text: /*
   * Copyright 1995-2020 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 "crypto/bn.h"
  #include "rsa_local.h"
  #include "internal/constant_time.h"
  
  static int rsa_ossl_public_encrypt(int flen, const unsigned char *from,
                                    unsigned char *to, RSA *rsa, int padding);
  static int rsa_ossl_private_encrypt(int flen, const unsigned char *from,
                                     unsigned char *to, RSA *rsa, int padding);
  static int rsa_ossl_public_decrypt(int flen, const unsigned char *from,
                                    unsigned char *to, RSA *rsa, int padding);
  static int rsa_ossl_private_decrypt(int flen, const unsigned char *from,
                                     unsigned char *to, RSA *rsa, int padding);
  static int rsa_ossl_mod_exp(BIGNUM *r0, const BIGNUM *i, RSA *rsa,
                             BN_CTX *ctx);
  static int rsa_ossl_init(RSA *rsa);
  static int rsa_ossl_finish(RSA *rsa);
  static RSA_METHOD rsa_pkcs1_ossl_meth = {
      "OpenSSL PKCS#1 RSA",
      rsa_ossl_public_encrypt,
      rsa_ossl_public_decrypt,     /* signature verification */
      rsa_ossl_private_encrypt,    /* signing */
      rsa_ossl_private_decrypt,
      rsa_ossl_mod_exp,
      BN_mod_exp_mont,            /* XXX probably we should not use Montgomery
                                   * if e == 3 */
      rsa_ossl_init,
      rsa_ossl_finish,
      RSA_FLAG_FIPS_METHOD,       /* flags */
      NULL,
      0,                          /* rsa_sign */
      0,                          /* rsa_verify */
      NULL,                       /* rsa_keygen */
      NULL                        /* rsa_multi_prime_keygen */
  };
  
  static const RSA_METHOD *default_RSA_meth = &rsa_pkcs1_ossl_meth;
  
  void RSA_set_default_method(const RSA_METHOD *meth)
  {
      default_RSA_meth = meth;
  }
  
  const RSA_METHOD *RSA_get_default_method(void)
  {
      return default_RSA_meth;
  }
  
  const RSA_METHOD *RSA_PKCS1_OpenSSL(void)
  {
      return &rsa_pkcs1_ossl_meth;
  }
  
  const RSA_METHOD *RSA_null_method(void)
  {
      return NULL;
  }
  
  static int rsa_ossl_public_encrypt(int flen, const unsigned char *from,
                                    unsigned char *to, RSA *rsa, int padding)
  {
      BIGNUM *f, *ret;
      int i, num = 0, r = -1;
      unsigned char *buf = NULL;
      BN_CTX *ctx = NULL;
  
      if (BN_num_bits(rsa->n) > OPENSSL_RSA_MAX_MODULUS_BITS) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT, RSA_R_MODULUS_TOO_LARGE);
          return -1;
      }
  
      if (BN_ucmp(rsa->n, rsa->e) <= 0) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT, 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) {
              RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT, RSA_R_BAD_E_VALUE);
              return -1;
          }
      }
  
      if ((ctx = BN_CTX_new_ex(rsa->libctx)) == NULL)
          goto err;
      BN_CTX_start(ctx);
      f = BN_CTX_get(ctx);
      ret = BN_CTX_get(ctx);
      num = BN_num_bytes(rsa->n);
      buf = OPENSSL_malloc(num);
      if (ret == NULL || buf == NULL) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT, ERR_R_MALLOC_FAILURE);
          goto err;
      }
  
      switch (padding) {
      case RSA_PKCS1_PADDING:
          i = rsa_padding_add_PKCS1_type_2_with_libctx(rsa->libctx, buf, num,
                                                       from, flen);
          break;
      case RSA_PKCS1_OAEP_PADDING:
          i = rsa_padding_add_PKCS1_OAEP_mgf1_with_libctx(rsa->libctx, buf, num,
                                                          from, flen, NULL, 0,
                                                          NULL, NULL);
          break;
  #ifndef FIPS_MODULE
      case RSA_SSLV23_PADDING:
          i = rsa_padding_add_SSLv23_with_libctx(rsa->libctx, buf, num, from,
                                                 flen);
          break;
  #endif
      case RSA_NO_PADDING:
          i = RSA_padding_add_none(buf, num, from, flen);
          break;
      default:
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT, 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 */
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_ENCRYPT,
                 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, rsa->lock,
                                      rsa->n, ctx))
              goto err;
  
      if (!rsa->meth->bn_mod_exp(ret, f, rsa->e, rsa->n, ctx,
                                 rsa->_method_mod_n))
          goto err;
  
      /*
       * BN_bn2binpad puts in leading 0 bytes if the number is less than
       * the length of the modulus.
       */
      r = BN_bn2binpad(ret, to, num);
   err:
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
      OPENSSL_clear_free(buf, num);
      return r;
  }
  
  static BN_BLINDING *rsa_get_blinding(RSA *rsa, int *local, BN_CTX *ctx)
  {
      BN_BLINDING *ret;
  
      CRYPTO_THREAD_write_lock(rsa->lock);
  
      if (rsa->blinding == NULL) {
          rsa->blinding = RSA_setup_blinding(rsa, ctx);
      }
  
      ret = rsa->blinding;
      if (ret == NULL)
          goto err;
  
      if (BN_BLINDING_is_current_thread(ret)) {
          /* rsa->blinding is ours! */
  
          *local = 1;
      } else {
          /* resort to rsa->mt_blinding instead */
  
          /*
           * instructs rsa_blinding_convert(), rsa_blinding_invert() that the
           * BN_BLINDING is shared, meaning that accesses require locks, and
           * that the blinding factor must be stored outside the BN_BLINDING
           */
          *local = 0;
  
          if (rsa->mt_blinding == NULL) {
              rsa->mt_blinding = RSA_setup_blinding(rsa, ctx);
          }
          ret = rsa->mt_blinding;
      }
  
   err:
      CRYPTO_THREAD_unlock(rsa->lock);
      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_ex(f, NULL, b, ctx);
      } else {
          /*
           * Shared blinding: store the unblinding factor outside BN_BLINDING.
           */
          int ret;
  
          BN_BLINDING_lock(b);
          ret = BN_BLINDING_convert_ex(f, unblind, b, ctx);
          BN_BLINDING_unlock(b);
  
          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_ex
       * will use the unblinding factor stored in BN_BLINDING. If BN_BLINDING
       * is shared between threads, unblind must be non-null:
       * BN_BLINDING_invert_ex 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_ex(f, unblind, b, ctx);
  }
  
  /* signing */
  static int rsa_ossl_private_encrypt(int flen, const unsigned char *from,
                                     unsigned char *to, RSA *rsa, int padding)
  {
      BIGNUM *f, *ret, *res;
      int i, 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_ex(rsa->libctx)) == NULL)
          goto err;
      BN_CTX_start(ctx);
      f = BN_CTX_get(ctx);
      ret = BN_CTX_get(ctx);
      num = BN_num_bytes(rsa->n);
      buf = OPENSSL_malloc(num);
      if (ret == NULL || buf == NULL) {
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, 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;
      case RSA_SSLV23_PADDING:
      default:
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, 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 */
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT,
                 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, rsa->lock,
                                      rsa->n, ctx))
              goto err;
  
      if (!(rsa->flags & RSA_FLAG_NO_BLINDING)) {
          blinding = rsa_get_blinding(rsa, &local_blinding, ctx);
          if (blinding == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, ERR_R_INTERNAL_ERROR);
              goto err;
          }
      }
  
      if (blinding != NULL) {
          if (!local_blinding && ((unblind = BN_CTX_get(ctx)) == NULL)) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, ERR_R_MALLOC_FAILURE);
              goto err;
          }
          if (!rsa_blinding_convert(blinding, f, unblind, ctx))
              goto err;
      }
  
      if ((rsa->flags & RSA_FLAG_EXT_PKEY) ||
          (rsa->version == RSA_ASN1_VERSION_MULTI) ||
          ((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_new();
          if (d == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, ERR_R_MALLOC_FAILURE);
              goto err;
          }
          if (rsa->d == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_ENCRYPT, RSA_R_MISSING_PRIVATE_KEY);
              BN_free(d);
              goto err;
          }
          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)) {
              BN_free(d);
              goto err;
          }
          /* We MUST free d before any further use of rsa->d */
          BN_free(d);
      }
  
      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;
      }
  
      /*
       * BN_bn2binpad puts in leading 0 bytes if the number is less than
       * the length of the modulus.
       */
      r = BN_bn2binpad(res, to, num);
   err:
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
      OPENSSL_clear_free(buf, num);
      return r;
  }
  
  static int rsa_ossl_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 *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_ex(rsa->libctx)) == NULL)
          goto err;
      BN_CTX_start(ctx);
      f = BN_CTX_get(ctx);
      ret = BN_CTX_get(ctx);
      num = BN_num_bytes(rsa->n);
      buf = OPENSSL_malloc(num);
      if (ret == NULL || buf == NULL) {
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, 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) {
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT,
                 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) {
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT,
                 RSA_R_DATA_TOO_LARGE_FOR_MODULUS);
          goto err;
      }
  
      if (!(rsa->flags & RSA_FLAG_NO_BLINDING)) {
          blinding = rsa_get_blinding(rsa, &local_blinding, ctx);
          if (blinding == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, ERR_R_INTERNAL_ERROR);
              goto err;
          }
      }
  
      if (blinding != NULL) {
          if (!local_blinding && ((unblind = BN_CTX_get(ctx)) == NULL)) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, 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->version == RSA_ASN1_VERSION_MULTI) ||
          ((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_new();
          if (d == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, ERR_R_MALLOC_FAILURE);
              goto err;
          }
          if (rsa->d == NULL) {
              RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, RSA_R_MISSING_PRIVATE_KEY);
              BN_free(d);
              goto err;
          }
          BN_with_flags(d, rsa->d, BN_FLG_CONSTTIME);
  
          if (rsa->flags & RSA_FLAG_CACHE_PUBLIC)
              if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n, rsa->lock,
                                          rsa->n, ctx)) {
                  BN_free(d);
                  goto err;
              }
          if (!rsa->meth->bn_mod_exp(ret, f, d, rsa->n, ctx,
                                     rsa->_method_mod_n)) {
              BN_free(d);
              goto err;
          }
          /* We MUST free d before any further use of rsa->d */
          BN_free(d);
      }
  
      if (blinding)
          if (!rsa_blinding_invert(blinding, ret, unblind, ctx))
              goto err;
  
      j = BN_bn2binpad(ret, buf, num);
      if (j < 0)
          goto err;
  
      switch (padding) {
      case RSA_PKCS1_PADDING:
          r = RSA_padding_check_PKCS1_type_2(to, num, buf, j, num);
          break;
      case RSA_PKCS1_OAEP_PADDING:
          r = RSA_padding_check_PKCS1_OAEP(to, num, buf, j, num, NULL, 0);
          break;
  #ifndef FIPS_MODULE
      case RSA_SSLV23_PADDING:
          r = RSA_padding_check_SSLv23(to, num, buf, j, num);
          break;
  #endif
      case RSA_NO_PADDING:
          memcpy(to, buf, (r = j));
          break;
      default:
          RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, RSA_R_UNKNOWN_PADDING_TYPE);
          goto err;
      }
  #ifndef FIPS_MODULE
      /*
       * This trick doesn't work in the FIPS provider because libcrypto manages
       * the error stack. Instead we opt not to put an error on the stack at all
       * in case of padding failure in the FIPS provider.
       */
      RSAerr(RSA_F_RSA_OSSL_PRIVATE_DECRYPT, RSA_R_PADDING_CHECK_FAILED);
      err_clear_last_constant_time(1 & ~constant_time_msb(r));
  #endif
  
   err:
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
      OPENSSL_clear_free(buf, num);
      return r;
  }
  
  /* signature verification */
  static int rsa_ossl_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 *buf = NULL;
      BN_CTX *ctx = NULL;
  
      if (BN_num_bits(rsa->n) > OPENSSL_RSA_MAX_MODULUS_BITS) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, RSA_R_MODULUS_TOO_LARGE);
          return -1;
      }
  
      if (BN_ucmp(rsa->n, rsa->e) <= 0) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, 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) {
              RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, RSA_R_BAD_E_VALUE);
              return -1;
          }
      }
  
      if ((ctx = BN_CTX_new_ex(rsa->libctx)) == NULL)
          goto err;
      BN_CTX_start(ctx);
      f = BN_CTX_get(ctx);
      ret = BN_CTX_get(ctx);
      num = BN_num_bytes(rsa->n);
      buf = OPENSSL_malloc(num);
      if (ret == NULL || buf == NULL) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, 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) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, 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) {
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT,
                 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, rsa->lock,
                                      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) && ((bn_get_words(ret)[0] & 0xf) != 12))
          if (!BN_sub(ret, rsa->n, ret))
              goto err;
  
      i = BN_bn2binpad(ret, buf, num);
      if (i < 0)
          goto err;
  
      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:
          memcpy(to, buf, (r = i));
          break;
      default:
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, RSA_R_UNKNOWN_PADDING_TYPE);
          goto err;
      }
      if (r < 0)
          RSAerr(RSA_F_RSA_OSSL_PUBLIC_DECRYPT, RSA_R_PADDING_CHECK_FAILED);
  
   err:
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
      OPENSSL_clear_free(buf, num);
      return r;
  }
  
  static int rsa_ossl_mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx)
  {
      BIGNUM *r1, *m1, *vrfy;
      int ret = 0, smooth = 0;
  #ifndef FIPS_MODULE
      BIGNUM *r2, *m[RSA_MAX_PRIME_NUM - 2];
      int i, ex_primes = 0;
      RSA_PRIME_INFO *pinfo;
  #endif
  
      BN_CTX_start(ctx);
  
      r1 = BN_CTX_get(ctx);
  #ifndef FIPS_MODULE
      r2 = BN_CTX_get(ctx);
  #endif
      m1 = BN_CTX_get(ctx);
      vrfy = BN_CTX_get(ctx);
      if (vrfy == NULL)
          goto err;
  
  #ifndef FIPS_MODULE
      if (rsa->version == RSA_ASN1_VERSION_MULTI
          && ((ex_primes = sk_RSA_PRIME_INFO_num(rsa->prime_infos)) <= 0
               || ex_primes > RSA_MAX_PRIME_NUM - 2))
          goto err;
  #endif
  
      if (rsa->flags & RSA_FLAG_CACHE_PRIVATE) {
          BIGNUM *factor = BN_new();
  
          if (factor == NULL)
              goto err;
  
          /*
           * Make sure BN_mod_inverse in Montgomery initialization uses the
           * BN_FLG_CONSTTIME flag
           */
          if (!(BN_with_flags(factor, rsa->p, BN_FLG_CONSTTIME),
                BN_MONT_CTX_set_locked(&rsa->_method_mod_p, rsa->lock,
                                       factor, ctx))
              || !(BN_with_flags(factor, rsa->q, BN_FLG_CONSTTIME),
                   BN_MONT_CTX_set_locked(&rsa->_method_mod_q, rsa->lock,
                                          factor, ctx))) {
              BN_free(factor);
              goto err;
          }
  #ifndef FIPS_MODULE
          for (i = 0; i < ex_primes; i++) {
              pinfo = sk_RSA_PRIME_INFO_value(rsa->prime_infos, i);
              BN_with_flags(factor, pinfo->r, BN_FLG_CONSTTIME);
              if (!BN_MONT_CTX_set_locked(&pinfo->m, rsa->lock, factor, ctx)) {
                  BN_free(factor);
                  goto err;
              }
          }
  #endif
          /*
           * We MUST free |factor| before any further use of the prime factors
           */
          BN_free(factor);
  
          smooth = (rsa->meth->bn_mod_exp == BN_mod_exp_mont)
  #ifndef FIPS_MODULE
                   && (ex_primes == 0)
  #endif
                   && (BN_num_bits(rsa->q) == BN_num_bits(rsa->p));
      }
  
      if (rsa->flags & RSA_FLAG_CACHE_PUBLIC)
          if (!BN_MONT_CTX_set_locked(&rsa->_method_mod_n, rsa->lock,
                                      rsa->n, ctx))
              goto err;
  
      if (smooth) {
          /*
           * Conversion from Montgomery domain, a.k.a. Montgomery reduction,
           * accepts values in [0-m*2^w) range. w is m's bit width rounded up
           * to limb width. So that at the very least if |I| is fully reduced,
           * i.e. less than p*q, we can count on from-to round to perform
           * below modulo operations on |I|. Unlike BN_mod it's constant time.
           */
          if (/* m1 = I moq q */
              !bn_from_mont_fixed_top(m1, I, rsa->_method_mod_q, ctx)
              || !bn_to_mont_fixed_top(m1, m1, rsa->_method_mod_q, ctx)
              /* m1 = m1^dmq1 mod q */
              || !BN_mod_exp_mont_consttime(m1, m1, rsa->dmq1, rsa->q, ctx,
                                            rsa->_method_mod_q)
              /* r1 = I mod p */
              || !bn_from_mont_fixed_top(r1, I, rsa->_method_mod_p, ctx)
              || !bn_to_mont_fixed_top(r1, r1, rsa->_method_mod_p, ctx)
              /* r1 = r1^dmp1 mod p */
              || !BN_mod_exp_mont_consttime(r1, r1, rsa->dmp1, rsa->p, ctx,
                                            rsa->_method_mod_p)
              /* r1 = (r1 - m1) mod p */
              /*
               * bn_mod_sub_fixed_top is not regular modular subtraction,
               * it can tolerate subtrahend to be larger than modulus, but
               * not bit-wise wider. This makes up for uncommon q>p case,
               * when |m1| can be larger than |rsa->p|.
               */
              || !bn_mod_sub_fixed_top(r1, r1, m1, rsa->p)
  
              /* r1 = r1 * iqmp mod p */
              || !bn_to_mont_fixed_top(r1, r1, rsa->_method_mod_p, ctx)
              || !bn_mul_mont_fixed_top(r1, r1, rsa->iqmp, rsa->_method_mod_p,
                                        ctx)
              /* r0 = r1 * q + m1 */
              || !bn_mul_fixed_top(r0, r1, rsa->q, ctx)
              || !bn_mod_add_fixed_top(r0, r0, m1, rsa->n))
              goto err;
  
          goto tail;
      }
  
      /* compute I mod q */
      {
          BIGNUM *c = BN_new();
          if (c == NULL)
              goto err;
          BN_with_flags(c, I, BN_FLG_CONSTTIME);
  
          if (!BN_mod(r1, c, rsa->q, ctx)) {
              BN_free(c);
              goto err;
          }
  
          {
              BIGNUM *dmq1 = BN_new();
              if (dmq1 == NULL) {
                  BN_free(c);
                  goto err;
              }
              BN_with_flags(dmq1, rsa->dmq1, BN_FLG_CONSTTIME);
  
              /* compute r1^dmq1 mod q */
              if (!rsa->meth->bn_mod_exp(m1, r1, dmq1, rsa->q, ctx,
                                         rsa->_method_mod_q)) {
                  BN_free(c);
                  BN_free(dmq1);
                  goto err;
              }
              /* We MUST free dmq1 before any further use of rsa->dmq1 */
              BN_free(dmq1);
          }
  
          /* compute I mod p */
          if (!BN_mod(r1, c, rsa->p, ctx)) {
              BN_free(c);
              goto err;
          }
          /* We MUST free c before any further use of I */
          BN_free(c);
      }
  
      {
          BIGNUM *dmp1 = BN_new();
          if (dmp1 == NULL)
              goto err;
          BN_with_flags(dmp1, rsa->dmp1, BN_FLG_CONSTTIME);
  
          /* compute r1^dmp1 mod p */
          if (!rsa->meth->bn_mod_exp(r0, r1, dmp1, rsa->p, ctx,
                                     rsa->_method_mod_p)) {
              BN_free(dmp1);
              goto err;
          }
          /* We MUST free dmp1 before any further use of rsa->dmp1 */
          BN_free(dmp1);
      }
  
  #ifndef FIPS_MODULE
      /*
       * calculate m_i in multi-prime case
       *
       * TODO:
       * 1. squash the following two loops and calculate |m_i| there.
       * 2. remove cc and reuse |c|.
       * 3. remove |dmq1| and |dmp1| in previous block and use |di|.
       *
       * If these things are done, the code will be more readable.
       */
      if (ex_primes > 0) {
          BIGNUM *di = BN_new(), *cc = BN_new();
  
          if (cc == NULL || di == NULL) {
              BN_free(cc);
              BN_free(di);
              goto err;
          }
  
          for (i = 0; i < ex_primes; i++) {
              /* prepare m_i */
              if ((m[i] = BN_CTX_get(ctx)) == NULL) {
                  BN_free(cc);
                  BN_free(di);
                  goto err;
              }
  
              pinfo = sk_RSA_PRIME_INFO_value(rsa->prime_infos, i);
  
              /* prepare c and d_i */
              BN_with_flags(cc, I, BN_FLG_CONSTTIME);
              BN_with_flags(di, pinfo->d, BN_FLG_CONSTTIME);
  
              if (!BN_mod(r1, cc, pinfo->r, ctx)) {
                  BN_free(cc);
                  BN_free(di);
                  goto err;
              }
              /* compute r1 ^ d_i mod r_i */
              if (!rsa->meth->bn_mod_exp(m[i], r1, di, pinfo->r, ctx, pinfo->m)) {
                  BN_free(cc);
                  BN_free(di);
                  goto err;
              }
          }
  
          BN_free(cc);
          BN_free(di);
      }
  #endif
  
      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;
  
      {
          BIGNUM *pr1 = BN_new();
          if (pr1 == NULL)
              goto err;
          BN_with_flags(pr1, r1, BN_FLG_CONSTTIME);
  
          if (!BN_mod(r0, pr1, rsa->p, ctx)) {
              BN_free(pr1);
              goto err;
          }
          /* We MUST free pr1 before any further use of r1 */
          BN_free(pr1);
      }
  
      /*
       * 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;
  
  #ifndef FIPS_MODULE
      /* add m_i to m in multi-prime case */
      if (ex_primes > 0) {
          BIGNUM *pr2 = BN_new();
  
          if (pr2 == NULL)
              goto err;
  
          for (i = 0; i < ex_primes; i++) {
              pinfo = sk_RSA_PRIME_INFO_value(rsa->prime_infos, i);
              if (!BN_sub(r1, m[i], r0)) {
                  BN_free(pr2);
                  goto err;
              }
  
              if (!BN_mul(r2, r1, pinfo->t, ctx)) {
                  BN_free(pr2);
                  goto err;
              }
  
              BN_with_flags(pr2, r2, BN_FLG_CONSTTIME);
  
              if (!BN_mod(r1, pr2, pinfo->r, ctx)) {
                  BN_free(pr2);
                  goto err;
              }
  
              if (BN_is_negative(r1))
                  if (!BN_add(r1, r1, pinfo->r)) {
                      BN_free(pr2);
                      goto err;
                  }
              if (!BN_mul(r1, r1, pinfo->pp, ctx)) {
                  BN_free(pr2);
                  goto err;
              }
              if (!BN_add(r0, r0, r1)) {
                  BN_free(pr2);
                  goto err;
              }
          }
          BN_free(pr2);
      }
  #endif
  
   tail:
      if (rsa->e && rsa->n) {
          if (rsa->meth->bn_mod_exp == BN_mod_exp_mont) {
              if (!BN_mod_exp_mont(vrfy, r0, rsa->e, rsa->n, ctx,
                                   rsa->_method_mod_n))
                  goto err;
          } else {
              bn_correct_top(r0);
              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_is_zero(vrfy)) {
              bn_correct_top(r0);
              ret = 1;
              goto err;   /* not actually error */
          }
          if (!BN_mod(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_new();
              if (d == NULL)
                  goto err;
              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)) {
                  BN_free(d);
                  goto err;
              }
              /* We MUST free d before any further use of rsa->d */
              BN_free(d);
          }
      }
      /*
       * It's unfortunate that we have to bn_correct_top(r0). What hopefully
       * saves the day is that correction is highly unlike, and private key
       * operations are customarily performed on blinded message. Which means
       * that attacker won't observe correlation with chosen plaintext.
       * Secondly, remaining code would still handle it in same computational
       * time and even conceal memory access pattern around corrected top.
       */
      bn_correct_top(r0);
      ret = 1;
   err:
      BN_CTX_end(ctx);
      return ret;
  }
  
  static int rsa_ossl_init(RSA *rsa)
  {
      rsa->flags |= RSA_FLAG_CACHE_PUBLIC | RSA_FLAG_CACHE_PRIVATE;
      return 1;
  }
  
  static int rsa_ossl_finish(RSA *rsa)
  {
  #ifndef FIPS_MODULE
      int i;
      RSA_PRIME_INFO *pinfo;
  
      for (i = 0; i < sk_RSA_PRIME_INFO_num(rsa->prime_infos); i++) {
          pinfo = sk_RSA_PRIME_INFO_value(rsa->prime_infos, i);
          BN_MONT_CTX_free(pinfo->m);
      }
  #endif
  
      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;
  }
  