/src/libressl/crypto/bn/bn_exp.c

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/* $OpenBSD: bn_exp.c,v 1.32 2022/04/20 13:32:34 tb Exp $ */
/* 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.]
 */
/* ====================================================================
 * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
 *
 * 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 above 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 acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <stdlib.h>
#include <string.h>

#include <openssl/err.h>

#include "bn_lcl.h"
#include "constant_time_locl.h"

/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE  32

/* this one works - simple but works */
int
BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
  int i, bits, ret = 0;
  BIGNUM *v, *rr;

  if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
    /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
    BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return -1;
  }

  BN_CTX_start(ctx);
  if ((r == a) || (r == p))
    rr = BN_CTX_get(ctx);
  else
    rr = r;
  v = BN_CTX_get(ctx);
  if (rr == NULL || v == NULL)
    goto err;

  if (BN_copy(v, a) == NULL)
    goto err;
  bits = BN_num_bits(p);

  if (BN_is_odd(p)) {
    if (BN_copy(rr, a) == NULL)
      goto err;
  } else {
    if (!BN_one(rr))
      goto err;
  }

  for (i = 1; i < bits; i++) {
    if (!BN_sqr(v, v, ctx))
      goto err;
    if (BN_is_bit_set(p, i)) {
      if (!BN_mul(rr, rr, v, ctx))
        goto err;
    }
  }
  ret = 1;

err:
  if (r != rr && rr != NULL)
    BN_copy(r, rr);
  BN_CTX_end(ctx);
  bn_check_top(r);
  return (ret);
}

static int
BN_mod_exp_internal(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, int ct)
{
  int ret;

  bn_check_top(a);
  bn_check_top(p);
  bn_check_top(m);

  /* For even modulus  m = 2^k*m_odd,  it might make sense to compute
   * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery
   * exponentiation for the odd part), using appropriate exponent
   * reductions, and combine the results using the CRT.
   *
   * For now, we use Montgomery only if the modulus is odd; otherwise,
   * exponentiation using the reciprocal-based quick remaindering
   * algorithm is used.
   *
   * (Timing obtained with expspeed.c [computations  a^p mod m
   * where  a, p, m  are of the same length: 256, 512, 1024, 2048,
   * 4096, 8192 bits], compared to the running time of the
   * standard algorithm:
   *
   *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]
         *                     55 .. 77 %  [UltraSparc processor, but
   *                                  debug-solaris-sparcv8-gcc conf.]
   *
   *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]
   *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
   *
   * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
   * at 2048 and more bits, but at 512 and 1024 bits, it was
   * slower even than the standard algorithm!
   *
   * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
   * should be obtained when the new Montgomery reduction code
   * has been integrated into OpenSSL.)
   */

  if (BN_is_odd(m)) {
    if (a->top == 1 && !a->neg && !ct) {
      BN_ULONG A = a->d[0];
      ret = BN_mod_exp_mont_word(r, A,p, m,ctx, NULL);
    } else
      ret = BN_mod_exp_mont_ct(r, a,p, m,ctx, NULL);
  } else {
    ret = BN_mod_exp_recp(r, a,p, m, ctx);
  }

  bn_check_top(r);
  return (ret);
}

int
BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx)
{
  return BN_mod_exp_internal(r, a, p, m, ctx,
      (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
}

int
BN_mod_exp_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx)
{
  return BN_mod_exp_internal(r, a, p, m, ctx, 1);
}


int
BN_mod_exp_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx)
{
  return BN_mod_exp_internal(r, a, p, m, ctx, 0);
}


int
BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx)
{
  int i, j, bits, ret = 0, wstart, wend, window, wvalue;
  int start = 1;
  BIGNUM *aa;
  /* Table of variables obtained from 'ctx' */
  BIGNUM *val[TABLE_SIZE];
  BN_RECP_CTX recp;

  if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
    /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
    BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return -1;
  }

  bits = BN_num_bits(p);
  if (bits == 0) {
    /* x**0 mod 1 is still zero. */
    if (BN_is_one(m)) {
      ret = 1;
      BN_zero(r);
    } else
      ret = BN_one(r);
    return ret;
  }

  BN_RECP_CTX_init(&recp);

  BN_CTX_start(ctx);
  if ((aa = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((val[0] = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (m->neg) {
    /* ignore sign of 'm' */
    if (!BN_copy(aa, m))
      goto err;
    aa->neg = 0;
    if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
      goto err;
  } else {
    if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
      goto err;
  }

  if (!BN_nnmod(val[0], a, m, ctx))
    goto err;   /* 1 */
  if (BN_is_zero(val[0])) {
    BN_zero(r);
    ret = 1;
    goto err;
  }

  window = BN_window_bits_for_exponent_size(bits);
  if (window > 1) {
    if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
      goto err;       /* 2 */
    j = 1 << (window - 1);
    for (i = 1; i < j; i++) {
      if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
          !BN_mod_mul_reciprocal(val[i], val[i - 1],
          aa, &recp, ctx))
        goto err;
    }
  }

  start = 1;    /* This is used to avoid multiplication etc
         * when there is only the value '1' in the
         * buffer. */
  wvalue = 0;   /* The 'value' of the window */
  wstart = bits - 1;  /* The top bit of the window */
  wend = 0;   /* The bottom bit of the window */

  if (!BN_one(r))
    goto err;

  for (;;) {
    if (BN_is_bit_set(p, wstart) == 0) {
      if (!start)
        if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
          goto err;
      if (wstart == 0)
        break;
      wstart--;
      continue;
    }
    /* We now have wstart on a 'set' bit, we now need to work out
     * how bit a window to do.  To do this we need to scan
     * forward until the last set bit before the end of the
     * window */
    j = wstart;
    wvalue = 1;
    wend = 0;
    for (i = 1; i < window; i++) {
      if (wstart - i < 0)
        break;
      if (BN_is_bit_set(p, wstart - i)) {
        wvalue <<= (i - wend);
        wvalue |= 1;
        wend = i;
      }
    }

    /* wend is the size of the current window */
    j = wend + 1;
    /* add the 'bytes above' */
    if (!start)
      for (i = 0; i < j; i++) {
        if (!BN_mod_mul_reciprocal(r, r,r, &recp, ctx))
          goto err;
      }

    /* wvalue will be an odd number < 2^window */
    if (!BN_mod_mul_reciprocal(r, r,val[wvalue >> 1], &recp, ctx))
      goto err;

    /* move the 'window' down further */
    wstart -= wend + 1;
    wvalue = 0;
    start = 0;
    if (wstart < 0)
      break;
  }
  ret = 1;

err:
  BN_CTX_end(ctx);
  BN_RECP_CTX_free(&recp);
  bn_check_top(r);
  return (ret);
}

static int
BN_mod_exp_mont_internal(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, BN_MONT_CTX *in_mont, int ct)
{
  int i, j, bits, ret = 0, wstart, wend, window, wvalue;
  int start = 1;
  BIGNUM *d, *r;
  const BIGNUM *aa;
  /* Table of variables obtained from 'ctx' */
  BIGNUM *val[TABLE_SIZE];
  BN_MONT_CTX *mont = NULL;

  if (ct) {
    return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
  }

  bn_check_top(a);
  bn_check_top(p);
  bn_check_top(m);

  if (!BN_is_odd(m)) {
    BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
    return (0);
  }

  bits = BN_num_bits(p);
  if (bits == 0) {
    /* x**0 mod 1 is still zero. */
    if (BN_is_one(m)) {
      ret = 1;
      BN_zero(rr);
    } else
      ret = BN_one(rr);
    return ret;
  }

  BN_CTX_start(ctx);
  if ((d = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((r = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((val[0] = BN_CTX_get(ctx)) == NULL)
    goto err;

  /* If this is not done, things will break in the montgomery
   * part */

  if (in_mont != NULL)
    mont = in_mont;
  else {
    if ((mont = BN_MONT_CTX_new()) == NULL)
      goto err;
    if (!BN_MONT_CTX_set(mont, m, ctx))
      goto err;
  }

  if (a->neg || BN_ucmp(a, m) >= 0) {
    if (!BN_nnmod(val[0], a,m, ctx))
      goto err;
    aa = val[0];
  } else
    aa = a;
  if (BN_is_zero(aa)) {
    BN_zero(rr);
    ret = 1;
    goto err;
  }
  if (!BN_to_montgomery(val[0], aa, mont, ctx))
    goto err; /* 1 */

  window = BN_window_bits_for_exponent_size(bits);
  if (window > 1) {
    if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
      goto err; /* 2 */
    j = 1 << (window - 1);
    for (i = 1; i < j; i++) {
      if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
          !BN_mod_mul_montgomery(val[i], val[i - 1],
          d, mont, ctx))
        goto err;
    }
  }

  start = 1;    /* This is used to avoid multiplication etc
         * when there is only the value '1' in the
         * buffer. */
  wvalue = 0;   /* The 'value' of the window */
  wstart = bits - 1;  /* The top bit of the window */
  wend = 0;   /* The bottom bit of the window */

  if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
    goto err;
  for (;;) {
    if (BN_is_bit_set(p, wstart) == 0) {
      if (!start) {
        if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
          goto err;
      }
      if (wstart == 0)
        break;
      wstart--;
      continue;
    }
    /* We now have wstart on a 'set' bit, we now need to work out
     * how bit a window to do.  To do this we need to scan
     * forward until the last set bit before the end of the
     * window */
    j = wstart;
    wvalue = 1;
    wend = 0;
    for (i = 1; i < window; i++) {
      if (wstart - i < 0)
        break;
      if (BN_is_bit_set(p, wstart - i)) {
        wvalue <<= (i - wend);
        wvalue |= 1;
        wend = i;
      }
    }

    /* wend is the size of the current window */
    j = wend + 1;
    /* add the 'bytes above' */
    if (!start)
      for (i = 0; i < j; i++) {
        if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
          goto err;
      }

    /* wvalue will be an odd number < 2^window */
    if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
      goto err;

    /* move the 'window' down further */
    wstart -= wend + 1;
    wvalue = 0;
    start = 0;
    if (wstart < 0)
      break;
  }
  if (!BN_from_montgomery(rr, r,mont, ctx))
    goto err;
  ret = 1;

err:
  if ((in_mont == NULL) && (mont != NULL))
    BN_MONT_CTX_free(mont);
  BN_CTX_end(ctx);
  bn_check_top(rr);
  return (ret);
}

int
BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
  return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont,
      (BN_get_flags(p, BN_FLG_CONSTTIME) != 0));
}

int
BN_mod_exp_mont_ct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
  return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 1);
}

int
BN_mod_exp_mont_nonct(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
  return BN_mod_exp_mont_internal(rr, a, p, m, ctx, in_mont, 0);
}

/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
 * so that accessing any of these table values shows the same access pattern as far
 * as cache lines are concerned.  The following functions are used to transfer a BIGNUM
 * from/to that table. */

static int
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf,
    int idx, int window)
{
  int i, j;
  int width = 1 << window;
  BN_ULONG *table = (BN_ULONG *)buf;

  if (top > b->top)
    top = b->top; /* this works because 'buf' is explicitly zeroed */

  for (i = 0, j = idx; i < top; i++, j += width) {
    table[j] = b->d[i];
  }

  return 1;
}

static int
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx,
    int window)
{
  int i, j;
  int width = 1 << window;
  volatile BN_ULONG *table = (volatile BN_ULONG *)buf;

  if (bn_wexpand(b, top) == NULL)
    return 0;

  if (window <= 3) {
    for (i = 0; i < top; i++, table += width) {
        BN_ULONG acc = 0;

        for (j = 0; j < width; j++) {
      acc |= table[j] &
             ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
        }

        b->d[i] = acc;
    }
  } else {
    int xstride = 1 << (window - 2);
    BN_ULONG y0, y1, y2, y3;

    i = idx >> (window - 2);        /* equivalent of idx / xstride */
    idx &= xstride - 1;             /* equivalent of idx % xstride */

    y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
    y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
    y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
    y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);

    for (i = 0; i < top; i++, table += width) {
        BN_ULONG acc = 0;

        for (j = 0; j < xstride; j++) {
      acc |= ( (table[j + 0 * xstride] & y0) |
         (table[j + 1 * xstride] & y1) |
         (table[j + 2 * xstride] & y2) |
         (table[j + 3 * xstride] & y3) )
             & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
        }

        b->d[i] = acc;
    }
  }
  b->top = top;
  bn_correct_top(b);
  return 1;
}

/* Given a pointer value, compute the next address that is a cache line multiple. */
#define MOD_EXP_CTIME_ALIGN(x_) \
  ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))

/* This variant of BN_mod_exp_mont() uses fixed windows and the special
 * precomputation memory layout to limit data-dependency to a minimum
 * to protect secret exponents (cf. the hyper-threading timing attacks
 * pointed out by Colin Percival,
 * http://www.daemonology.net/hyperthreading-considered-harmful/)
 */
int
BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
  int i, bits, ret = 0, window, wvalue;
  int top;
  BN_MONT_CTX *mont = NULL;
  int numPowers;
  unsigned char *powerbufFree = NULL;
  int powerbufLen = 0;
  unsigned char *powerbuf = NULL;
  BIGNUM tmp, am;

  bn_check_top(a);
  bn_check_top(p);
  bn_check_top(m);

  if (!BN_is_odd(m)) {
    BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
    return (0);
  }

  top = m->top;

  bits = BN_num_bits(p);
  if (bits == 0) {
    /* x**0 mod 1 is still zero. */
    if (BN_is_one(m)) {
      ret = 1;
      BN_zero(rr);
    } else
      ret = BN_one(rr);
    return ret;
  }

  BN_CTX_start(ctx);

  /* Allocate a montgomery context if it was not supplied by the caller.
   * If this is not done, things will break in the montgomery part.
   */
  if (in_mont != NULL)
    mont = in_mont;
  else {
    if ((mont = BN_MONT_CTX_new()) == NULL)
      goto err;
    if (!BN_MONT_CTX_set(mont, m, ctx))
      goto err;
  }

  /* Get the window size to use with size of p. */
  window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(OPENSSL_BN_ASM_MONT5)
  if (window == 6 && bits <= 1024)
    window = 5; /* ~5% improvement of 2048-bit RSA sign */
#endif

  /* Allocate a buffer large enough to hold all of the pre-computed
   * powers of am, am itself and tmp.
   */
  numPowers = 1 << window;
  powerbufLen = sizeof(m->d[0]) * (top * numPowers +
      ((2*top) > numPowers ? (2*top) : numPowers));
  if ((powerbufFree = calloc(powerbufLen +
      MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH, 1)) == NULL)
    goto err;
  powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);

  /* lay down tmp and am right after powers table */
  tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
  am.d = tmp.d + top;
  tmp.top = am.top = 0;
  tmp.dmax = am.dmax = top;
  tmp.neg = am.neg = 0;
  tmp.flags = am.flags = BN_FLG_STATIC_DATA;

  /* prepare a^0 in Montgomery domain */
#if 1
  if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
    goto err;
#else
  tmp.d[0] = (0 - m - >d[0]) & BN_MASK2;  /* 2^(top*BN_BITS2) - m */
  for (i = 1; i < top; i++)
    tmp.d[i] = (~m->d[i]) & BN_MASK2;
  tmp.top = top;
#endif

  /* prepare a^1 in Montgomery domain */
  if (a->neg || BN_ucmp(a, m) >= 0) {
    if (!BN_mod_ct(&am, a,m, ctx))
      goto err;
    if (!BN_to_montgomery(&am, &am, mont, ctx))
      goto err;
  } else if (!BN_to_montgomery(&am, a,mont, ctx))
    goto err;

#if defined(OPENSSL_BN_ASM_MONT5)
  /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
   * specifically optimization of cache-timing attack countermeasures
   * and pre-computation optimization. */

  /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
   * 512-bit RSA is hardly relevant, we omit it to spare size... */
  if (window == 5 && top > 1) {
    void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
        const void *table, const BN_ULONG *np,
        const BN_ULONG *n0, int num, int power);
    void bn_scatter5(const BN_ULONG *inp, size_t num,
        void *table, size_t power);
    void bn_gather5(BN_ULONG *out, size_t num,
        void *table, size_t power);

    BN_ULONG *np = mont->N.d, *n0 = mont->n0;

    /* BN_to_montgomery can contaminate words above .top
     * [in BN_DEBUG[_DEBUG] build]... */
    for (i = am.top; i < top; i++)
      am.d[i] = 0;
    for (i = tmp.top; i < top; i++)
      tmp.d[i] = 0;

    bn_scatter5(tmp.d, top, powerbuf, 0);
    bn_scatter5(am.d, am.top, powerbuf, 1);
    bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
    bn_scatter5(tmp.d, top, powerbuf, 2);

#if 0
    for (i = 3; i < 32; i++) {
      /* Calculate a^i = a^(i-1) * a */
      bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
          n0, top, i - 1);
      bn_scatter5(tmp.d, top, powerbuf, i);
    }
#else
    /* same as above, but uses squaring for 1/2 of operations */
    for (i = 4; i < 32; i*=2) {
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_scatter5(tmp.d, top, powerbuf, i);
    }
    for (i = 3; i < 8; i += 2) {
      int j;
      bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
          n0, top, i - 1);
      bn_scatter5(tmp.d, top, powerbuf, i);
      for (j = 2 * i; j < 32; j *= 2) {
        bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
        bn_scatter5(tmp.d, top, powerbuf, j);
      }
    }
    for (; i < 16; i += 2) {
      bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
          n0, top, i - 1);
      bn_scatter5(tmp.d, top, powerbuf, i);
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_scatter5(tmp.d, top, powerbuf, 2*i);
    }
    for (; i < 32; i += 2) {
      bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np,
          n0, top, i - 1);
      bn_scatter5(tmp.d, top, powerbuf, i);
    }
#endif
    bits--;
    for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
      wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
    bn_gather5(tmp.d, top, powerbuf, wvalue);

    /* Scan the exponent one window at a time starting from the most
     * significant bits.
     */
    while (bits >= 0) {
      for (wvalue = 0, i = 0; i < 5; i++, bits--)
        wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);

      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
      bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
    }

    tmp.top = top;
    bn_correct_top(&tmp);
  } else
#endif
  {
    if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0,
        window))
      goto err;
    if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am,  top, powerbuf, 1,
        window))
      goto err;

    /* If the window size is greater than 1, then calculate
     * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
     * (even powers could instead be computed as (a^(i/2))^2
     * to use the slight performance advantage of sqr over mul).
     */
    if (window > 1) {
      if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
        goto err;
      if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf,
          2, window))
        goto err;
      for (i = 3; i < numPowers; i++) {
        /* Calculate a^i = a^(i-1) * a */
        if (!BN_mod_mul_montgomery(&tmp, &am, &tmp,
            mont, ctx))
          goto err;
        if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top,
            powerbuf, i, window))
          goto err;
      }
    }

    bits--;
    for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
      wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
    if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf,
        wvalue, window))
      goto err;

    /* Scan the exponent one window at a time starting from the most
     * significant bits.
     */
    while (bits >= 0) {
      wvalue = 0; /* The 'value' of the window */

      /* Scan the window, squaring the result as we go */
      for (i = 0; i < window; i++, bits--) {
        if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp,
            mont, ctx))
          goto err;
        wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
      }

      /* Fetch the appropriate pre-computed value from the pre-buf */
      if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf,
          wvalue, window))
        goto err;

      /* Multiply the result into the intermediate result */
      if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
        goto err;
    }
  }

  /* Convert the final result from montgomery to standard format */
  if (!BN_from_montgomery(rr, &tmp, mont, ctx))
    goto err;
  ret = 1;

err:
  if ((in_mont == NULL) && (mont != NULL))
    BN_MONT_CTX_free(mont);
  freezero(powerbufFree, powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
  BN_CTX_end(ctx);
  return (ret);
}

int
BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
  BN_MONT_CTX *mont = NULL;
  int b, bits, ret = 0;
  int r_is_one;
  BN_ULONG w, next_w;
  BIGNUM *d, *r, *t;
  BIGNUM *swap_tmp;

#define BN_MOD_MUL_WORD(r, w, m) \
    (BN_mul_word(r, (w)) && \
    (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
      (BN_mod_ct(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
    /* BN_MOD_MUL_WORD is only used with 'w' large,
     * so the BN_ucmp test is probably more overhead
     * than always using BN_mod (which uses BN_copy if
     * a similar test returns true). */
    /* We can use BN_mod and do not need BN_nnmod because our
     * accumulator is never negative (the result of BN_mod does
     * not depend on the sign of the modulus).
     */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
    (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))

  if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
    /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
    BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return -1;
  }

  bn_check_top(p);
  bn_check_top(m);

  if (!BN_is_odd(m)) {
    BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
    return (0);
  }
  if (m->top == 1)
    a %= m->d[0]; /* make sure that 'a' is reduced */

  bits = BN_num_bits(p);
  if (bits == 0) {
    /* x**0 mod 1 is still zero. */
    if (BN_is_one(m)) {
      ret = 1;
      BN_zero(rr);
    } else
      ret = BN_one(rr);
    return ret;
  }
  if (a == 0) {
    BN_zero(rr);
    ret = 1;
    return ret;
  }

  BN_CTX_start(ctx);
  if ((d = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((r = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((t = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (in_mont != NULL)
    mont = in_mont;
  else {
    if ((mont = BN_MONT_CTX_new()) == NULL)
      goto err;
    if (!BN_MONT_CTX_set(mont, m, ctx))
      goto err;
  }

  r_is_one = 1; /* except for Montgomery factor */

  /* bits-1 >= 0 */

  /* The result is accumulated in the product r*w. */
  w = a; /* bit 'bits-1' of 'p' is always set */
  for (b = bits - 2; b >= 0; b--) {
    /* First, square r*w. */
    next_w = w * w;
    if ((next_w / w) != w) /* overflow */
    {
      if (r_is_one) {
        if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
          goto err;
        r_is_one = 0;
      } else {
        if (!BN_MOD_MUL_WORD(r, w, m))
          goto err;
      }
      next_w = 1;
    }
    w = next_w;
    if (!r_is_one) {
      if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
        goto err;
    }

    /* Second, multiply r*w by 'a' if exponent bit is set. */
    if (BN_is_bit_set(p, b)) {
      next_w = w * a;
      if ((next_w / a) != w) /* overflow */
      {
        if (r_is_one) {
          if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
            goto err;
          r_is_one = 0;
        } else {
          if (!BN_MOD_MUL_WORD(r, w, m))
            goto err;
        }
        next_w = a;
      }
      w = next_w;
    }
  }

  /* Finally, set r:=r*w. */
  if (w != 1) {
    if (r_is_one) {
      if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
        goto err;
      r_is_one = 0;
    } else {
      if (!BN_MOD_MUL_WORD(r, w, m))
        goto err;
    }
  }

  if (r_is_one) /* can happen only if a == 1*/
  {
    if (!BN_one(rr))
      goto err;
  } else {
    if (!BN_from_montgomery(rr, r, mont, ctx))
      goto err;
  }
  ret = 1;

err:
  if ((in_mont == NULL) && (mont != NULL))
    BN_MONT_CTX_free(mont);
  BN_CTX_end(ctx);
  bn_check_top(rr);
  return (ret);
}


/* The old fallback, simple version :-) */
int
BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
    BN_CTX *ctx)
{
  int i, j, bits, ret = 0, wstart, wend, window, wvalue;
  int start = 1;
  BIGNUM *d;
  /* Table of variables obtained from 'ctx' */
  BIGNUM *val[TABLE_SIZE];

  if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
    /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
    BNerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return -1;
  }

  bits = BN_num_bits(p);
  if (bits == 0) {
    /* x**0 mod 1 is still zero. */
    if (BN_is_one(m)) {
      ret = 1;
      BN_zero(r);
    } else
      ret = BN_one(r);
    return ret;
  }

  BN_CTX_start(ctx);
  if ((d = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((val[0] = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (!BN_nnmod(val[0],a,m,ctx))
    goto err;    /* 1 */
  if (BN_is_zero(val[0])) {
    BN_zero(r);
    ret = 1;
    goto err;
  }

  window = BN_window_bits_for_exponent_size(bits);
  if (window > 1) {
    if (!BN_mod_mul(d, val[0], val[0], m, ctx))
      goto err;       /* 2 */
    j = 1 << (window - 1);
    for (i = 1; i < j; i++) {
      if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
          !BN_mod_mul(val[i], val[i - 1], d,m, ctx))
        goto err;
    }
  }

  start = 1;    /* This is used to avoid multiplication etc
         * when there is only the value '1' in the
         * buffer. */
  wvalue = 0;   /* The 'value' of the window */
  wstart = bits - 1;  /* The top bit of the window */
  wend = 0;   /* The bottom bit of the window */

  if (!BN_one(r))
    goto err;

  for (;;) {
    if (BN_is_bit_set(p, wstart) == 0) {
      if (!start)
        if (!BN_mod_mul(r, r, r, m, ctx))
          goto err;
      if (wstart == 0)
        break;
      wstart--;
      continue;
    }
    /* We now have wstart on a 'set' bit, we now need to work out
     * how bit a window to do.  To do this we need to scan
     * forward until the last set bit before the end of the
     * window */
    j = wstart;
    wvalue = 1;
    wend = 0;
    for (i = 1; i < window; i++) {
      if (wstart - i < 0)
        break;
      if (BN_is_bit_set(p, wstart - i)) {
        wvalue <<= (i - wend);
        wvalue |= 1;
        wend = i;
      }
    }

    /* wend is the size of the current window */
    j = wend + 1;
    /* add the 'bytes above' */
    if (!start)
      for (i = 0; i < j; i++) {
        if (!BN_mod_mul(r, r, r, m, ctx))
          goto err;
      }

    /* wvalue will be an odd number < 2^window */
    if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
      goto err;

    /* move the 'window' down further */
    wstart -= wend + 1;
    wvalue = 0;
    start = 0;
    if (wstart < 0)
      break;
  }
  ret = 1;

err:
  BN_CTX_end(ctx);
  bn_check_top(r);
  return (ret);
}

Coverage Report

Created: 2022-08-24 06:30