text: /*
   * Copyright 1995-2017 The OpenSSL Project Authors. All Rights Reserved.
   *
   * Licensed under the OpenSSL license (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 at
   * http://security.ece.orst.edu/publications.html, e.g.
   * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
   * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
   */
  
  #include "internal/cryptlib.h"
  #include "bn_lcl.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)
  {
      BIGNUM *tmp;
      int ret = 0;
  #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
      int num = mont->N.top;
  
      if (num > 1 && 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;
              bn_correct_top(r);
              return 1;
          }
      }
  #endif
  
      BN_CTX_start(ctx);
      tmp = BN_CTX_get(ctx);
      if (tmp == NULL)
          goto err;
  
      bn_check_top(tmp);
      if (a == b) {
          if (!BN_sqr(tmp, a, ctx))
              goto err;
      } else {
          if (!BN_mul(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
      bn_check_top(r);
      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;
  
      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 */
      i = max - r->top;
      if (i)
          memset(&rp[r->top], 0, sizeof(*rp) * i);
  
      r->top = max;
      n0 = mont->n0[0];
  
      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->neg = r->neg;
  
      rp = ret->d;
      ap = &(r->d[nl]);
  
  # define BRANCH_FREE 1
  # if BRANCH_FREE
      {
          BN_ULONG *nrp;
          size_t m;
  
          v = bn_sub_words(rp, ap, np, nl) - carry;
          /*
           * if subtraction result is real, then trick unconditional memcpy
           * below to perform in-place "refresh" instead of actual copy.
           */
          m = (0 - (size_t)v);
          nrp =
              (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
  
          for (i = 0, nl -= 4; i < nl; i += 4) {
              BN_ULONG t1, t2, t3, t4;
  
              t1 = nrp[i + 0];
              t2 = nrp[i + 1];
              t3 = nrp[i + 2];
              ap[i + 0] = 0;
              t4 = nrp[i + 3];
              ap[i + 1] = 0;
              rp[i + 0] = t1;
              ap[i + 2] = 0;
              rp[i + 1] = t2;
              ap[i + 3] = 0;
              rp[i + 2] = t3;
              rp[i + 3] = t4;
          }
          for (nl += 4; i < nl; i++)
              rp[i] = nrp[i], ap[i] = 0;
      }
  # else
      if (bn_sub_words(rp, ap, np, nl) - carry)
          memcpy(rp, ap, nl * sizeof(BN_ULONG));
  # endif
      bn_correct_top(r);
      bn_correct_top(ret);
      bn_check_top(ret);
  
      return 1;
  }
  #endif                          /* MONT_WORD */
  
  int BN_from_montgomery(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);
  }
  
  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 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 */
      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_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_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;
  
      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;
  
      CRYPTO_THREAD_read_lock(lock);
      ret = *pmont;
      CRYPTO_THREAD_unlock(lock);
      if (ret)
          return ret;
  
      /*
       * We don't want to serialise 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. */
      CRYPTO_THREAD_write_lock(lock);
      if (*pmont) {
          BN_MONT_CTX_free(ret);
          ret = *pmont;
      } else
          *pmont = ret;
      CRYPTO_THREAD_unlock(lock);
      return ret;
  }
  