path: root/mpn/generic/powm_sec.c

/* mpn_powm_sec -- Compute R = U^E mod M.  Secure variant, side-channel silent
   under the assumption that the multiply instruction is side channel silent.

   Contributed to the GNU project by Torbjorn Granlund.

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2007, 2008, 2009, 2011 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */


/*
  BASIC ALGORITHM, Compute U^E mod M, where M < B^n is odd.

  1. T <- (B^n * U) mod M                Convert to REDC form

  2. Compute table U^0, U^1, U^2... of E-dependent size

  3. While there are more bits in E
       W <- power left-to-right base-k


  TODO:

   * Make getbits a macro, thereby allowing it to update the index operand.
     That will simplify the code using getbits.  (Perhaps make getbits' sibling
     getbit then have similar form, for symmetry.)

   * Write an itch function.  Or perhaps get rid of tp parameter since the huge
     pp area is allocated locally anyway?

   * Choose window size without looping.  (Superoptimize or think(tm).)

   * Call new division functions, not mpn_tdiv_qr.
*/

#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"

#define WANT_CACHE_SECURITY 1

#undef MPN_REDC_1_SEC
#define MPN_REDC_1_SEC(rp, up, mp, n, invm)				\
  do {									\
    mp_limb_t cy;							\
    mpn_redc_1 (up, mp, n, invm);					\
    cy = mpn_add_n (rp, up + n, up, n);					\
    mpn_subcnd_n (rp, rp, mp, n, cy);					\
  } while (0)

/* Define our own mpn squaring function.  We do this since we cannot use a
   native mpn_sqr_basecase over TUNE_SQR_TOOM2_MAX, or a non-native one over
   SQR_TOOM2_THRESHOLD.  This is so because of fixed size stack allocations
   made inside mpn_sqr_basecase.  */

#if HAVE_NATIVE_mpn_sqr_diagonal
#define MPN_SQR_DIAGONAL(rp, up, n)					\
  mpn_sqr_diagonal (rp, up, n)
#else
#define MPN_SQR_DIAGONAL(rp, up, n)					\
  do {									\
    mp_size_t _i;							\
    for (_i = 0; _i < (n); _i++)					\
      {									\
	mp_limb_t ul, lpl;						\
	ul = (up)[_i];							\
	umul_ppmm ((rp)[2 * _i + 1], lpl, ul, ul << GMP_NAIL_BITS);	\
	(rp)[2 * _i] = lpl >> GMP_NAIL_BITS;				\
      }									\
  } while (0)
#endif


#if ! HAVE_NATIVE_mpn_sqr_basecase
/* The limit of the generic code is SQR_TOOM2_THRESHOLD.  */
#define SQR_BASECASE_MAX  SQR_TOOM2_THRESHOLD
#endif

#if HAVE_NATIVE_mpn_sqr_basecase
#ifdef TUNE_SQR_TOOM2_MAX
/* We slightly abuse TUNE_SQR_TOOM2_MAX here.  If it is set for an assembly
   mpn_sqr_basecase, it comes from SQR_TOOM2_THRESHOLD_MAX in the assembly
   file.  An assembly mpn_sqr_basecase that does not define it, should allow
   any size.  */
#define SQR_BASECASE_MAX  SQR_TOOM2_THRESHOLD
#endif
#endif

#ifndef SQR_BASECASE_MAX
/* If SQR_BASECASE_MAX is now not defined, use mpn_sqr_basecase for any operand
   size.  */
#define mpn_local_sqr(rp,up,n,tp) mpn_sqr_basecase(rp,up,n)
#else
/* Define our own squaring function, which uses mpn_sqr_basecase for its
   allowed sizes, but its own code for larger sizes.  */
static void
mpn_local_sqr (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr tp)
{
  mp_size_t i;

  ASSERT (n >= 1);
  ASSERT (! MPN_OVERLAP_P (rp, 2*n, up, n));

  if (n < SQR_BASECASE_MAX)
    {
      mpn_sqr_basecase (rp, up, n);
      return;
    }

  {
    mp_limb_t ul, lpl;
    ul = up[0];
    umul_ppmm (rp[1], lpl, ul, ul << GMP_NAIL_BITS);
    rp[0] = lpl >> GMP_NAIL_BITS;
  }
  if (n > 1)
    {
      mp_limb_t cy;
      TMP_DECL;
      TMP_MARK;

      cy = mpn_mul_1 (tp, up + 1, n - 1, up[0]);
      tp[n - 1] = cy;
      for (i = 2; i < n; i++)
	{
	  mp_limb_t cy;
	  cy = mpn_addmul_1 (tp + 2 * i - 2, up + i, n - i, up[i - 1]);
	  tp[n + i - 2] = cy;
	}
      MPN_SQR_DIAGONAL (rp + 2, up + 1, n - 1);

      {
	mp_limb_t cy;
#if HAVE_NATIVE_mpn_addlsh1_n
	cy = mpn_addlsh1_n (rp + 1, rp + 1, tp, 2 * n - 2);
#else
	cy = mpn_lshift (tp, tp, 2 * n - 2, 1);
	cy += mpn_add_n (rp + 1, rp + 1, tp, 2 * n - 2);
#endif
	rp[2 * n - 1] += cy;
      }

      TMP_FREE;
    }
}
#endif

#define getbit(p,bi) \
  ((p[(bi - 1) / GMP_LIMB_BITS] >> (bi - 1) % GMP_LIMB_BITS) & 1)

static inline mp_limb_t
getbits (const mp_limb_t *p, mp_bitcnt_t bi, int nbits)
{
  int nbits_in_r;
  mp_limb_t r;
  mp_size_t i;

  if (bi < nbits)
    {
      return p[0] & (((mp_limb_t) 1 << bi) - 1);
    }
  else
    {
      bi -= nbits;			/* bit index of low bit to extract */
      i = bi / GMP_LIMB_BITS;		/* word index of low bit to extract */
      bi %= GMP_LIMB_BITS;		/* bit index in low word */
      r = p[i] >> bi;			/* extract (low) bits */
      nbits_in_r = GMP_LIMB_BITS - bi;	/* number of bits now in r */
      if (nbits_in_r < nbits)		/* did we get enough bits? */
	r += p[i + 1] << nbits_in_r;	/* prepend bits from higher word */
      return r & (((mp_limb_t ) 1 << nbits) - 1);
    }
}

static inline int
win_size (mp_bitcnt_t eb)
{
  int k;
  static mp_bitcnt_t x[] = {0,4,27,100,325,1026,2905,7848,20457,51670,~(mp_bitcnt_t)0};
  for (k = 1; eb > x[k]; k++)
    ;
  return k;
}

/* Convert U to REDC form, U_r = B^n * U mod M */
static void
redcify (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr mp, mp_size_t n, mp_ptr tp)
{
  mp_ptr qp;
  TMP_DECL;
  TMP_MARK;

  qp = tp + un + n;

  MPN_ZERO (tp, n);
  MPN_COPY (tp + n, up, un);
  mpn_tdiv_qr (qp, rp, 0L, tp, un + n, mp, n);
  TMP_FREE;
}

/* rp[n-1..0] = bp[bn-1..0] ^ ep[en-1..0] mod mp[n-1..0]
   Requires that mp[n-1..0] is odd.  FIXME: is this true?
   Requires that ep[en-1..0] is > 1.
   Uses scratch space at tp of 3n+1 limbs.  */
void
mpn_powm_sec (mp_ptr rp, mp_srcptr bp, mp_size_t bn,
	      mp_srcptr ep, mp_size_t en,
	      mp_srcptr mp, mp_size_t n, mp_ptr tp)
{
  mp_limb_t minv;
  int cnt;
  mp_bitcnt_t ebi;
  int windowsize, this_windowsize;
  mp_limb_t expbits;
  mp_ptr pp, this_pp;
  long i;
  int cnd;
  TMP_DECL;

  ASSERT (en > 1 || (en == 1 && ep[0] > 0));
  ASSERT (n >= 1 && ((mp[0] & 1) != 0));

  TMP_MARK;

  count_leading_zeros (cnt, ep[en - 1]);
  ebi = (mp_bitcnt_t) en * GMP_LIMB_BITS - cnt;

  windowsize = win_size (ebi);

  binvert_limb (minv, mp[0]);
  minv = -minv;

  pp = tp + 4 * n;

  this_pp = pp;
  this_pp[n] = 1;
  redcify (this_pp, this_pp + n, 1, mp, n, tp + 6 * n);
  this_pp += n;
  redcify (this_pp, bp, bn, mp, n, tp + 6 * n);

  /* Precompute powers of b and put them in the temporary area at pp.  */
  for (i = (1 << windowsize) - 2; i > 0; i--)
    {
      mpn_mul_basecase (tp, this_pp, n, pp + n, n);
      this_pp += n;
      MPN_REDC_1_SEC (this_pp, tp, mp, n, minv);
    }

  expbits = getbits (ep, ebi, windowsize);
  if (ebi < windowsize)
    ebi = 0;
  else
    ebi -= windowsize;

  MPN_COPY (rp, pp + n * expbits, n);

  while (ebi != 0)
    {
      expbits = getbits (ep, ebi, windowsize);
      this_windowsize = windowsize;
      if (ebi < windowsize)
	{
	  this_windowsize -= windowsize - ebi;
	  ebi = 0;
	}
      else
	ebi -= windowsize;

      do
	{
	  mpn_local_sqr (tp, rp, n, tp + 2 * n);
	  MPN_REDC_1_SEC (rp, tp, mp, n, minv);
	  this_windowsize--;
	}
      while (this_windowsize != 0);

#if WANT_CACHE_SECURITY
      mpn_tabselect (tp + 2*n, pp, n, 1 << windowsize, expbits);
      mpn_mul_basecase (tp, rp, n, tp + 2*n, n);
#else
      mpn_mul_basecase (tp, rp, n, pp + n * expbits, n);
#endif
      MPN_REDC_1_SEC (rp, tp, mp, n, minv);
    }

  MPN_COPY (tp, rp, n);
  MPN_ZERO (tp + n, n);
  MPN_REDC_1_SEC (rp, tp, mp, n, minv);
  cnd = mpn_sub_n (tp, rp, mp, n);	/* we need just retval */
  mpn_subcnd_n (rp, rp, mp, n, !cnd);
  TMP_FREE;
}

#if ! HAVE_NATIVE_mpn_tabselect
/* Select entry `which' from table `tab', which has nents entries, each `n'
   limbs.  Store the selected entry at rp.  Reads entire table to avoid
   side-channel information leaks.  O(n*nents).
   FIXME: Move to its own file.  */
void
mpn_tabselect (volatile mp_limb_t *rp, volatile mp_limb_t *tab, mp_size_t n,
	       mp_size_t nents, mp_size_t which)
{
  mp_size_t k, i;
  mp_limb_t mask;
  volatile mp_limb_t *tp;

  for (k = 0; k < nents; k++)
    {
      mask = -(mp_limb_t) (which == k);
      tp = tab + n * k;
      for (i = 0; i < n; i++)
	{
	  rp[i] = (rp[i] & ~mask) | (tp[i] & mask);
	}
    }
}
#endif

mp_size_t
mpn_powm_sec_itch (mp_size_t bn, mp_size_t en, mp_size_t n)
{
  int windowsize;
  mp_size_t redcify_itch, itch;

  windowsize = win_size (en * GMP_NUMB_BITS); /* slight over-estimate of exp */
  itch = 4 * n + (n << windowsize);
  redcify_itch = 2 * bn + n + 1;
  /* The 6n is due to the placement of reduce scratch 6n into the start of the
     scratch area.  */
  return MAX (itch, redcify_itch + 6 * n);
}