Coverage Report

Created: 2025-03-06 06:58

/src/gmp/mpn/sec_powm.c
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/* mpn_sec_powm -- Compute R = U^E mod M.  Secure variant, side-channel silent
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   under the assumption that the multiply instruction is side channel silent.
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   Contributed to the GNU project by Torbjörn Granlund.
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Copyright 2007-2009, 2011-2014, 2018-2019, 2021 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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  * the GNU Lesser General Public License as published by the Free
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    Software Foundation; either version 3 of the License, or (at your
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    option) any later version.
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or
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  * the GNU General Public License as published by the Free Software
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    Foundation; either version 2 of the License, or (at your option) any
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    later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library.  If not,
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see https://www.gnu.org/licenses/.  */
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/*
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  BASIC ALGORITHM, Compute U^E mod M, where M < B^n is odd.
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  1. T <- (B^n * U) mod M; convert to REDC form
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  2. Compute table U^0, U^1, U^2... of floor(log(E))-dependent size
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  3. While there are more bits in E
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       W <- power left-to-right base-k
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  The article "Defeating modexp side-channel attacks with data-independent
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  execution traces", https://gmplib.org/~tege/modexp-silent.pdf, has details.
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  TODO:
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   * Make getbits a macro, thereby allowing it to update the index operand.
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     That will simplify the code using getbits.  (Perhaps make getbits' sibling
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     getbit then have similar form, for symmetry.)
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   * Choose window size without looping.  (Superoptimize or think(tm).)
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   * REDC_1_TO_REDC_2_THRESHOLD might actually represent the cutoff between
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     redc_1 and redc_n.  On such systems, we will switch to redc_2 causing
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     slowdown.
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*/
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#include "gmp-impl.h"
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#include "longlong.h"
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#undef MPN_REDC_1_SEC
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#if HAVE_NATIVE_mpn_sbpi1_bdiv_r
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#define MPN_REDC_1_SEC(rp, up, mp, n, invm)       \
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0
  do {                 \
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0
    mp_limb_t cy;             \
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0
    cy = mpn_sbpi1_bdiv_r (up, 2 * n, mp, n, invm);      \
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0
    mpn_cnd_sub_n (cy, rp, up + n, mp, n);       \
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0
  } while (0)
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#else
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#define MPN_REDC_1_SEC(rp, up, mp, n, invm)       \
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  do {                  \
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    mp_limb_t cy;             \
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    cy = mpn_redc_1 (rp, up, mp, n, invm);        \
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    mpn_cnd_sub_n (cy, rp, rp, mp, n);          \
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  } while (0)
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#endif
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#if HAVE_NATIVE_mpn_addmul_2 || HAVE_NATIVE_mpn_redc_2
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#undef MPN_REDC_2_SEC
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#define MPN_REDC_2_SEC(rp, up, mp, n, mip)        \
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  do {                  \
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    mp_limb_t cy;             \
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    cy = mpn_redc_2 (rp, up, mp, n, mip);       \
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    mpn_cnd_sub_n (cy, rp, rp, mp, n);          \
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  } while (0)
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#else
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#define MPN_REDC_2_SEC(rp, up, mp, n, mip) /* empty */
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#undef REDC_1_TO_REDC_2_THRESHOLD
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#define REDC_1_TO_REDC_2_THRESHOLD MP_SIZE_T_MAX
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#endif
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/* Define our own mpn squaring function.  We do this since we cannot use a
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   native mpn_sqr_basecase over TUNE_SQR_TOOM2_MAX, or a non-native one over
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   SQR_TOOM2_THRESHOLD.  This is so because of fixed size stack allocations
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   made inside mpn_sqr_basecase.  */
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#if ! HAVE_NATIVE_mpn_sqr_basecase
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/* The limit of the generic code is SQR_TOOM2_THRESHOLD.  */
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#define SQR_BASECASE_LIM  SQR_TOOM2_THRESHOLD
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#endif
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#if HAVE_NATIVE_mpn_sqr_basecase
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#ifdef TUNE_SQR_TOOM2_MAX
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/* We slightly abuse TUNE_SQR_TOOM2_MAX here.  If it is set for an assembly
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   mpn_sqr_basecase, it comes from SQR_TOOM2_THRESHOLD_MAX in the assembly
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   file.  An assembly mpn_sqr_basecase that does not define it should allow
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   any size.  */
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#define SQR_BASECASE_LIM  SQR_TOOM2_THRESHOLD
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#endif
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#endif
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#ifdef WANT_FAT_BINARY
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/* For fat builds, we use SQR_TOOM2_THRESHOLD which will expand to a read from
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   __gmpn_cpuvec.  Perhaps any possible sqr_basecase.asm allow any size, and we
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   limit the use unnecessarily.  We cannot tell, so play it safe.  FIXME.  */
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#define SQR_BASECASE_LIM  SQR_TOOM2_THRESHOLD
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#endif
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#ifndef SQR_BASECASE_LIM
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/* If SQR_BASECASE_LIM is now not defined, use mpn_sqr_basecase for any operand
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   size.  */
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#define SQR_BASECASE_LIM  MP_SIZE_T_MAX
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#endif
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#define mpn_local_sqr(rp,up,n)            \
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0
  do {                 \
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0
    if (ABOVE_THRESHOLD (n, SQR_BASECASE_THRESHOLD)      \
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0
  && BELOW_THRESHOLD (n, SQR_BASECASE_LIM))     \
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0
      mpn_sqr_basecase (rp, up, n);         \
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0
    else                \
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0
      mpn_mul_basecase(rp, up, n, up, n);       \
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0
  } while (0)
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#define getbit(p,bi) \
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  ((p[(bi - 1) / GMP_NUMB_BITS] >> (bi - 1) % GMP_NUMB_BITS) & 1)
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/* FIXME: Maybe some things would get simpler if all callers ensure
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   that bi >= nbits. As far as I understand, with the current code bi
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   < nbits can happen only for the final iteration. */
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static inline mp_limb_t
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getbits (const mp_limb_t *p, mp_bitcnt_t bi, int nbits)
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0
{
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0
  int nbits_in_r;
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0
  mp_limb_t r;
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0
  mp_size_t i;
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151
0
  if (bi < nbits)
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0
    {
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0
      return p[0] & (((mp_limb_t) 1 << bi) - 1);
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0
    }
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0
  else
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0
    {
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0
      bi -= nbits;      /* bit index of low bit to extract */
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0
      i = bi / GMP_NUMB_BITS;   /* word index of low bit to extract */
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0
      bi %= GMP_NUMB_BITS;   /* bit index in low word */
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0
      r = p[i] >> bi;     /* extract (low) bits */
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0
      nbits_in_r = GMP_NUMB_BITS - bi;  /* number of bits now in r */
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0
      if (nbits_in_r < nbits)   /* did we get enough bits? */
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0
  r += p[i + 1] << nbits_in_r; /* prepend bits from higher word */
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0
      return r & (((mp_limb_t ) 1 << nbits) - 1);
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0
    }
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0
}
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#ifndef POWM_SEC_TABLE
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#if GMP_NUMB_BITS < 50
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#define POWM_SEC_TABLE  2,33,96,780,2741
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#else
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#define POWM_SEC_TABLE  2,130,524,2578
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#endif
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#endif
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#if TUNE_PROGRAM_BUILD
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extern int win_size (mp_bitcnt_t);
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#else
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static inline int
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win_size (mp_bitcnt_t enb)
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0
{
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0
  int k;
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  /* Find k, such that x[k-1] < enb <= x[k].
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     We require that x[k] >= k, then it follows that enb > x[k-1] >=
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     k-1, which implies k <= enb.
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  */
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0
  static const mp_bitcnt_t x[] = {POWM_SEC_TABLE,~(mp_bitcnt_t)0};
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0
  for (k = 0; enb > x[k++]; )
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0
    ;
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0
  ASSERT (k <= enb);
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0
  return k;
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0
}
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#endif
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/* Convert U to REDC form, U_r = B^n * U mod M.
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   Uses scratch space at tp of size 2un + n + 1.  */
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static void
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redcify (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr mp, mp_size_t n, mp_ptr tp)
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0
{
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0
  MPN_ZERO (tp, n);
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0
  MPN_COPY (tp + n, up, un);
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0
  mpn_sec_div_r (tp, un + n, mp, n, tp + un + n);
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  MPN_COPY (rp, tp, n);
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0
}
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static mp_limb_t
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sec_binvert_limb (mp_limb_t n)
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0
{
211
0
  mp_limb_t inv, t;
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0
  ASSERT ((n & 1) == 1);
213
  /* 3 + 2 -> 5 */
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0
  inv = n + (((n + 1) << 1) & 0x18);
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0
  t = n * inv;
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#if GMP_NUMB_BITS <= 10
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  /* 5 x 2 -> 10 */
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  inv = 2 * inv - inv * t;
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#else /* GMP_NUMB_BITS > 10 */
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  /* 5 x 2 + 2 -> 12 */
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0
  inv = 2 * inv - inv * t + ((inv<<10)&-(t&(1<<5)));
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0
#endif /* GMP_NUMB_BITS <= 10 */
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225
0
  if (GMP_NUMB_BITS > 12)
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0
    {
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0
      t = n * inv - 1;
228
0
      if (GMP_NUMB_BITS <= 36)
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0
  {
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    /* 12 x 3 -> 36 */
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0
    inv += inv * t * (t - 1);
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0
  }
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0
      else /* GMP_NUMB_BITS > 36 */
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  {
235
0
    mp_limb_t t2 = t * t;
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#if GMP_NUMB_BITS <= 60
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    /* 12 x 5 -> 60 */
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    inv += inv * (t2 + 1) * (t2 - t);
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#else /* GMP_NUMB_BITS > 60 */
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    /* 12 x 5 + 4 -> 64 */
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0
    inv *= (t2 + 1) * (t2 - t) + 1 - ((t<<48)&-(t&(1<<12)));
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    /* 64 -> 128 -> 256 -> ... */
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0
    for (int todo = (GMP_NUMB_BITS - 1) >> 6; todo != 0; todo >>= 1)
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0
      inv = 2 * inv - inv * inv * n;
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0
#endif /* GMP_NUMB_BITS <= 60 */
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0
  }
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0
    }
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0
  ASSERT ((inv * n & GMP_NUMB_MASK) == 1);
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0
  return inv & GMP_NUMB_MASK;
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0
}
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/* {rp, n} <-- {bp, bn} ^ {ep, en} mod {mp, n},
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   where en = ceil (enb / GMP_NUMB_BITS)
256
   Requires that {mp, n} is odd (and hence also mp[0] odd).
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   Uses scratch space at tp as defined by mpn_sec_powm_itch.  */
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void
259
mpn_sec_powm (mp_ptr rp, mp_srcptr bp, mp_size_t bn,
260
        mp_srcptr ep, mp_bitcnt_t enb,
261
        mp_srcptr mp, mp_size_t n, mp_ptr tp)
262
0
{
263
0
  mp_limb_t ip[2], *mip;
264
0
  int windowsize, this_windowsize;
265
0
  mp_limb_t expbits;
266
0
  mp_ptr pp, this_pp, ps;
267
0
  long i;
268
0
  int cnd;
269
270
0
  ASSERT (enb > 0);
271
0
  ASSERT (n > 0);
272
  /* The code works for bn = 0, but the defined scratch space is 2 limbs
273
     greater than we supply, when converting 1 to redc form .  */
274
0
  ASSERT (bn > 0);
275
0
  ASSERT ((mp[0] & 1) != 0);
276
277
0
  windowsize = win_size (enb);
278
279
0
  mip = ip;
280
0
  mip[0] = sec_binvert_limb (mp[0]);
281
0
  if (ABOVE_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
282
0
    {
283
0
      mp_limb_t t, dummy, mip0 = mip[0];
284
285
0
      umul_ppmm (t, dummy, mip0, mp[0]);
286
0
      ASSERT (dummy == 1);
287
0
      t += mip0 * mp[1]; /* t = (mp * mip0)[1] */
288
289
0
      mip[1] = t * mip0 - 1; /* ~( - t * mip0) */
290
0
    }
291
0
  mip[0] = -mip[0];
292
293
0
  pp = tp;
294
0
  tp += (n << windowsize);  /* put tp after power table */
295
296
  /* Compute pp[0] table entry */
297
  /* scratch: |   n   | 1 |   n+2    |  */
298
  /*          | pp[0] | 1 | redcify  |  */
299
0
  this_pp = pp;
300
0
  this_pp[n] = 1;
301
0
  redcify (this_pp, this_pp + n, 1, mp, n, this_pp + n + 1);
302
0
  this_pp += n;
303
304
  /* Compute pp[1] table entry.  To avoid excessive scratch usage in the
305
     degenerate situation where B >> M, we let redcify use scratch space which
306
     will later be used by the pp table (element 2 and up).  */
307
  /* scratch: |   n   |   n   |  bn + n + 1  |  */
308
  /*          | pp[0] | pp[1] |   redcify    |  */
309
0
  redcify (this_pp, bp, bn, mp, n, this_pp + n);
310
311
  /* Precompute powers of b and put them in the temporary area at pp.  */
312
  /* scratch: |   n   |   n   | ...  |                    |   2n      |  */
313
  /*          | pp[0] | pp[1] | ...  | pp[2^windowsize-1] |  product  |  */
314
0
  ps = pp + n;    /* initially B^1 */
315
0
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
316
0
    {
317
0
      for (i = (1 << windowsize) - 2; i > 0; i -= 2)
318
0
  {
319
0
    mpn_local_sqr (tp, ps, n);
320
0
    ps += n;
321
0
    this_pp += n;
322
0
    MPN_REDC_1_SEC (this_pp, tp, mp, n, mip[0]);
323
324
0
    mpn_mul_basecase (tp, this_pp, n, pp + n, n);
325
0
    this_pp += n;
326
0
    MPN_REDC_1_SEC (this_pp, tp, mp, n, mip[0]);
327
0
  }
328
0
    }
329
0
  else
330
0
    {
331
0
      for (i = (1 << windowsize) - 2; i > 0; i -= 2)
332
0
  {
333
0
    mpn_local_sqr (tp, ps, n);
334
0
    ps += n;
335
0
    this_pp += n;
336
0
    MPN_REDC_2_SEC (this_pp, tp, mp, n, mip);
337
338
0
    mpn_mul_basecase (tp, this_pp, n, pp + n, n);
339
0
    this_pp += n;
340
0
    MPN_REDC_2_SEC (this_pp, tp, mp, n, mip);
341
0
  }
342
0
    }
343
344
0
  expbits = getbits (ep, enb, windowsize);
345
0
  ASSERT_ALWAYS (enb >= windowsize);
346
0
  enb -= windowsize;
347
348
0
  mpn_sec_tabselect (rp, pp, n, 1 << windowsize, expbits);
349
350
  /* Main exponentiation loop.  */
351
  /* scratch: |   n   |   n   | ...  |                    |     3n-4n     |  */
352
  /*          | pp[0] | pp[1] | ...  | pp[2^windowsize-1] |  loop scratch |  */
353
354
0
#define INNERLOOP             \
355
0
  while (enb != 0)             \
356
0
    {                 \
357
0
      expbits = getbits (ep, enb, windowsize);        \
358
0
      this_windowsize = windowsize;         \
359
0
      if (enb < windowsize)           \
360
0
  {               \
361
0
    this_windowsize -= windowsize - enb;        \
362
0
    enb = 0;              \
363
0
  }                \
364
0
      else                \
365
0
  enb -= windowsize;           \
366
0
                  \
367
0
      do                \
368
0
  {               \
369
0
    mpn_local_sqr (tp, rp, n);         \
370
0
    MPN_REDUCE (rp, tp, mp, n, mip);        \
371
0
    this_windowsize--;            \
372
0
  }               \
373
0
      while (this_windowsize != 0);          \
374
0
                  \
375
0
      mpn_sec_tabselect (tp + 2*n, pp, n, 1 << windowsize, expbits); \
376
0
      mpn_mul_basecase (tp, rp, n, tp + 2*n, n);      \
377
0
                  \
378
0
      MPN_REDUCE (rp, tp, mp, n, mip);          \
379
0
    }
380
381
0
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
382
0
    {
383
0
#undef MPN_REDUCE
384
0
#define MPN_REDUCE(rp,tp,mp,n,mip)  MPN_REDC_1_SEC (rp, tp, mp, n, mip[0])
385
0
      INNERLOOP;
386
0
    }
387
0
  else
388
0
    {
389
0
#undef MPN_REDUCE
390
0
#define MPN_REDUCE(rp,tp,mp,n,mip)  MPN_REDC_2_SEC (rp, tp, mp, n, mip)
391
0
      INNERLOOP;
392
0
    }
393
394
0
  MPN_COPY (tp, rp, n);
395
0
  MPN_ZERO (tp + n, n);
396
397
0
  if (BELOW_THRESHOLD (n, REDC_1_TO_REDC_2_THRESHOLD))
398
0
    MPN_REDC_1_SEC (rp, tp, mp, n, mip[0]);
399
0
  else
400
0
    MPN_REDC_2_SEC (rp, tp, mp, n, mip);
401
402
0
  cnd = mpn_sub_n (tp, rp, mp, n); /* we need just retval */
403
0
  mpn_cnd_sub_n (!cnd, rp, rp, mp, n);
404
0
}
405
406
mp_size_t
407
mpn_sec_powm_itch (mp_size_t bn, mp_bitcnt_t enb, mp_size_t n)
408
0
{
409
0
  int windowsize;
410
0
  mp_size_t redcify_itch, itch;
411
412
  /* FIXME: no more _local/_basecase difference. */
413
  /* The top scratch usage will either be when reducing B in the 2nd redcify
414
     call, or more typically n*2^windowsize + 3n or 4n, in the main loop.  (It
415
     is 3n or 4n depending on if we use mpn_local_sqr or a native
416
     mpn_sqr_basecase.  We assume 4n always for now.) */
417
418
0
  windowsize = win_size (enb);
419
420
  /* The 2n term is due to pp[0] and pp[1] at the time of the 2nd redcify call,
421
     the (bn + n) term is due to redcify's own usage, and the rest is due to
422
     mpn_sec_div_r's usage when called from redcify.  */
423
0
  redcify_itch = (2 * n) + (bn + n) + ((bn + n) + 2 * n + 2);
424
425
  /* The n * 2^windowsize term is due to the power table, the 4n term is due to
426
     scratch needs of squaring/multiplication in the exponentiation loop.  */
427
0
  itch = (n << windowsize) + (4 * n);
428
429
0
  return MAX (itch, redcify_itch);
430
0
}