return r == NULL ? 0 : r->meth->flags;
}
LCRYPTO_ALIAS(RSA_flags);