/* 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, 2012 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 side-channel silent division function for converting to REDC residue.

   * REDC_1_TO_REDC_2_THRESHOLD might actually represent the cutoff between
     redc_1 and redc_n.  On such systems, we will switch to redc_2 causing
     slowdown.
*/

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

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

#undef MPN_REDC_2_SEC
#define MPN_REDC_2_SEC(rp, up, mp, n, mip)				\
  do {									\
    mp_limb_t cy;							\
    cy = mpn_redc_2 (rp, up, mp, n, mip);				\
    mpn_subcnd_n (rp, rp, mp, n, cy);					\
  } while (0)

#if HAVE_NATIVE_mpn_addmul_2 || HAVE_NATIVE_mpn_redc_2
#define WANT_REDC_2 1
#endif

/* 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_LIM  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_LIM  SQR_TOOM2_THRESHOLD
#endif
#endif

#ifdef WANT_FAT_BINARY
/* For fat builds, we use SQR_TOOM2_THRESHOLD which will expand to a read from
   __gmpn_cpuvec.  Perhaps any possible sqr_basecase.asm allow any size, and we
   limit the use unnecessarily.  We cannot tell, so play it safe.  FIXME.  */
#define SQR_BASECASE_LIM  SQR_TOOM2_THRESHOLD
#endif

#ifndef SQR_BASECASE_LIM
/* If SQR_BASECASE_LIM 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 (BELOW_THRESHOLD (n, SQR_BASECASE_LIM))
    {
      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;

      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;
      }
    }
}
#endif

#define getbit(p,bi) \
  ((p[(bi - 1) / GMP_NUMB_BITS] >> (bi - 1) % GMP_NUMB_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_NUMB_BITS;		/* word index of low bit to extract */
      bi %= GMP_NUMB_BITS;		/* bit index in low word */
      r = p[i] >> bi;			/* extract (low) bits */
      nbits_in_r = GMP_NUMB_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);
    }
}

#ifndef POWM_SEC_TABLE
#if GMP_NUMB_BITS < 50
#define POWM_SEC_TABLE  2,33,96,780,2741
#else
#define POWM_SEC_TABLE  2,130,524,2578
#endif
#endif

#if TUNE_PROGRAM_BUILD
extern int win_size (mp_bitcnt_t);
#else
static inline int
win_size (mp_bitcnt_t eb)
{
  int k;
  static mp_bitcnt_t x[] = {0,POWM_SEC_TABLE,~(mp_bitcnt_t)0};
  for (k = 1; eb > x[k]; k++)
    ;
  return k;
}
#endif

/* Convert U to REDC form, U_r = B^n * U mod M.
   Uses scratch space at tp of size 2un + n + 1.  */
static void
redcify (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr mp, mp_size_t n, mp_ptr tp)
{
#if 0
  mp_ptr qp;

  qp = tp + un + n;		/* un + n - n + 1 = un + 1 limbs */

  MPN_ZERO (tp, n);
  MPN_COPY (tp + n, up, un);

  mpn_tdiv_qr (qp, rp, 0L, tp, un + n, mp, n);
#else
  /* FIXME: Use passed scratch space instead of allocating our own!  */
  mp_ptr scratch;
  TMP_DECL;
  TMP_MARK;

  MPN_ZERO (tp, n);
  MPN_COPY (tp + n, up, un);

  scratch = TMP_ALLOC_LIMBS ((un + n) + 2 * n + 2);
  mpn_sb_div_r_sec (tp, un + n, mp, n, scratch);
  MPN_COPY (rp, tp, n);
  TMP_FREE;
#endif
}

/* 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.
   Requires that ep[en-1..0] > 1.
   Uses scratch space at tp as defined by mpn_powm_sec_itch.  */
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 ip[2], *mip;
  mp_bitcnt_t ebi;
  int windowsize, this_windowsize;
  mp_limb_t expbits;
  mp_ptr pp, this_pp;
  long i;
  int cnd;

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

  MPN_SIZEINBASE_2EXP(ebi, ep, en, 1);

  windowsize = win_size (ebi);

#if WANT_REDC_2
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
    {
      mip = ip;
      binvert_limb (mip[0], mp[0]);
      mip[0] = -mip[0];
    }
  else
    {
      mip = ip;
      mpn_binvert (mip, mp, 2, tp);
      mip[0] = -mip[0]; mip[1] = ~mip[1];
    }
#else
  mip = ip;
  binvert_limb (mip[0], mp[0]);
  mip[0] = -mip[0];
#endif


  pp = tp;
  tp += (n << windowsize);	/* put tp after power table */

  /* Compute pp[0] table entry */
  /* scratch: |   n   | 1 |   n+2    |  */
  /*          | pp[0] | 1 | redcify  |  */
  this_pp = pp;
  this_pp[n] = 1;
  redcify (this_pp, this_pp + n, 1, mp, n, this_pp + n + 1);
  this_pp += n;

  /* Compute pp[1] table entry.  To avoid excessive scratch usage in the
     degenerate situation where B >> M, we let redcify use scratch space which
     will later be used by the pp table (element 2 and up).  */
  /* scratch: |   n   |   n   |  bn + n + 1  |  */
  /*          | pp[0] | pp[1] |   redcify    |  */
  redcify (this_pp, bp, bn, mp, n, this_pp + n);

  /* Precompute powers of b and put them in the temporary area at pp.  */
  /* scratch: |   n   |   n   | ...  |                    |   2n      |  */
  /*          | pp[0] | pp[1] | ...  | pp[2^windowsize-1] |  product  |  */
  for (i = (1 << windowsize) - 2; i > 0; i--)
    {
      mpn_mul_basecase (tp, this_pp, n, pp + n, n);
      this_pp += n;
#if WANT_REDC_2
      if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
	MPN_REDC_1_SEC (this_pp, tp, mp, n, mip[0]);
      else
	MPN_REDC_2_SEC (this_pp, tp, mp, n, mip);
#else
      MPN_REDC_1_SEC (this_pp, tp, mp, n, mip[0]);
#endif
    }

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

  mpn_tabselect (rp, pp, n, 1 << windowsize, expbits);

  /* Main exponentiation loop.  */
  /* scratch: |   n   |   n   | ...  |                    |     3n-4n     |  */
  /*          | pp[0] | pp[1] | ...  | pp[2^windowsize-1] |  loop scratch |  */

#define INNERLOOP							\
  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_REDUCE (rp, tp, mp, n, mip);				\
	  this_windowsize--;						\
	}								\
      while (this_windowsize != 0);					\
									\
      mpn_tabselect (tp + 2*n, pp, n, 1 << windowsize, expbits);	\
      mpn_mul_basecase (tp, rp, n, tp + 2*n, n);			\
									\
      MPN_REDUCE (rp, tp, mp, n, mip);					\
    }

#if WANT_REDC_2
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
    {
#undef MPN_MUL_N
#undef MPN_SQR
#undef MPN_REDUCE
#define MPN_MUL_N(r,a,b,n)		mpn_mul_basecase (r,a,n,b,n)
#define MPN_SQR(r,a,n)			mpn_sqr_basecase (r,a,n)
#define MPN_REDUCE(rp,tp,mp,n,mip)	MPN_REDC_1_SEC (rp, tp, mp, n, mip[0])
      INNERLOOP;
    }
  else
    {
#undef MPN_MUL_N
#undef MPN_SQR
#undef MPN_REDUCE
#define MPN_MUL_N(r,a,b,n)		mpn_mul_basecase (r,a,n,b,n)
#define MPN_SQR(r,a,n)			mpn_sqr_basecase (r,a,n)
#define MPN_REDUCE(rp,tp,mp,n,mip)	MPN_REDC_2_SEC (rp, tp, mp, n, mip)
      INNERLOOP;
    }
#else
#undef MPN_MUL_N
#undef MPN_SQR
#undef MPN_REDUCE
#define MPN_MUL_N(r,a,b,n)		mpn_mul_basecase (r,a,n,b,n)
#define MPN_SQR(r,a,n)			mpn_sqr_basecase (r,a,n)
#define MPN_REDUCE(rp,tp,mp,n,mip)	MPN_REDC_1_SEC (rp, tp, mp, n, mip[0])
  INNERLOOP;
#endif

  MPN_COPY (tp, rp, n);
  MPN_ZERO (tp + n, n);

#if WANT_REDC_2
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
    MPN_REDC_1_SEC (rp, tp, mp, n, mip[0]);
  else
    MPN_REDC_2_SEC (rp, tp, mp, n, mip);
#else
  MPN_REDC_1_SEC (rp, tp, mp, n, mip[0]);
#endif
  cnd = mpn_sub_n (tp, rp, mp, n);	/* we need just retval */
  mpn_subcnd_n (rp, rp, mp, n, !cnd);
}

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;

  /* The top scratch usage will either be when reducing B in the 2nd redcify
     call, or more typically n*2^windowsize + 3n or 4n, in the main loop.  (It
     is 3n or 4n depending on if we use mpn_local_sqr or a native
     mpn_sqr_basecase.  We assume 4n always for now.) */

  windowsize = win_size (en * GMP_NUMB_BITS); /* slight over-estimate of exp */

  /* The 2n term is due to pp[0] and pp[1] at the time of the 2nd redcify call,
     the 2bn + n + 1 term is due to redcify's own usage.  */
  redcify_itch = (2 * n) + (2 * bn + n + 1);

  /* The n * 2^windowsize term is due to the power table, the 4n term is due to
     scratch needs of squaring/multiplication in the exponentiation loop.  */
  itch = (n << windowsize) + (4 * n);

  return MAX (itch, redcify_itch);
}