text: /*
   * Copyright 1995-2018 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 <stdio.h>
  #include <openssl/crypto.h>
  #include "internal/cryptlib.h"
  #include "internal/refcount.h"
  #include "crypto/bn.h"
  #include <openssl/engine.h>
  #include <openssl/evp.h>
  #include "crypto/evp.h"
  #include "crypto/rsa.h"
  #include "rsa_local.h"
  
  RSA *RSA_new(void)
  {
      return RSA_new_method(NULL);
  }
  
  const RSA_METHOD *RSA_get_method(const RSA *rsa)
  {
      return rsa->meth;
  }
  
  int RSA_set_method(RSA *rsa, const RSA_METHOD *meth)
  {
      /*
       * NB: The caller is specifically setting a method, so it's not up to us
       * to deal with which ENGINE it comes from.
       */
      const RSA_METHOD *mtmp;
      mtmp = rsa->meth;
      if (mtmp->finish)
          mtmp->finish(rsa);
  #ifndef OPENSSL_NO_ENGINE
      ENGINE_finish(rsa->engine);
      rsa->engine = NULL;
  #endif
      rsa->meth = meth;
      if (meth->init)
          meth->init(rsa);
      return 1;
  }
  
  RSA *RSA_new_method(ENGINE *engine)
  {
      RSA *ret = OPENSSL_zalloc(sizeof(*ret));
  
      if (ret == NULL) {
          RSAerr(RSA_F_RSA_NEW_METHOD, ERR_R_MALLOC_FAILURE);
          return NULL;
      }
  
      ret->references = 1;
      ret->lock = CRYPTO_THREAD_lock_new();
      if (ret->lock == NULL) {
          RSAerr(RSA_F_RSA_NEW_METHOD, ERR_R_MALLOC_FAILURE);
          OPENSSL_free(ret);
          return NULL;
      }
  
      ret->meth = RSA_get_default_method();
  #ifndef OPENSSL_NO_ENGINE
      ret->flags = ret->meth->flags & ~RSA_FLAG_NON_FIPS_ALLOW;
      if (engine) {
          if (!ENGINE_init(engine)) {
              RSAerr(RSA_F_RSA_NEW_METHOD, ERR_R_ENGINE_LIB);
              goto err;
          }
          ret->engine = engine;
      } else {
          ret->engine = ENGINE_get_default_RSA();
      }
      if (ret->engine) {
          ret->meth = ENGINE_get_RSA(ret->engine);
          if (ret->meth == NULL) {
              RSAerr(RSA_F_RSA_NEW_METHOD, ERR_R_ENGINE_LIB);
              goto err;
          }
      }
  #endif
  
      ret->flags = ret->meth->flags & ~RSA_FLAG_NON_FIPS_ALLOW;
      if (!CRYPTO_new_ex_data(CRYPTO_EX_INDEX_RSA, ret, &ret->ex_data)) {
          goto err;
      }
  
      if ((ret->meth->init != NULL) && !ret->meth->init(ret)) {
          RSAerr(RSA_F_RSA_NEW_METHOD, ERR_R_INIT_FAIL);
          goto err;
      }
  
      return ret;
  
   err:
      RSA_free(ret);
      return NULL;
  }
  
  void RSA_free(RSA *r)
  {
      int i;
  
      if (r == NULL)
          return;
  
      CRYPTO_DOWN_REF(&r->references, &i, r->lock);
      REF_PRINT_COUNT("RSA", r);
      if (i > 0)
          return;
      REF_ASSERT_ISNT(i < 0);
  
      if (r->meth != NULL && r->meth->finish != NULL)
          r->meth->finish(r);
  #ifndef OPENSSL_NO_ENGINE
      ENGINE_finish(r->engine);
  #endif
  
      CRYPTO_free_ex_data(CRYPTO_EX_INDEX_RSA, r, &r->ex_data);
  
      CRYPTO_THREAD_lock_free(r->lock);
  
      BN_free(r->n);
      BN_free(r->e);
      BN_clear_free(r->d);
      BN_clear_free(r->p);
      BN_clear_free(r->q);
      BN_clear_free(r->dmp1);
      BN_clear_free(r->dmq1);
      BN_clear_free(r->iqmp);
      RSA_PSS_PARAMS_free(r->pss);
      sk_RSA_PRIME_INFO_pop_free(r->prime_infos, rsa_multip_info_free);
      BN_BLINDING_free(r->blinding);
      BN_BLINDING_free(r->mt_blinding);
      OPENSSL_free(r->bignum_data);
      OPENSSL_free(r);
  }
  
  int RSA_up_ref(RSA *r)
  {
      int i;
  
      if (CRYPTO_UP_REF(&r->references, &i, r->lock) <= 0)
          return 0;
  
      REF_PRINT_COUNT("RSA", r);
      REF_ASSERT_ISNT(i < 2);
      return i > 1 ? 1 : 0;
  }
  
  int RSA_set_ex_data(RSA *r, int idx, void *arg)
  {
      return CRYPTO_set_ex_data(&r->ex_data, idx, arg);
  }
  
  void *RSA_get_ex_data(const RSA *r, int idx)
  {
      return CRYPTO_get_ex_data(&r->ex_data, idx);
  }
  
  /*
   * Define a scaling constant for our fixed point arithmetic.
   * This value must be a power of two because the base two logarithm code
   * makes this assumption.  The exponent must also be a multiple of three so
   * that the scale factor has an exact cube root.  Finally, the scale factor
   * should not be so large that a multiplication of two scaled numbers
   * overflows a 64 bit unsigned integer.
   */
  static const unsigned int scale = 1 << 18;
  static const unsigned int cbrt_scale = 1 << (2 * 18 / 3);
  
  /* Define some constants, none exceed 32 bits */
  static const unsigned int log_2  = 0x02c5c8;    /* scale * log(2) */
  static const unsigned int log_e  = 0x05c551;    /* scale * log2(M_E) */
  static const unsigned int c1_923 = 0x07b126;    /* scale * 1.923 */
  static const unsigned int c4_690 = 0x12c28f;    /* scale * 4.690 */
  
  /*
   * Multiply two scaled integers together and rescale the result.
   */
  static ossl_inline uint64_t mul2(uint64_t a, uint64_t b)
  {
      return a * b / scale;
  }
  
  /*
   * Calculate the cube root of a 64 bit scaled integer.
   * Although the cube root of a 64 bit number does fit into a 32 bit unsigned
   * integer, this is not guaranteed after scaling, so this function has a
   * 64 bit return.  This uses the shifting nth root algorithm with some
   * algebraic simplifications.
   */
  static uint64_t icbrt64(uint64_t x)
  {
      uint64_t r = 0;
      uint64_t b;
      int s;
  
      for (s = 63; s >= 0; s -= 3) {
          r <<= 1;
          b = 3 * r * (r + 1) + 1;
          if ((x >> s) >= b) {
              x -= b << s;
              r++;
          }
      }
      return r * cbrt_scale;
  }
  
  /*
   * Calculate the natural logarithm of a 64 bit scaled integer.
   * This is done by calculating a base two logarithm and scaling.
   * The maximum logarithm (base 2) is 64 and this reduces base e, so
   * a 32 bit result should not overflow.  The argument passed must be
   * greater than unity so we don't need to handle negative results.
   */
  static uint32_t ilog_e(uint64_t v)
  {
      uint32_t i, r = 0;
  
      /*
       * Scale down the value into the range 1 .. 2.
       *
       * If fractional numbers need to be processed, another loop needs
       * to go here that checks v < scale and if so multiplies it by 2 and
       * reduces r by scale.  This also means making r signed.
       */
      while (v >= 2 * scale) {
          v >>= 1;
          r += scale;
      }
      for (i = scale / 2; i != 0; i /= 2) {
          v = mul2(v, v);
          if (v >= 2 * scale) {
              v >>= 1;
              r += i;
          }
      }
      r = (r * (uint64_t)scale) / log_e;
      return r;
  }
  
  /*
   * NIST SP 800-56B rev 2 Appendix D: Maximum Security Strength Estimates for IFC
   * Modulus Lengths.
   *
   * E = \frac{1.923 \sqrt[3]{nBits \cdot log_e(2)}
   *           \cdot(log_e(nBits \cdot log_e(2))^{2/3} - 4.69}{log_e(2)}
   * The two cube roots are merged together here.
   */
  uint16_t rsa_compute_security_bits(int n)
  {
      uint64_t x;
      uint32_t lx;
      uint16_t y;
  
      /* Look for common values as listed in SP 800-56B rev 2 Appendix D */
      switch (n) {
      case 2048:
          return 112;
      case 3072:
          return 128;
      case 4096:
          return 152;
      case 6144:
          return 176;
      case 8192:
          return 200;
      }
      /*
       * The first incorrect result (i.e. not accurate or off by one low) occurs
       * for n = 699668.  The true value here is 1200.  Instead of using this n
       * as the check threshold, the smallest n such that the correct result is
       * 1200 is used instead.
       */
      if (n >= 687737)
          return 1200;
      if (n < 8)
          return 0;
  
      x = n * (uint64_t)log_2;
      lx = ilog_e(x);
      y = (uint16_t)((mul2(c1_923, icbrt64(mul2(mul2(x, lx), lx))) - c4_690)
                     / log_2);
      return (y + 4) & ~7;
  }
  
  int RSA_security_bits(const RSA *rsa)
  {
      int bits = BN_num_bits(rsa->n);
  
      if (rsa->version == RSA_ASN1_VERSION_MULTI) {
          /* This ought to mean that we have private key at hand. */
          int ex_primes = sk_RSA_PRIME_INFO_num(rsa->prime_infos);
  
          if (ex_primes <= 0 || (ex_primes + 2) > rsa_multip_cap(bits))
              return 0;
      }
      return rsa_compute_security_bits(bits);
  }
  
  int RSA_set0_key(RSA *r, BIGNUM *n, BIGNUM *e, BIGNUM *d)
  {
      /* If the fields n and e in r are NULL, the corresponding input
       * parameters MUST be non-NULL for n and e.  d may be
       * left NULL (in case only the public key is used).
       */
      if ((r->n == NULL && n == NULL)
          || (r->e == NULL && e == NULL))
          return 0;
  
      if (n != NULL) {
          BN_free(r->n);
          r->n = n;
      }
      if (e != NULL) {
          BN_free(r->e);
          r->e = e;
      }
      if (d != NULL) {
          BN_clear_free(r->d);
          r->d = d;
          BN_set_flags(r->d, BN_FLG_CONSTTIME);
      }
      r->dirty_cnt++;
  
      return 1;
  }
  
  int RSA_set0_factors(RSA *r, BIGNUM *p, BIGNUM *q)
  {
      /* If the fields p and q in r are NULL, the corresponding input
       * parameters MUST be non-NULL.
       */
      if ((r->p == NULL && p == NULL)
          || (r->q == NULL && q == NULL))
          return 0;
  
      if (p != NULL) {
          BN_clear_free(r->p);
          r->p = p;
          BN_set_flags(r->p, BN_FLG_CONSTTIME);
      }
      if (q != NULL) {
          BN_clear_free(r->q);
          r->q = q;
          BN_set_flags(r->q, BN_FLG_CONSTTIME);
      }
      r->dirty_cnt++;
  
      return 1;
  }
  
  int RSA_set0_crt_params(RSA *r, BIGNUM *dmp1, BIGNUM *dmq1, BIGNUM *iqmp)
  {
      /* If the fields dmp1, dmq1 and iqmp in r are NULL, the corresponding input
       * parameters MUST be non-NULL.
       */
      if ((r->dmp1 == NULL && dmp1 == NULL)
          || (r->dmq1 == NULL && dmq1 == NULL)
          || (r->iqmp == NULL && iqmp == NULL))
          return 0;
  
      if (dmp1 != NULL) {
          BN_clear_free(r->dmp1);
          r->dmp1 = dmp1;
          BN_set_flags(r->dmp1, BN_FLG_CONSTTIME);
      }
      if (dmq1 != NULL) {
          BN_clear_free(r->dmq1);
          r->dmq1 = dmq1;
          BN_set_flags(r->dmq1, BN_FLG_CONSTTIME);
      }
      if (iqmp != NULL) {
          BN_clear_free(r->iqmp);
          r->iqmp = iqmp;
          BN_set_flags(r->iqmp, BN_FLG_CONSTTIME);
      }
      r->dirty_cnt++;
  
      return 1;
  }
  
  /*
   * Is it better to export RSA_PRIME_INFO structure
   * and related functions to let user pass a triplet?
   */
  int RSA_set0_multi_prime_params(RSA *r, BIGNUM *primes[], BIGNUM *exps[],
                                  BIGNUM *coeffs[], int pnum)
  {
      STACK_OF(RSA_PRIME_INFO) *prime_infos, *old = NULL;
      RSA_PRIME_INFO *pinfo;
      int i;
  
      if (primes == NULL || exps == NULL || coeffs == NULL || pnum == 0)
          return 0;
  
      prime_infos = sk_RSA_PRIME_INFO_new_reserve(NULL, pnum);
      if (prime_infos == NULL)
          return 0;
  
      if (r->prime_infos != NULL)
          old = r->prime_infos;
  
      for (i = 0; i < pnum; i++) {
          pinfo = rsa_multip_info_new();
          if (pinfo == NULL)
              goto err;
          if (primes[i] != NULL && exps[i] != NULL && coeffs[i] != NULL) {
              BN_clear_free(pinfo->r);
              BN_clear_free(pinfo->d);
              BN_clear_free(pinfo->t);
              pinfo->r = primes[i];
              pinfo->d = exps[i];
              pinfo->t = coeffs[i];
              BN_set_flags(pinfo->r, BN_FLG_CONSTTIME);
              BN_set_flags(pinfo->d, BN_FLG_CONSTTIME);
              BN_set_flags(pinfo->t, BN_FLG_CONSTTIME);
          } else {
              rsa_multip_info_free(pinfo);
              goto err;
          }
          (void)sk_RSA_PRIME_INFO_push(prime_infos, pinfo);
      }
  
      r->prime_infos = prime_infos;
  
      if (!rsa_multip_calc_product(r)) {
          r->prime_infos = old;
          goto err;
      }
  
      if (old != NULL) {
          /*
           * This is hard to deal with, since the old infos could
           * also be set by this function and r, d, t should not
           * be freed in that case. So currently, stay consistent
           * with other *set0* functions: just free it...
           */
          sk_RSA_PRIME_INFO_pop_free(old, rsa_multip_info_free);
      }
  
      r->version = RSA_ASN1_VERSION_MULTI;
      r->dirty_cnt++;
  
      return 1;
   err:
      /* r, d, t should not be freed */
      sk_RSA_PRIME_INFO_pop_free(prime_infos, rsa_multip_info_free_ex);
      return 0;
  }
  
  void RSA_get0_key(const RSA *r,
                    const BIGNUM **n, const BIGNUM **e, const BIGNUM **d)
  {
      if (n != NULL)
          *n = r->n;
      if (e != NULL)
          *e = r->e;
      if (d != NULL)
          *d = r->d;
  }
  
  void RSA_get0_factors(const RSA *r, const BIGNUM **p, const BIGNUM **q)
  {
      if (p != NULL)
          *p = r->p;
      if (q != NULL)
          *q = r->q;
  }
  
  int RSA_get_multi_prime_extra_count(const RSA *r)
  {
      int pnum;
  
      pnum = sk_RSA_PRIME_INFO_num(r->prime_infos);
      if (pnum <= 0)
          pnum = 0;
      return pnum;
  }
  
  int RSA_get0_multi_prime_factors(const RSA *r, const BIGNUM *primes[])
  {
      int pnum, i;
      RSA_PRIME_INFO *pinfo;
  
      if ((pnum = RSA_get_multi_prime_extra_count(r)) == 0)
          return 0;
  
      /*
       * return other primes
       * it's caller's responsibility to allocate oth_primes[pnum]
       */
      for (i = 0; i < pnum; i++) {
          pinfo = sk_RSA_PRIME_INFO_value(r->prime_infos, i);
          primes[i] = pinfo->r;
      }
  
      return 1;
  }
  
  void RSA_get0_crt_params(const RSA *r,
                           const BIGNUM **dmp1, const BIGNUM **dmq1,
                           const BIGNUM **iqmp)
  {
      if (dmp1 != NULL)
          *dmp1 = r->dmp1;
      if (dmq1 != NULL)
          *dmq1 = r->dmq1;
      if (iqmp != NULL)
          *iqmp = r->iqmp;
  }
  
  int RSA_get0_multi_prime_crt_params(const RSA *r, const BIGNUM *exps[],
                                      const BIGNUM *coeffs[])
  {
      int pnum;
  
      if ((pnum = RSA_get_multi_prime_extra_count(r)) == 0)
          return 0;
  
      /* return other primes */
      if (exps != NULL || coeffs != NULL) {
          RSA_PRIME_INFO *pinfo;
          int i;
  
          /* it's the user's job to guarantee the buffer length */
          for (i = 0; i < pnum; i++) {
              pinfo = sk_RSA_PRIME_INFO_value(r->prime_infos, i);
              if (exps != NULL)
                  exps[i] = pinfo->d;
              if (coeffs != NULL)
                  coeffs[i] = pinfo->t;
          }
      }
  
      return 1;
  }
  
  const BIGNUM *RSA_get0_n(const RSA *r)
  {
      return r->n;
  }
  
  const BIGNUM *RSA_get0_e(const RSA *r)
  {
      return r->e;
  }
  
  const BIGNUM *RSA_get0_d(const RSA *r)
  {
      return r->d;
  }
  
  const BIGNUM *RSA_get0_p(const RSA *r)
  {
      return r->p;
  }
  
  const BIGNUM *RSA_get0_q(const RSA *r)
  {
      return r->q;
  }
  
  const BIGNUM *RSA_get0_dmp1(const RSA *r)
  {
      return r->dmp1;
  }
  
  const BIGNUM *RSA_get0_dmq1(const RSA *r)
  {
      return r->dmq1;
  }
  
  const BIGNUM *RSA_get0_iqmp(const RSA *r)
  {
      return r->iqmp;
  }
  
  void RSA_clear_flags(RSA *r, int flags)
  {
      r->flags &= ~flags;
  }
  
  int RSA_test_flags(const RSA *r, int flags)
  {
      return r->flags & flags;
  }
  
  void RSA_set_flags(RSA *r, int flags)
  {
      r->flags |= flags;
  }
  
  int RSA_get_version(RSA *r)
  {
      /* { two-prime(0), multi(1) } */
      return r->version;
  }
  
  ENGINE *RSA_get0_engine(const RSA *r)
  {
      return r->engine;
  }
  
  int RSA_pkey_ctx_ctrl(EVP_PKEY_CTX *ctx, int optype, int cmd, int p1, void *p2)
  {
      /* If key type not RSA or RSA-PSS return error */
      if (ctx != NULL && ctx->pmeth != NULL
          && ctx->pmeth->pkey_id != EVP_PKEY_RSA
          && ctx->pmeth->pkey_id != EVP_PKEY_RSA_PSS)
          return -1;
       return EVP_PKEY_CTX_ctrl(ctx, -1, optype, cmd, p1, p2);
  }
  
  DEFINE_STACK_OF(BIGNUM)
  
  int rsa_set0_all_params(RSA *r, const STACK_OF(BIGNUM) *primes,
                          const STACK_OF(BIGNUM) *exps,
                          const STACK_OF(BIGNUM) *coeffs)
  {
      STACK_OF(RSA_PRIME_INFO) *prime_infos, *old_infos = NULL;
      int pnum;
  
      if (primes == NULL || exps == NULL || coeffs == NULL)
          return 0;
  
      pnum = sk_BIGNUM_num(primes);
      if (pnum < 2
          || pnum != sk_BIGNUM_num(exps)
          || pnum != sk_BIGNUM_num(coeffs) + 1)
          return 0;
  
      if (!RSA_set0_factors(r, sk_BIGNUM_value(primes, 0),
                            sk_BIGNUM_value(primes, 1))
          || !RSA_set0_crt_params(r, sk_BIGNUM_value(exps, 0),
                                  sk_BIGNUM_value(exps, 1),
                                  sk_BIGNUM_value(coeffs, 0)))
          return 0;
  
      old_infos = r->prime_infos;
  
      if (pnum > 2) {
          int i;
  
          prime_infos = sk_RSA_PRIME_INFO_new_reserve(NULL, pnum);
          if (prime_infos == NULL)
              return 0;
  
          for (i = 2; i < pnum; i++) {
              BIGNUM *prime = sk_BIGNUM_value(primes, i);
              BIGNUM *exp = sk_BIGNUM_value(exps, i);
              BIGNUM *coeff = sk_BIGNUM_value(coeffs, i - 1);
              RSA_PRIME_INFO *pinfo = NULL;
  
              if (!ossl_assert(prime != NULL && exp != NULL && coeff != NULL))
                  goto err;
  
              /* Using rsa_multip_info_new() is wasteful, so allocate directly */
              if ((pinfo = OPENSSL_zalloc(sizeof(*pinfo))) == NULL) {
                  ERR_raise(ERR_LIB_RSA, ERR_R_MALLOC_FAILURE);
                  goto err;
              }
  
              pinfo->r = prime;
              pinfo->d = exp;
              pinfo->t = coeff;
              BN_set_flags(pinfo->r, BN_FLG_CONSTTIME);
              BN_set_flags(pinfo->d, BN_FLG_CONSTTIME);
              BN_set_flags(pinfo->t, BN_FLG_CONSTTIME);
              (void)sk_RSA_PRIME_INFO_push(prime_infos, pinfo);
          }
  
          r->prime_infos = prime_infos;
  
          if (!rsa_multip_calc_product(r)) {
              r->prime_infos = old_infos;
              goto err;
          }
      }
  
      if (old_infos != NULL) {
          /*
           * This is hard to deal with, since the old infos could
           * also be set by this function and r, d, t should not
           * be freed in that case. So currently, stay consistent
           * with other *set0* functions: just free it...
           */
          sk_RSA_PRIME_INFO_pop_free(old_infos, rsa_multip_info_free);
      }
  
      r->version = pnum > 2 ? RSA_ASN1_VERSION_MULTI : RSA_ASN1_VERSION_DEFAULT;
      r->dirty_cnt++;
  
      return 1;
   err:
      /* r, d, t should not be freed */
      sk_RSA_PRIME_INFO_pop_free(prime_infos, rsa_multip_info_free_ex);
      return 0;
  }
  
  DEFINE_SPECIAL_STACK_OF_CONST(BIGNUM_const, BIGNUM)
  
  int rsa_get0_all_params(RSA *r, STACK_OF(BIGNUM_const) *primes,
                          STACK_OF(BIGNUM_const) *exps,
                          STACK_OF(BIGNUM_const) *coeffs)
  {
      RSA_PRIME_INFO *pinfo;
      int i, pnum;
  
      if (r == NULL)
          return 0;
  
      pnum = RSA_get_multi_prime_extra_count(r);
  
      sk_BIGNUM_const_push(primes, RSA_get0_p(r));
      sk_BIGNUM_const_push(primes, RSA_get0_q(r));
      sk_BIGNUM_const_push(exps, RSA_get0_dmp1(r));
      sk_BIGNUM_const_push(exps, RSA_get0_dmq1(r));
      sk_BIGNUM_const_push(coeffs, RSA_get0_iqmp(r));
      for (i = 0; i < pnum; i++) {
          pinfo = sk_RSA_PRIME_INFO_value(r->prime_infos, i);
          sk_BIGNUM_const_push(primes, pinfo->r);
          sk_BIGNUM_const_push(exps, pinfo->d);
          sk_BIGNUM_const_push(coeffs, pinfo->t);
      }
  
      return 1;
  }
  