/* 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.] */

#include <openssl/bn.h>

#include <assert.h>

#include <stdlib.h>

#include <string.h>

#include <openssl/err.h>

#include <openssl/mem.h>

#include "internal.h"

#include "../../internal.h"

#define BN_MUL_RECURSIVE_SIZE_NORMAL 16

#define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL

static void bn_abs_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,

                             size_t num, BN_ULONG *tmp) {

  BN_ULONG borrow = bn_sub_words(tmp, a, b, num);

  bn_sub_words(r, b, a, num);

  bn_select_words(r, 0 - borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);

}

static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na,

                          const BN_ULONG *b, size_t nb) {

  if (na < nb) {

    size_t itmp = na;

    na = nb;

    nb = itmp;

    const BN_ULONG *ltmp = a;

    a = b;

    b = ltmp;

  }

  BN_ULONG *rr = &(r[na]);

  if (nb == 0) {

    OPENSSL_memset(r, 0, na * sizeof(BN_ULONG));

    return;

  }

  rr[0] = bn_mul_words(r, a, na, b[0]);

  for (;;) {

    if (--nb == 0) {

      return;

    }

    rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);

    if (--nb == 0) {

      return;

    }

    rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);

    if (--nb == 0) {

      return;

    }

    rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);

    if (--nb == 0) {

      return;

    }

    rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);

    rr += 4;

    r += 4;

    b += 4;

  }

}

// bn_sub_part_words sets |r| to |a| - |b|. It returns the borrow bit, which is

// one if the operation underflowed and zero otherwise. |cl| is the common

// length, that is, the shorter of len(a) or len(b). |dl| is the delta length,

// that is, len(a) - len(b). |r|'s length matches the larger of |a| and |b|, or

// cl + abs(dl).

//

// TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention

// is confusing.

static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,

                                  const BN_ULONG *b, int cl, int dl) {

  assert(cl >= 0);

  BN_ULONG borrow = bn_sub_words(r, a, b, cl);

  if (dl == 0) {

    return borrow;

  }

  r += cl;

  a += cl;

  b += cl;

  if (dl < 0) {

    // |a| is shorter than |b|. Complete the subtraction as if the excess words

    // in |a| were zeros.

    dl = -dl;

    for (int i = 0; i < dl; i++) {

      r[i] = CRYPTO_subc_w(0, b[i], borrow, &borrow);

    }

  } else {

    // |b| is shorter than |a|. Complete the subtraction as if the excess words

    // in |b| were zeros.

    for (int i = 0; i < dl; i++) {

      r[i] = CRYPTO_subc_w(a[i], 0, borrow, &borrow);

    }

  }

  return borrow;

}

// bn_abs_sub_part_words computes |r| = |a| - |b|, storing the absolute value

// and returning a mask of all ones if the result was negative and all zeros if

// the result was positive. |cl| and |dl| follow the |bn_sub_part_words| calling

// convention.

//

// TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention

// is confusing.

static BN_ULONG bn_abs_sub_part_words(BN_ULONG *r, const BN_ULONG *a,

                                      const BN_ULONG *b, int cl, int dl,

                                      BN_ULONG *tmp) {

  BN_ULONG borrow = bn_sub_part_words(tmp, a, b, cl, dl);

  bn_sub_part_words(r, b, a, cl, -dl);

  int r_len = cl + (dl < 0 ? -dl : dl);

  borrow = 0 - borrow;

  bn_select_words(r, borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, r_len);

  return borrow;

}

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

                         BN_CTX *ctx) {

  int cl = a->width < b->width ? a->width : b->width;

  int dl = a->width - b->width;

  int r_len = a->width < b->width ? b->width : a->width;

  BN_CTX_start(ctx);

  BIGNUM *tmp = BN_CTX_get(ctx);

  int ok = tmp != NULL &&

           bn_wexpand(r, r_len) &&

           bn_wexpand(tmp, r_len);

  if (ok) {

    bn_abs_sub_part_words(r->d, a->d, b->d, cl, dl, tmp->d);

    r->width = r_len;

  }

  BN_CTX_end(ctx);

  return ok;

}

// Karatsuba recursive multiplication algorithm

// (cf. Knuth, The Art of Computer Programming, Vol. 2)

// bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has

// length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and

// |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have

// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and

// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0.

//

// TODO(davidben): Simplify and |size_t| the calling convention around lengths

// here.

static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,

                             int n2, int dna, int dnb, BN_ULONG *t) {

  // |n2| is a power of two.

  assert(n2 != 0 && (n2 & (n2 - 1)) == 0);

  // Check |dna| and |dnb| are in range.

  assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dna && dna <= 0);

  assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dnb && dnb <= 0);

  // Only call bn_mul_comba 8 if n2 == 8 and the

  // two arrays are complete [steve]

  if (n2 == 8 && dna == 0 && dnb == 0) {

    bn_mul_comba8(r, a, b);

    return;

  }

  // Else do normal multiply

  if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {

    bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);

    if (dna + dnb < 0) {

      OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,

                     sizeof(BN_ULONG) * -(dna + dnb));

    }

    return;

  }

  // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|.

  // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used

  // for recursive calls.

  // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1

  // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:

  //

  //   a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0

  //

  // Note that we know |n| >= |BN_MUL_RECURSIVE_SIZE_NORMAL|/2 above, so

  // |tna| and |tnb| are non-negative.

  int n = n2 / 2, tna = n + dna, tnb = n + dnb;

  // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR

  // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1

  // themselves store the absolute value.

  BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);

  neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);

  // Compute:

  // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|

  // r0,r1 = a0 * b0

  // r2,r3 = a1 * b1

  if (n == 4 && dna == 0 && dnb == 0) {

    bn_mul_comba4(&t[n2], t, &t[n]);

    bn_mul_comba4(r, a, b);

    bn_mul_comba4(&r[n2], &a[n], &b[n]);

  } else if (n == 8 && dna == 0 && dnb == 0) {

    bn_mul_comba8(&t[n2], t, &t[n]);

    bn_mul_comba8(r, a, b);

    bn_mul_comba8(&r[n2], &a[n], &b[n]);

  } else {

    BN_ULONG *p = &t[n2 * 2];

    bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);

    bn_mul_recursive(r, a, b, n, 0, 0, p);

    bn_mul_recursive(&r[n2], &a[n], &b[n], n, dna, dnb, p);

  }

  // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1

  BN_ULONG c = bn_add_words(t, r, &r[n2], n2);

  // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.

  // The second term is stored as the absolute value, so we do this with a

  // constant-time select.

  BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);

  BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);

  bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);

  static_assert(sizeof(BN_ULONG) <= sizeof(crypto_word_t),

                "crypto_word_t is too small");

  c = constant_time_select_w(neg, c_neg, c_pos);

  // We now have our three components. Add them together.

  // r1,r2,c = r1,r2 + t2,t3,c

  c += bn_add_words(&r[n], &r[n], &t[n2], n2);

  // Propagate the carry bit to the end.

  for (int i = n + n2; i < n2 + n2; i++) {

    BN_ULONG old = r[i];

    r[i] = old + c;

    c = r[i] < old;

  }

  // The product should fit without carries.

  declassify_assert(c == 0);

}

// bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r|

// has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and

// |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have

// 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most

// one.

//

// TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a|

// and |b|.

static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,

                                  const BN_ULONG *b, int n, int tna, int tnb,

                                  BN_ULONG *t) {

  // |n| is a power of two.

  assert(n != 0 && (n & (n - 1)) == 0);

  // Check |tna| and |tnb| are in range.

  assert(0 <= tna && tna < n);

  assert(0 <= tnb && tnb < n);

  assert(-1 <= tna - tnb && tna - tnb <= 1);

  int n2 = n * 2;

  if (n < 8) {

    bn_mul_normal(r, a, n + tna, b, n + tnb);

    OPENSSL_memset(r + n2 + tna + tnb, 0, n2 - tna - tnb);

    return;

  }

  // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|. |a1|

  // and |b1| have size |tna| and |tnb|, respectively.

  // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used

  // for recursive calls.

  // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1

  // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:

  //

  //   a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0

  // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR

  // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1

  // themselves store the absolute value.

  BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);

  neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);

  // Compute:

  // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|

  // r0,r1 = a0 * b0

  // r2,r3 = a1 * b1

  if (n == 8) {

    bn_mul_comba8(&t[n2], t, &t[n]);

    bn_mul_comba8(r, a, b);

    bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);

    // |bn_mul_normal| only writes |tna| + |tna| words. Zero the rest.

    OPENSSL_memset(&r[n2 + tna + tnb], 0, sizeof(BN_ULONG) * (n2 - tna - tnb));

  } else {

    BN_ULONG *p = &t[n2 * 2];

    bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);

    bn_mul_recursive(r, a, b, n, 0, 0, p);

    OPENSSL_memset(&r[n2], 0, sizeof(BN_ULONG) * n2);

    if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&

        tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {

      bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);

    } else {

      int i = n;

      for (;;) {

        i /= 2;

        if (i < tna || i < tnb) {

          // E.g., n == 16, i == 8 and tna == 11. |tna| and |tnb| are within one

          // of each other, so if |tna| is larger and tna > i, then we know

          // tnb >= i, and this call is valid.

          bn_mul_part_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);

          break;

        }

        if (i == tna || i == tnb) {

          // If there is only a bottom half to the number, just do it. We know

          // the larger of |tna - i| and |tnb - i| is zero. The other is zero or

          // -1 by because of |tna| and |tnb| differ by at most one.

          bn_mul_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);

          break;

        }

        // This loop will eventually terminate when |i| falls below

        // |BN_MUL_RECURSIVE_SIZE_NORMAL| because we know one of |tna| and |tnb|

        // exceeds that.

      }

    }

  }

  // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1

  BN_ULONG c = bn_add_words(t, r, &r[n2], n2);

  // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.

  // The second term is stored as the absolute value, so we do this with a

  // constant-time select.

  BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);

  BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);

  bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);

  static_assert(sizeof(BN_ULONG) <= sizeof(crypto_word_t),

                "crypto_word_t is too small");

  c = constant_time_select_w(neg, c_neg, c_pos);

  // We now have our three components. Add them together.

  // r1,r2,c = r1,r2 + t2,t3,c

  c += bn_add_words(&r[n], &r[n], &t[n2], n2);

  // Propagate the carry bit to the end.

  for (int i = n + n2; i < n2 + n2; i++) {

    BN_ULONG old = r[i];

    r[i] = old + c;

    c = r[i] < old;

  }

  // The product should fit without carries.

  declassify_assert(c == 0);

}

// bn_mul_impl implements |BN_mul| and |bn_mul_consttime|. Note this function

// breaks |BIGNUM| invariants and may return a negative zero. This is handled by

// the callers.

static int bn_mul_impl(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,

                       BN_CTX *ctx) {

  int al = a->width;

  int bl = b->width;

  if (al == 0 || bl == 0) {

    BN_zero(r);

    return 1;

  }

  int ret = 0;

  BIGNUM *rr;

  BN_CTX_start(ctx);

  if (r == a || r == b) {

    rr = BN_CTX_get(ctx);

    if (rr == NULL) {

      goto err;

    }

  } else {

    rr = r;

  }

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

  int i = al - bl;

  if (i == 0) {

    if (al == 8) {

      if (!bn_wexpand(rr, 16)) {

        goto err;

      }

      rr->width = 16;

      bn_mul_comba8(rr->d, a->d, b->d);

      goto end;

    }

  }

  int top = al + bl;

  static const int kMulNormalSize = 16;

  if (al >= kMulNormalSize && bl >= kMulNormalSize) {

    if (-1 <= i && i <= 1) {

      // Find the largest power of two less than or equal to the larger length.

      int j;

      if (i >= 0) {

        j = BN_num_bits_word((BN_ULONG)al);

      } else {

        j = BN_num_bits_word((BN_ULONG)bl);

      }

      j = 1 << (j - 1);

      assert(j <= al || j <= bl);

      BIGNUM *t = BN_CTX_get(ctx);

      if (t == NULL) {

        goto err;

      }

      if (al > j || bl > j) {

        // We know |al| and |bl| are at most one from each other, so if al > j,

        // bl >= j, and vice versa. Thus we can use |bn_mul_part_recursive|.

        //

        // TODO(davidben): This codepath is almost unused in standard

        // algorithms. Is this optimization necessary? See notes in

        // https://boringssl-review.googlesource.com/q/I0bd604e2cd6a75c266f64476c23a730ca1721ea6

        assert(al >= j && bl >= j);

        if (!bn_wexpand(t, j * 8) ||

            !bn_wexpand(rr, j * 4)) {

          goto err;

        }

        bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);

      } else {

        // al <= j && bl <= j. Additionally, we know j <= al or j <= bl, so one

        // of al - j or bl - j is zero. The other, by the bound on |i| above, is

        // zero or -1. Thus, we can use |bn_mul_recursive|.

        if (!bn_wexpand(t, j * 4) ||

            !bn_wexpand(rr, j * 2)) {

          goto err;

        }

        bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);

      }

      rr->width = top;

      goto end;

    }

  }

  if (!bn_wexpand(rr, top)) {

    goto err;

  }

  rr->width = top;

  bn_mul_normal(rr->d, a->d, al, b->d, bl);

end:

  if (r != rr && !BN_copy(r, rr)) {

    goto err;

  }

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {

  if (!bn_mul_impl(r, a, b, ctx)) {

    return 0;

  }

  // This additionally fixes any negative zeros created by |bn_mul_impl|.

  bn_set_minimal_width(r);

  return 1;

}

int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {

  // Prevent negative zeros.

  if (a->neg || b->neg) {

    OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);

    return 0;

  }

  return bn_mul_impl(r, a, b, ctx);

}

void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,

                  const BN_ULONG *b, size_t num_b) {

  if (num_r != num_a + num_b) {

    abort();

  }

  // TODO(davidben): Should this call |bn_mul_comba4| too? |BN_mul| does not

  // hit that code.

  if (num_a == 8 && num_b == 8) {

    bn_mul_comba8(r, a, b);

  } else {

    bn_mul_normal(r, a, num_a, b, num_b);

  }

}

// tmp must have 2*n words

static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n,

                          BN_ULONG *tmp) {

  if (n == 0) {

    return;

  }

  size_t max = n * 2;

  const BN_ULONG *ap = a;

  BN_ULONG *rp = r;

  rp[0] = rp[max - 1] = 0;

  rp++;

  // Compute the contribution of a[i] * a[j] for all i < j.

  if (n > 1) {

    ap++;

    rp[n - 1] = bn_mul_words(rp, ap, n - 1, ap[-1]);

    rp += 2;

  }

  if (n > 2) {

    for (size_t i = n - 2; i > 0; i--) {

      ap++;

      rp[i] = bn_mul_add_words(rp, ap, i, ap[-1]);

      rp += 2;

    }

  }

  // The final result fits in |max| words, so none of the following operations

  // will overflow.

  // Double |r|, giving the contribution of a[i] * a[j] for all i != j.

  bn_add_words(r, r, r, max);

  // Add in the contribution of a[i] * a[i] for all i.

  bn_sqr_words(tmp, a, n);

  bn_add_words(r, r, tmp, max);

}

// bn_sqr_recursive sets |r| to |a|^2, using |t| as scratch space. |r| has

// length 2*|n2|, |a| has length |n2|, and |t| has length 4*|n2|. |n2| must be

// a power of two.

static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, size_t n2,

                             BN_ULONG *t) {

  // |n2| is a power of two.

  assert(n2 != 0 && (n2 & (n2 - 1)) == 0);

  if (n2 == 4) {

    bn_sqr_comba4(r, a);

    return;

  }

  if (n2 == 8) {

    bn_sqr_comba8(r, a);

    return;

  }

  if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {

    bn_sqr_normal(r, a, n2, t);

    return;

  }

  // Split |a| into a0,a1, each of size |n|.

  // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used

  // for recursive calls.

  // Split |r| into r0,r1,r2,r3. We must contribute a0^2 to r0,r1, 2*a0*a1 to

  // r1,r2, and a1^2 to r2,r3.

  size_t n = n2 / 2;

  BN_ULONG *t_recursive = &t[n2 * 2];

  // t0 = |a0 - a1|.

  bn_abs_sub_words(t, a, &a[n], n, &t[n]);

  // t2,t3 = t0^2 = |a0 - a1|^2 = a0^2 - 2*a0*a1 + a1^2

  bn_sqr_recursive(&t[n2], t, n, t_recursive);

  // r0,r1 = a0^2

  bn_sqr_recursive(r, a, n, t_recursive);

  // r2,r3 = a1^2

  bn_sqr_recursive(&r[n2], &a[n], n, t_recursive);

  // t0,t1,c = r0,r1 + r2,r3 = a0^2 + a1^2

  BN_ULONG c = bn_add_words(t, r, &r[n2], n2);

  // t2,t3,c = t0,t1,c - t2,t3 = 2*a0*a1

  c -= bn_sub_words(&t[n2], t, &t[n2], n2);

  // We now have our three components. Add them together.

  // r1,r2,c = r1,r2 + t2,t3,c

  c += bn_add_words(&r[n], &r[n], &t[n2], n2);

  // Propagate the carry bit to the end.

  for (size_t i = n + n2; i < n2 + n2; i++) {

    BN_ULONG old = r[i];

    r[i] = old + c;

    c = r[i] < old;

  }

  // The square should fit without carries.

  assert(c == 0);

}

int BN_mul_word(BIGNUM *bn, BN_ULONG w) {

  if (!bn->width) {

    return 1;

  }

  if (w == 0) {

    BN_zero(bn);

    return 1;

  }

  BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->width, w);

  if (ll) {

    if (!bn_wexpand(bn, bn->width + 1)) {

      return 0;

    }

    bn->d[bn->width++] = ll;

  }

  return 1;

}

int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {

  int al = a->width;

  if (al <= 0) {

    r->width = 0;

    r->neg = 0;

    return 1;

  }

  int ret = 0;

  BN_CTX_start(ctx);

  BIGNUM *rr = (a != r) ? r : BN_CTX_get(ctx);

  BIGNUM *tmp = BN_CTX_get(ctx);

  if (!rr || !tmp) {

    goto err;

  }

  int max = 2 * al;  // Non-zero (from above)

  if (!bn_wexpand(rr, max)) {

    goto err;

  }

  if (al == 4) {

    bn_sqr_comba4(rr->d, a->d);

  } else if (al == 8) {

    bn_sqr_comba8(rr->d, a->d);

  } else {

    if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {

      BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];

      bn_sqr_normal(rr->d, a->d, al, t);

    } else {

      // If |al| is a power of two, we can use |bn_sqr_recursive|.

      if (al != 0 && (al & (al - 1)) == 0) {

        if (!bn_wexpand(tmp, al * 4)) {

          goto err;

        }

        bn_sqr_recursive(rr->d, a->d, al, tmp->d);

      } else {

        if (!bn_wexpand(tmp, max)) {

          goto err;

        }

        bn_sqr_normal(rr->d, a->d, al, tmp->d);

      }

    }

  }

  rr->neg = 0;

  rr->width = max;

  if (rr != r && !BN_copy(r, rr)) {

    goto err;

  }

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {

  if (!bn_sqr_consttime(r, a, ctx)) {

    return 0;

  }

  bn_set_minimal_width(r);

  return 1;

}

void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) {

  if (num_r != 2 * num_a || num_a > BN_SMALL_MAX_WORDS) {

    abort();

  }

  if (num_a == 4) {

    bn_sqr_comba4(r, a);

  } else if (num_a == 8) {

    bn_sqr_comba8(r, a);

  } else {

    BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];

    bn_sqr_normal(r, a, num_a, tmp);

    OPENSSL_cleanse(tmp, 2 * num_a * sizeof(BN_ULONG));

  }

}