crypto/bn/convert.c

/* 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 <ctype.h>
#include <limits.h>
#include <stdio.h>
#include <string.h>

#include <openssl/bio.h>
#include <openssl/bytestring.h>
#include <openssl/err.h>
#include <openssl/mem.h>

#include "internal.h"

BIGNUM *BN_bin2bn(const uint8_t *in, size_t len, BIGNUM *ret) {
  size_t num_words;
  unsigned m;
  BN_ULONG word = 0;
  BIGNUM *bn = NULL;

  if (ret == NULL) {
    ret = bn = BN_new();
  }

  if (ret == NULL) {
    return NULL;
  }

  if (len == 0) {
    ret->top = 0;
    return ret;
  }

  num_words = ((len - 1) / BN_BYTES) + 1;
  m = (len - 1) % BN_BYTES;
  if (bn_wexpand(ret, num_words) == NULL) {
    if (bn) {
      BN_free(bn);
    }
    return NULL;
  }

  /* |bn_wexpand| must check bounds on |num_words| to write it into
   * |ret->dmax|. */
  assert(num_words <= INT_MAX);
  ret->top = (int)num_words;
  ret->neg = 0;

  while (len--) {
    word = (word << 8) | *(in++);
    if (m-- == 0) {
      ret->d[--num_words] = word;
      word = 0;
      m = BN_BYTES - 1;
    }
  }

  /* need to call this due to clear byte at top if avoiding having the top bit
   * set (-ve number) */
  bn_correct_top(ret);
  return ret;
}

size_t BN_bn2bin(const BIGNUM *in, uint8_t *out) {
  size_t n, i;
  BN_ULONG l;

  n = i = BN_num_bytes(in);
  while (i--) {
    l = in->d[i / BN_BYTES];
    *(out++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
  }
  return n;
}

/* constant_time_select_ulong returns |x| if |v| is 1 and |y| if |v| is 0. Its
 * behavior is undefined if |v| takes any other value. */
static BN_ULONG constant_time_select_ulong(int v, BN_ULONG x, BN_ULONG y) {
  BN_ULONG mask = v;
  mask--;

  return (~mask & x) | (mask & y);
}

/* constant_time_le_size_t returns 1 if |x| <= |y| and 0 otherwise. |x| and |y|
 * must not have their MSBs set. */
static int constant_time_le_size_t(size_t x, size_t y) {
  return ((x - y - 1) >> (sizeof(size_t) * 8 - 1)) & 1;
}

/* read_word_padded returns the |i|'th word of |in|, if it is not out of
 * bounds. Otherwise, it returns 0. It does so without branches on the size of
 * |in|, however it necessarily does not have the same memory access pattern. If
 * the access would be out of bounds, it reads the last word of |in|. |in| must
 * not be zero. */
static BN_ULONG read_word_padded(const BIGNUM *in, size_t i) {
  /* Read |in->d[i]| if valid. Otherwise, read the last word. */
  BN_ULONG l = in->d[constant_time_select_ulong(
      constant_time_le_size_t(in->dmax, i), in->dmax - 1, i)];

  /* Clamp to zero if above |d->top|. */
  return constant_time_select_ulong(constant_time_le_size_t(in->top, i), 0, l);
}

int BN_bn2bin_padded(uint8_t *out, size_t len, const BIGNUM *in) {
  size_t i;
  BN_ULONG l;

  /* Special case for |in| = 0. Just branch as the probability is negligible. */
  if (BN_is_zero(in)) {
    memset(out, 0, len);
    return 1;
  }

  /* Check if the integer is too big. This case can exit early in non-constant
   * time. */
  if ((size_t)in->top > (len + (BN_BYTES - 1)) / BN_BYTES) {
    return 0;
  }
  if ((len % BN_BYTES) != 0) {
    l = read_word_padded(in, len / BN_BYTES);
    if (l >> (8 * (len % BN_BYTES)) != 0) {
      return 0;
    }
  }

  /* Write the bytes out one by one. Serialization is done without branching on
   * the bits of |in| or on |in->top|, but if the routine would otherwise read
   * out of bounds, the memory access pattern can't be fixed. However, for an
   * RSA key of size a multiple of the word size, the probability of BN_BYTES
   * leading zero octets is low.
   *
   * See Falko Stenzke, "Manger's Attack revisited", ICICS 2010. */
  i = len;
  while (i--) {
    l = read_word_padded(in, i / BN_BYTES);
    *(out++) = (uint8_t)(l >> (8 * (i % BN_BYTES))) & 0xff;
  }
  return 1;
}

int BN_bn2cbb_padded(CBB *out, size_t len, const BIGNUM *in) {
  uint8_t *ptr;
  return CBB_add_space(out, &ptr, len) && BN_bn2bin_padded(ptr, len, in);
}

static const char hextable[] = "0123456789abcdef";

char *BN_bn2hex(const BIGNUM *bn) {
  char *buf = OPENSSL_malloc(1 /* leading '-' */ + 1 /* zero is non-empty */ +
                             bn->top * BN_BYTES * 2 + 1 /* trailing NUL */);
  if (buf == NULL) {
    OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE);
    return NULL;
  }

  char *p = buf;
  if (bn->neg) {
    *(p++) = '-';
  }

  if (BN_is_zero(bn)) {
    *(p++) = '0';
  }

  int z = 0;
  for (int i = bn->top - 1; i >= 0; i--) {
    for (int j = BN_BITS2 - 8; j >= 0; j -= 8) {
      /* strip leading zeros */
      int v = ((int)(bn->d[i] >> (long)j)) & 0xff;
      if (z || v != 0) {
        *(p++) = hextable[v >> 4];
        *(p++) = hextable[v & 0x0f];
        z = 1;
      }
    }
  }
  *p = '\0';

  return buf;
}

/* decode_hex decodes |in_len| bytes of hex data from |in| and updates |bn|. */
static int decode_hex(BIGNUM *bn, const char *in, int in_len) {
  if (in_len > INT_MAX/4) {
    OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
    return 0;
  }
  /* |in_len| is the number of hex digits. */
  if (bn_expand(bn, in_len * 4) == NULL) {
    return 0;
  }

  int i = 0;
  while (in_len > 0) {
    /* Decode one |BN_ULONG| at a time. */
    int todo = BN_BYTES * 2;
    if (todo > in_len) {
      todo = in_len;
    }

    BN_ULONG word = 0;
    int j;
    for (j = todo; j > 0; j--) {
      char c = in[in_len - j];

      BN_ULONG hex;
      if (c >= '0' && c <= '9') {
        hex = c - '0';
      } else if (c >= 'a' && c <= 'f') {
        hex = c - 'a' + 10;
      } else if (c >= 'A' && c <= 'F') {
        hex = c - 'A' + 10;
      } else {
        hex = 0;
        /* This shouldn't happen. The caller checks |isxdigit|. */
        assert(0);
      }
      word = (word << 4) | hex;
    }

    bn->d[i++] = word;
    in_len -= todo;
  }
  assert(i <= bn->dmax);
  bn->top = i;
  return 1;
}

/* decode_dec decodes |in_len| bytes of decimal data from |in| and updates |bn|. */
static int decode_dec(BIGNUM *bn, const char *in, int in_len) {
  int i, j;
  BN_ULONG l = 0;

  /* Decode |BN_DEC_NUM| digits at a time. */
  j = BN_DEC_NUM - (in_len % BN_DEC_NUM);
  if (j == BN_DEC_NUM) {
    j = 0;
  }
  l = 0;
  for (i = 0; i < in_len; i++) {
    l *= 10;
    l += in[i] - '0';
    if (++j == BN_DEC_NUM) {
      if (!BN_mul_word(bn, BN_DEC_CONV) ||
          !BN_add_word(bn, l)) {
        return 0;
      }
      l = 0;
      j = 0;
    }
  }
  return 1;
}

typedef int (*decode_func) (BIGNUM *bn, const char *in, int in_len);
typedef int (*char_test_func) (int c);

static int bn_x2bn(BIGNUM **outp, const char *in, decode_func decode, char_test_func want_char) {
  BIGNUM *ret = NULL;
  int neg = 0, i;
  int num;

  if (in == NULL || *in == 0) {
    return 0;
  }

  if (*in == '-') {
    neg = 1;
    in++;
  }

  for (i = 0; want_char((unsigned char)in[i]) && i + neg < INT_MAX; i++) {}

  num = i + neg;
  if (outp == NULL) {
    return num;
  }

  /* in is the start of the hex digits, and it is 'i' long */
  if (*outp == NULL) {
    ret = BN_new();
    if (ret == NULL) {
      return 0;
    }
  } else {
    ret = *outp;
    BN_zero(ret);
  }

  if (!decode(ret, in, i)) {
    goto err;
  }

  bn_correct_top(ret);
  if (!BN_is_zero(ret)) {
    ret->neg = neg;
  }

  *outp = ret;
  return num;

err:
  if (*outp == NULL) {
    BN_free(ret);
  }

  return 0;
}

int BN_hex2bn(BIGNUM **outp, const char *in) {
  return bn_x2bn(outp, in, decode_hex, isxdigit);
}

char *BN_bn2dec(const BIGNUM *a) {
  int i = 0, num, ok = 0;
  char *buf = NULL;
  char *p;
  BIGNUM *t = NULL;
  BN_ULONG *bn_data = NULL, *lp;
  int bn_data_num;

  /* get an upper bound for the length of the decimal integer
   * num <= (BN_num_bits(a) + 1) * log(2)
   *     <= 3 * BN_num_bits(a) * 0.1001 + log(2) + 1     (rounding error)
   *     <= BN_num_bits(a)/10 + BN_num_bits/1000 + 1 + 1
   */
  i = BN_num_bits(a) * 3;
  num = i / 10 + i / 1000 + 1 + 1;
  bn_data_num = num / BN_DEC_NUM + 1;
  bn_data = OPENSSL_malloc(bn_data_num * sizeof(BN_ULONG));
  buf = OPENSSL_malloc(num + 3);
  if ((buf == NULL) || (bn_data == NULL)) {
    OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE);
    goto err;
  }
  t = BN_dup(a);
  if (t == NULL) {
    goto err;
  }

#define BUF_REMAIN (num + 3 - (size_t)(p - buf))
  p = buf;
  lp = bn_data;

  if (BN_is_negative(t)) {
    *p++ = '-';
  }

  if (BN_is_zero(t)) {
    *(p++) = '0';
    *(p++) = '\0';
  } else {
    while (!BN_is_zero(t)) {
      *lp = BN_div_word(t, BN_DEC_CONV);
      if (*lp == (BN_ULONG)-1) {
        goto err;
      }
      lp++;
      if (lp - bn_data >= bn_data_num) {
        goto err;
      }
    }
    lp--;
    /* We now have a series of blocks, BN_DEC_NUM chars
     * in length, where the last one needs truncation.
     * The blocks need to be reversed in order. */
    BIO_snprintf(p, BUF_REMAIN, BN_DEC_FMT1, *lp);
    while (*p) {
      p++;
    }
    while (lp != bn_data) {
      lp--;
      BIO_snprintf(p, BUF_REMAIN, BN_DEC_FMT2, *lp);
      while (*p) {
        p++;
      }
    }
  }
  ok = 1;

err:
  OPENSSL_free(bn_data);
  BN_free(t);
  if (!ok) {
    OPENSSL_free(buf);
    buf = NULL;
  }

  return buf;
}

int BN_dec2bn(BIGNUM **outp, const char *in) {
  return bn_x2bn(outp, in, decode_dec, isdigit);
}

int BN_asc2bn(BIGNUM **outp, const char *in) {
  const char *const orig_in = in;
  if (*in == '-') {
    in++;
  }

  if (in[0] == '0' && (in[1] == 'X' || in[1] == 'x')) {
    if (!BN_hex2bn(outp, in+2)) {
      return 0;
    }
  } else {
    if (!BN_dec2bn(outp, in)) {
      return 0;
    }
  }

  if (*orig_in == '-' && !BN_is_zero(*outp)) {
    (*outp)->neg = 1;
  }

  return 1;
}

int BN_print(BIO *bp, const BIGNUM *a) {
  int i, j, v, z = 0;
  int ret = 0;

  if (a->neg && BIO_write(bp, "-", 1) != 1) {
    goto end;
  }

  if (BN_is_zero(a) && BIO_write(bp, "0", 1) != 1) {
    goto end;
  }

  for (i = a->top - 1; i >= 0; i--) {
    for (j = BN_BITS2 - 4; j >= 0; j -= 4) {
      /* strip leading zeros */
      v = ((int)(a->d[i] >> (long)j)) & 0x0f;
      if (z || v != 0) {
        if (BIO_write(bp, &hextable[v], 1) != 1) {
          goto end;
        }
        z = 1;
      }
    }
  }
  ret = 1;

end:
  return ret;
}

int BN_print_fp(FILE *fp, const BIGNUM *a) {
  BIO *b;
  int ret;

  b = BIO_new(BIO_s_file());
  if (b == NULL) {
    return 0;
  }
  BIO_set_fp(b, fp, BIO_NOCLOSE);
  ret = BN_print(b, a);
  BIO_free(b);

  return ret;
}

BN_ULONG BN_get_word(const BIGNUM *bn) {
  switch (bn->top) {
    case 0:
      return 0;
    case 1:
      return bn->d[0];
    default:
      return BN_MASK2;
  }
}

size_t BN_bn2mpi(const BIGNUM *in, uint8_t *out) {
  const size_t bits = BN_num_bits(in);
  const size_t bytes = (bits + 7) / 8;
  /* If the number of bits is a multiple of 8, i.e. if the MSB is set,
   * prefix with a zero byte. */
  int extend = 0;
  if (bytes != 0 && (bits & 0x07) == 0) {
    extend = 1;
  }

  const size_t len = bytes + extend;
  if (len < bytes ||
      4 + len < len ||
      (len & 0xffffffff) != len) {
    /* If we cannot represent the number then we emit zero as the interface
     * doesn't allow an error to be signalled. */
    if (out) {
      memset(out, 0, 4);
    }
    return 4;
  }

  if (out == NULL) {
    return 4 + len;
  }

  out[0] = len >> 24;
  out[1] = len >> 16;
  out[2] = len >> 8;
  out[3] = len;
  if (extend) {
    out[4] = 0;
  }
  BN_bn2bin(in, out + 4 + extend);
  if (in->neg && len > 0) {
    out[4] |= 0x80;
  }
  return len + 4;
}

BIGNUM *BN_mpi2bn(const uint8_t *in, size_t len, BIGNUM *out) {
  if (len < 4) {
    OPENSSL_PUT_ERROR(BN, BN_R_BAD_ENCODING);
    return NULL;
  }
  const size_t in_len = ((size_t)in[0] << 24) |
                        ((size_t)in[1] << 16) |
                        ((size_t)in[2] << 8) |
                        ((size_t)in[3]);
  if (in_len != len - 4) {
    OPENSSL_PUT_ERROR(BN, BN_R_BAD_ENCODING);
    return NULL;
  }

  int out_is_alloced = 0;
  if (out == NULL) {
    out = BN_new();
    if (out == NULL) {
      OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE);
      return NULL;
    }
    out_is_alloced = 1;
  }

  if (in_len == 0) {
    BN_zero(out);
    return out;
  }

  in += 4;
  if (BN_bin2bn(in, in_len, out) == NULL) {
    if (out_is_alloced) {
      BN_free(out);
    }
    return NULL;
  }
  out->neg = ((*in) & 0x80) != 0;
  if (out->neg) {
    BN_clear_bit(out, BN_num_bits(out) - 1);
  }
  return out;
}