crypto/fipsmodule/bn/generic.cc.inc

// Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include <openssl/bn.h>

#include <assert.h>

#include "internal.h"


#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86)
// See asm/bn-586.pl.
#define BN_ADD_ASM
#define BN_MUL_ASM
#endif

#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
    (defined(__GNUC__) || defined(__clang__))
// See asm/x86_64-gcc.c
#define BN_ADD_ASM
#define BN_MUL_ASM
#endif

#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_AARCH64)
// See asm/bn-armv8.pl.
#define BN_ADD_ASM
#endif

#if !defined(BN_MUL_ASM)

#ifdef BN_ULLONG
#define mul_add(r, a, w, c)               \
  do {                                    \
    BN_ULLONG t;                          \
    t = (BN_ULLONG)(w) * (a) + (r) + (c); \
    (r) = (BN_ULONG)(t);                  \
    (c) = (BN_ULONG)((t) >> BN_BITS2);    \
  } while (0)

#define mul(r, a, w, c)                \
  do {                                 \
    BN_ULLONG t;                       \
    t = (BN_ULLONG)(w) * (a) + (c);    \
    (r) = (BN_ULONG)(t);               \
    (c) = (BN_ULONG)((t) >> BN_BITS2); \
  } while (0)

#define sqr(r0, r1, a)                  \
  do {                                  \
    BN_ULLONG t;                        \
    t = (BN_ULLONG)(a) * (a);           \
    (r0) = (BN_ULONG)(t);               \
    (r1) = (BN_ULONG)((t) >> BN_BITS2); \
  } while (0)

#else

#define mul_add(r, a, w, c)             \
  do {                                  \
    BN_ULONG high, low, ret, tmp = (a); \
    ret = (r);                          \
    BN_UMULT_LOHI(low, high, w, tmp);   \
    ret += (c);                         \
    (c) = (ret < (c)) ? 1 : 0;          \
    (c) += high;                        \
    ret += low;                         \
    (c) += (ret < low) ? 1 : 0;         \
    (r) = ret;                          \
  } while (0)

#define mul(r, a, w, c)                \
  do {                                 \
    BN_ULONG high, low, ret, ta = (a); \
    BN_UMULT_LOHI(low, high, w, ta);   \
    ret = low + (c);                   \
    (c) = high;                        \
    (c) += (ret < low) ? 1 : 0;        \
    (r) = ret;                         \
  } while (0)

#define sqr(r0, r1, a)               \
  do {                               \
    BN_ULONG tmp = (a);              \
    BN_UMULT_LOHI(r0, r1, tmp, tmp); \
  } while (0)

#endif  // !BN_ULLONG

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
                          BN_ULONG w) {
  BN_ULONG c1 = 0;

  if (num == 0) {
    return c1;
  }

  while (num & ~3) {
    mul_add(rp[0], ap[0], w, c1);
    mul_add(rp[1], ap[1], w, c1);
    mul_add(rp[2], ap[2], w, c1);
    mul_add(rp[3], ap[3], w, c1);
    ap += 4;
    rp += 4;
    num -= 4;
  }

  while (num) {
    mul_add(rp[0], ap[0], w, c1);
    ap++;
    rp++;
    num--;
  }

  return c1;
}

BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
                      BN_ULONG w) {
  BN_ULONG c1 = 0;

  if (num == 0) {
    return c1;
  }

  while (num & ~3) {
    mul(rp[0], ap[0], w, c1);
    mul(rp[1], ap[1], w, c1);
    mul(rp[2], ap[2], w, c1);
    mul(rp[3], ap[3], w, c1);
    ap += 4;
    rp += 4;
    num -= 4;
  }
  while (num) {
    mul(rp[0], ap[0], w, c1);
    ap++;
    rp++;
    num--;
  }
  return c1;
}

void bn_sqr_add_words(BN_ULONG *r, const BN_ULONG *a, size_t n) {
  if (n == 0) {
    return;
  }

  BN_ULONG carry = 0, lo, hi;
  while (n & ~3) {
    sqr(lo, hi, a[0]);
    r[0] = CRYPTO_addc_w(r[0], lo, carry, &carry);
    r[1] = CRYPTO_addc_w(r[1], hi, carry, &carry);
    sqr(lo, hi, a[1]);
    r[2] = CRYPTO_addc_w(r[2], lo, carry, &carry);
    r[3] = CRYPTO_addc_w(r[3], hi, carry, &carry);
    sqr(lo, hi, a[2]);
    r[4] = CRYPTO_addc_w(r[4], lo, carry, &carry);
    r[5] = CRYPTO_addc_w(r[5], hi, carry, &carry);
    sqr(lo, hi, a[3]);
    r[6] = CRYPTO_addc_w(r[6], lo, carry, &carry);
    r[7] = CRYPTO_addc_w(r[7], hi, carry, &carry);
    a += 4;
    r += 8;
    n -= 4;
  }
  while (n) {
    sqr(lo, hi, a[0]);
    r[0] = CRYPTO_addc_w(r[0], lo, carry, &carry);
    r[1] = CRYPTO_addc_w(r[1], hi, carry, &carry);
    a++;
    r += 2;
    n--;
  }
}

// mul_add_c(a,b,c0,c1,c2)  -- c+=a*b for three word number c=(c2,c1,c0)
// mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0)
// sqr_add_c(a,i,c0,c1,c2)  -- c+=a[i]^2 for three word number c=(c2,c1,c0)
// sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0)

#ifdef BN_ULLONG

// Keep in mind that additions to multiplication result can not overflow,
// because its high half cannot be all-ones.
#define mul_add_c(a, b, c0, c1, c2)     \
  do {                                  \
    BN_ULONG hi;                        \
    BN_ULLONG t = (BN_ULLONG)(a) * (b); \
    t += (c0); /* no carry */           \
    (c0) = (BN_ULONG)(t);               \
    hi = (BN_ULONG)((t) >> BN_BITS2);   \
    (c1) += (hi);                       \
    (c2) += (c1) < hi;                  \
  } while (0)

#define mul_add_c2(a, b, c0, c1, c2)        \
  do {                                      \
    BN_ULONG hi;                            \
    BN_ULLONG t = (BN_ULLONG)(a) * (b);     \
    BN_ULLONG tt = t + (c0); /* no carry */ \
    (c0) = (BN_ULONG)(tt);                  \
    hi = (BN_ULONG)((tt) >> BN_BITS2);      \
    (c1) += hi;                             \
    (c2) += (c1) < hi;                      \
    t += (c0); /* no carry */               \
    (c0) = (BN_ULONG)(t);                   \
    hi = (BN_ULONG)((t) >> BN_BITS2);       \
    (c1) += hi;                             \
    (c2) += (c1) < hi;                      \
  } while (0)

#define sqr_add_c(a, i, c0, c1, c2)           \
  do {                                        \
    BN_ULONG hi;                              \
    BN_ULLONG t = (BN_ULLONG)(a)[i] * (a)[i]; \
    t += (c0); /* no carry */                 \
    (c0) = (BN_ULONG)(t);                     \
    hi = (BN_ULONG)((t) >> BN_BITS2);         \
    (c1) += hi;                               \
    (c2) += (c1) < hi;                        \
  } while (0)

#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)

#else

// Keep in mind that additions to hi can not overflow, because the high word of
// a multiplication result cannot be all-ones.
#define mul_add_c(a, b, c0, c1, c2) \
  do {                              \
    BN_ULONG ta = (a), tb = (b);    \
    BN_ULONG lo, hi;                \
    BN_UMULT_LOHI(lo, hi, ta, tb);  \
    (c0) += lo;                     \
    hi += ((c0) < lo) ? 1 : 0;      \
    (c1) += hi;                     \
    (c2) += ((c1) < hi) ? 1 : 0;    \
  } while (0)

#define mul_add_c2(a, b, c0, c1, c2) \
  do {                               \
    BN_ULONG ta = (a), tb = (b);     \
    BN_ULONG lo, hi, tt;             \
    BN_UMULT_LOHI(lo, hi, ta, tb);   \
    (c0) += lo;                      \
    tt = hi + (((c0) < lo) ? 1 : 0); \
    (c1) += tt;                      \
    (c2) += ((c1) < tt) ? 1 : 0;     \
    (c0) += lo;                      \
    hi += (c0 < lo) ? 1 : 0;         \
    (c1) += hi;                      \
    (c2) += ((c1) < hi) ? 1 : 0;     \
  } while (0)

#define sqr_add_c(a, i, c0, c1, c2) \
  do {                              \
    BN_ULONG ta = (a)[i];           \
    BN_ULONG lo, hi;                \
    BN_UMULT_LOHI(lo, hi, ta, ta);  \
    (c0) += lo;                     \
    hi += (c0 < lo) ? 1 : 0;        \
    (c1) += hi;                     \
    (c2) += ((c1) < hi) ? 1 : 0;    \
  } while (0)

#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)

#endif  // !BN_ULLONG

void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]) {
  BN_ULONG c1, c2, c3;

  c1 = 0;
  c2 = 0;
  c3 = 0;
  mul_add_c(a[0], b[0], c1, c2, c3);
  r[0] = c1;
  c1 = 0;
  mul_add_c(a[0], b[1], c2, c3, c1);
  mul_add_c(a[1], b[0], c2, c3, c1);
  r[1] = c2;
  c2 = 0;
  mul_add_c(a[2], b[0], c3, c1, c2);
  mul_add_c(a[1], b[1], c3, c1, c2);
  mul_add_c(a[0], b[2], c3, c1, c2);
  r[2] = c3;
  c3 = 0;
  mul_add_c(a[0], b[3], c1, c2, c3);
  mul_add_c(a[1], b[2], c1, c2, c3);
  mul_add_c(a[2], b[1], c1, c2, c3);
  mul_add_c(a[3], b[0], c1, c2, c3);
  r[3] = c1;
  c1 = 0;
  mul_add_c(a[4], b[0], c2, c3, c1);
  mul_add_c(a[3], b[1], c2, c3, c1);
  mul_add_c(a[2], b[2], c2, c3, c1);
  mul_add_c(a[1], b[3], c2, c3, c1);
  mul_add_c(a[0], b[4], c2, c3, c1);
  r[4] = c2;
  c2 = 0;
  mul_add_c(a[0], b[5], c3, c1, c2);
  mul_add_c(a[1], b[4], c3, c1, c2);
  mul_add_c(a[2], b[3], c3, c1, c2);
  mul_add_c(a[3], b[2], c3, c1, c2);
  mul_add_c(a[4], b[1], c3, c1, c2);
  mul_add_c(a[5], b[0], c3, c1, c2);
  r[5] = c3;
  c3 = 0;
  mul_add_c(a[6], b[0], c1, c2, c3);
  mul_add_c(a[5], b[1], c1, c2, c3);
  mul_add_c(a[4], b[2], c1, c2, c3);
  mul_add_c(a[3], b[3], c1, c2, c3);
  mul_add_c(a[2], b[4], c1, c2, c3);
  mul_add_c(a[1], b[5], c1, c2, c3);
  mul_add_c(a[0], b[6], c1, c2, c3);
  r[6] = c1;
  c1 = 0;
  mul_add_c(a[0], b[7], c2, c3, c1);
  mul_add_c(a[1], b[6], c2, c3, c1);
  mul_add_c(a[2], b[5], c2, c3, c1);
  mul_add_c(a[3], b[4], c2, c3, c1);
  mul_add_c(a[4], b[3], c2, c3, c1);
  mul_add_c(a[5], b[2], c2, c3, c1);
  mul_add_c(a[6], b[1], c2, c3, c1);
  mul_add_c(a[7], b[0], c2, c3, c1);
  r[7] = c2;
  c2 = 0;
  mul_add_c(a[7], b[1], c3, c1, c2);
  mul_add_c(a[6], b[2], c3, c1, c2);
  mul_add_c(a[5], b[3], c3, c1, c2);
  mul_add_c(a[4], b[4], c3, c1, c2);
  mul_add_c(a[3], b[5], c3, c1, c2);
  mul_add_c(a[2], b[6], c3, c1, c2);
  mul_add_c(a[1], b[7], c3, c1, c2);
  r[8] = c3;
  c3 = 0;
  mul_add_c(a[2], b[7], c1, c2, c3);
  mul_add_c(a[3], b[6], c1, c2, c3);
  mul_add_c(a[4], b[5], c1, c2, c3);
  mul_add_c(a[5], b[4], c1, c2, c3);
  mul_add_c(a[6], b[3], c1, c2, c3);
  mul_add_c(a[7], b[2], c1, c2, c3);
  r[9] = c1;
  c1 = 0;
  mul_add_c(a[7], b[3], c2, c3, c1);
  mul_add_c(a[6], b[4], c2, c3, c1);
  mul_add_c(a[5], b[5], c2, c3, c1);
  mul_add_c(a[4], b[6], c2, c3, c1);
  mul_add_c(a[3], b[7], c2, c3, c1);
  r[10] = c2;
  c2 = 0;
  mul_add_c(a[4], b[7], c3, c1, c2);
  mul_add_c(a[5], b[6], c3, c1, c2);
  mul_add_c(a[6], b[5], c3, c1, c2);
  mul_add_c(a[7], b[4], c3, c1, c2);
  r[11] = c3;
  c3 = 0;
  mul_add_c(a[7], b[5], c1, c2, c3);
  mul_add_c(a[6], b[6], c1, c2, c3);
  mul_add_c(a[5], b[7], c1, c2, c3);
  r[12] = c1;
  c1 = 0;
  mul_add_c(a[6], b[7], c2, c3, c1);
  mul_add_c(a[7], b[6], c2, c3, c1);
  r[13] = c2;
  c2 = 0;
  mul_add_c(a[7], b[7], c3, c1, c2);
  r[14] = c3;
  r[15] = c1;
}

void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]) {
  BN_ULONG c1, c2, c3;

  c1 = 0;
  c2 = 0;
  c3 = 0;
  mul_add_c(a[0], b[0], c1, c2, c3);
  r[0] = c1;
  c1 = 0;
  mul_add_c(a[0], b[1], c2, c3, c1);
  mul_add_c(a[1], b[0], c2, c3, c1);
  r[1] = c2;
  c2 = 0;
  mul_add_c(a[2], b[0], c3, c1, c2);
  mul_add_c(a[1], b[1], c3, c1, c2);
  mul_add_c(a[0], b[2], c3, c1, c2);
  r[2] = c3;
  c3 = 0;
  mul_add_c(a[0], b[3], c1, c2, c3);
  mul_add_c(a[1], b[2], c1, c2, c3);
  mul_add_c(a[2], b[1], c1, c2, c3);
  mul_add_c(a[3], b[0], c1, c2, c3);
  r[3] = c1;
  c1 = 0;
  mul_add_c(a[3], b[1], c2, c3, c1);
  mul_add_c(a[2], b[2], c2, c3, c1);
  mul_add_c(a[1], b[3], c2, c3, c1);
  r[4] = c2;
  c2 = 0;
  mul_add_c(a[2], b[3], c3, c1, c2);
  mul_add_c(a[3], b[2], c3, c1, c2);
  r[5] = c3;
  c3 = 0;
  mul_add_c(a[3], b[3], c1, c2, c3);
  r[6] = c1;
  r[7] = c2;
}

void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[8]) {
  BN_ULONG c1, c2, c3;

  c1 = 0;
  c2 = 0;
  c3 = 0;
  sqr_add_c(a, 0, c1, c2, c3);
  r[0] = c1;
  c1 = 0;
  sqr_add_c2(a, 1, 0, c2, c3, c1);
  r[1] = c2;
  c2 = 0;
  sqr_add_c(a, 1, c3, c1, c2);
  sqr_add_c2(a, 2, 0, c3, c1, c2);
  r[2] = c3;
  c3 = 0;
  sqr_add_c2(a, 3, 0, c1, c2, c3);
  sqr_add_c2(a, 2, 1, c1, c2, c3);
  r[3] = c1;
  c1 = 0;
  sqr_add_c(a, 2, c2, c3, c1);
  sqr_add_c2(a, 3, 1, c2, c3, c1);
  sqr_add_c2(a, 4, 0, c2, c3, c1);
  r[4] = c2;
  c2 = 0;
  sqr_add_c2(a, 5, 0, c3, c1, c2);
  sqr_add_c2(a, 4, 1, c3, c1, c2);
  sqr_add_c2(a, 3, 2, c3, c1, c2);
  r[5] = c3;
  c3 = 0;
  sqr_add_c(a, 3, c1, c2, c3);
  sqr_add_c2(a, 4, 2, c1, c2, c3);
  sqr_add_c2(a, 5, 1, c1, c2, c3);
  sqr_add_c2(a, 6, 0, c1, c2, c3);
  r[6] = c1;
  c1 = 0;
  sqr_add_c2(a, 7, 0, c2, c3, c1);
  sqr_add_c2(a, 6, 1, c2, c3, c1);
  sqr_add_c2(a, 5, 2, c2, c3, c1);
  sqr_add_c2(a, 4, 3, c2, c3, c1);
  r[7] = c2;
  c2 = 0;
  sqr_add_c(a, 4, c3, c1, c2);
  sqr_add_c2(a, 5, 3, c3, c1, c2);
  sqr_add_c2(a, 6, 2, c3, c1, c2);
  sqr_add_c2(a, 7, 1, c3, c1, c2);
  r[8] = c3;
  c3 = 0;
  sqr_add_c2(a, 7, 2, c1, c2, c3);
  sqr_add_c2(a, 6, 3, c1, c2, c3);
  sqr_add_c2(a, 5, 4, c1, c2, c3);
  r[9] = c1;
  c1 = 0;
  sqr_add_c(a, 5, c2, c3, c1);
  sqr_add_c2(a, 6, 4, c2, c3, c1);
  sqr_add_c2(a, 7, 3, c2, c3, c1);
  r[10] = c2;
  c2 = 0;
  sqr_add_c2(a, 7, 4, c3, c1, c2);
  sqr_add_c2(a, 6, 5, c3, c1, c2);
  r[11] = c3;
  c3 = 0;
  sqr_add_c(a, 6, c1, c2, c3);
  sqr_add_c2(a, 7, 5, c1, c2, c3);
  r[12] = c1;
  c1 = 0;
  sqr_add_c2(a, 7, 6, c2, c3, c1);
  r[13] = c2;
  c2 = 0;
  sqr_add_c(a, 7, c3, c1, c2);
  r[14] = c3;
  r[15] = c1;
}

void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]) {
  BN_ULONG c1, c2, c3;

  c1 = 0;
  c2 = 0;
  c3 = 0;
  sqr_add_c(a, 0, c1, c2, c3);
  r[0] = c1;
  c1 = 0;
  sqr_add_c2(a, 1, 0, c2, c3, c1);
  r[1] = c2;
  c2 = 0;
  sqr_add_c(a, 1, c3, c1, c2);
  sqr_add_c2(a, 2, 0, c3, c1, c2);
  r[2] = c3;
  c3 = 0;
  sqr_add_c2(a, 3, 0, c1, c2, c3);
  sqr_add_c2(a, 2, 1, c1, c2, c3);
  r[3] = c1;
  c1 = 0;
  sqr_add_c(a, 2, c2, c3, c1);
  sqr_add_c2(a, 3, 1, c2, c3, c1);
  r[4] = c2;
  c2 = 0;
  sqr_add_c2(a, 3, 2, c3, c1, c2);
  r[5] = c3;
  c3 = 0;
  sqr_add_c(a, 3, c1, c2, c3);
  r[6] = c1;
  r[7] = c2;
}

#undef mul_add
#undef mul
#undef sqr
#undef mul_add_c
#undef mul_add_c2
#undef sqr_add_c
#undef sqr_add_c2

#endif  // !BN_MUL_ASM

#if !defined(BN_ADD_ASM)

BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                      size_t n) {
  if (n == 0) {
    return 0;
  }

  BN_ULONG carry = 0;
  while (n & ~3) {
    r[0] = CRYPTO_addc_w(a[0], b[0], carry, &carry);
    r[1] = CRYPTO_addc_w(a[1], b[1], carry, &carry);
    r[2] = CRYPTO_addc_w(a[2], b[2], carry, &carry);
    r[3] = CRYPTO_addc_w(a[3], b[3], carry, &carry);
    a += 4;
    b += 4;
    r += 4;
    n -= 4;
  }
  while (n) {
    r[0] = CRYPTO_addc_w(a[0], b[0], carry, &carry);
    a++;
    b++;
    r++;
    n--;
  }
  return carry;
}

BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                      size_t n) {
  if (n == 0) {
    return (BN_ULONG)0;
  }

  BN_ULONG borrow = 0;
  while (n & ~3) {
    r[0] = CRYPTO_subc_w(a[0], b[0], borrow, &borrow);
    r[1] = CRYPTO_subc_w(a[1], b[1], borrow, &borrow);
    r[2] = CRYPTO_subc_w(a[2], b[2], borrow, &borrow);
    r[3] = CRYPTO_subc_w(a[3], b[3], borrow, &borrow);
    a += 4;
    b += 4;
    r += 4;
    n -= 4;
  }
  while (n) {
    r[0] = CRYPTO_subc_w(a[0], b[0], borrow, &borrow);
    a++;
    b++;
    r++;
    n--;
  }
  return borrow;
}

#endif  // !BN_ADD_ASM