diff options
Diffstat (limited to 'mpi/mpi-pow.c')
| -rw-r--r-- | mpi/mpi-pow.c | 454 |
1 files changed, 454 insertions, 0 deletions
diff --git a/mpi/mpi-pow.c b/mpi/mpi-pow.c index 85d6fd8f..469c382a 100644 --- a/mpi/mpi-pow.c +++ b/mpi/mpi-pow.c @@ -34,6 +34,14 @@ #include "longlong.h" +/* + * When you need old implementation, please add compilation option + * -DUSE_ALGORITHM_SIMPLE_EXPONENTIATION + * or expose this line: +#define USE_ALGORITHM_SIMPLE_EXPONENTIATION 1 + */ + +#if defined(USE_ALGORITHM_SIMPLE_EXPONENTIATION) /**************** * RES = BASE ^ EXPO mod MOD */ @@ -336,3 +344,449 @@ gcry_mpi_powm (gcry_mpi_t res, if (tspace) _gcry_mpi_free_limb_space( tspace, 0 ); } +#else +/** + * Internal function to compute + * + * X = R * S mod M + * + * and set the size of X at the pointer XSIZE_P. + * Use karatsuba structure at KARACTX_P. + * + * Condition: + * RSIZE >= SSIZE + * Enough space for X is allocated beforehand. + * + * For generic cases, we can/should use gcry_mpi_mulm. + * This function is use for specific internal case. + */ +static void +mul_mod (mpi_ptr_t xp, mpi_size_t *xsize_p, + mpi_ptr_t rp, mpi_size_t rsize, + mpi_ptr_t sp, mpi_size_t ssize, + mpi_ptr_t mp, mpi_size_t msize, + struct karatsuba_ctx *karactx_p) +{ + if( ssize < KARATSUBA_THRESHOLD ) + _gcry_mpih_mul ( xp, rp, rsize, sp, ssize ); + else + _gcry_mpih_mul_karatsuba_case (xp, rp, rsize, sp, ssize, karactx_p); + + if (rsize + ssize > msize) + { + _gcry_mpih_divrem (xp + msize, 0, xp, rsize + ssize, mp, msize); + *xsize_p = msize; + } + else + *xsize_p = rsize + ssize; +} + +#define SIZE_B_2I3 ((1 << (5 - 1)) - 1) + +/**************** + * RES = BASE ^ EXPO mod MOD + * + * To mitigate the Yarom/Falkner flush+reload cache side-channel + * attack on the RSA secret exponent, we don't use the square + * routine but multiplication. + * + * Reference: + * Handbook of Applied Cryptography + * Algorithm 14.83: Modified left-to-right k-ary exponentiation + */ +void +gcry_mpi_powm (gcry_mpi_t res, + gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod) +{ + /* Pointer to the limbs of the arguments, their size and signs. */ + mpi_ptr_t rp, ep, mp, bp; + mpi_size_t esize, msize, bsize, rsize; + int msign, bsign, rsign; + /* Flags telling the secure allocation status of the arguments. */ + int esec, msec, bsec; + /* Size of the result including space for temporary values. */ + mpi_size_t size; + /* Helper. */ + int mod_shift_cnt; + int negative_result; + mpi_ptr_t mp_marker = NULL; + mpi_ptr_t bp_marker = NULL; + mpi_ptr_t ep_marker = NULL; + mpi_ptr_t xp_marker = NULL; + unsigned int mp_nlimbs = 0; + unsigned int bp_nlimbs = 0; + unsigned int ep_nlimbs = 0; + unsigned int xp_nlimbs = 0; + mpi_ptr_t b_2i3[SIZE_B_2I3]; /* Pre-computed array: BASE^3, ^5, ^7, ... */ + mpi_size_t b_2i3size[SIZE_B_2I3]; + mpi_size_t W; + mpi_ptr_t base_u; + mpi_size_t base_u_size; + + esize = expo->nlimbs; + msize = mod->nlimbs; + size = 2 * msize; + msign = mod->sign; + + if (esize * BITS_PER_MPI_LIMB > 512) + W = 5; + else if (esize * BITS_PER_MPI_LIMB > 256) + W = 4; + else if (esize * BITS_PER_MPI_LIMB > 128) + W = 3; + else if (esize * BITS_PER_MPI_LIMB > 64) + W = 2; + else + W = 1; + + esec = mpi_is_secure(expo); + msec = mpi_is_secure(mod); + bsec = mpi_is_secure(base); + + rp = res->d; + ep = expo->d; + + if (!msize) + _gcry_divide_by_zero(); + + if (!esize) + { + /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 depending + on if MOD equals 1. */ + res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1; + if (res->nlimbs) + { + RESIZE_IF_NEEDED (res, 1); + rp = res->d; + rp[0] = 1; + } + res->sign = 0; + goto leave; + } + + /* Normalize MOD (i.e. make its most significant bit set) as + required by mpn_divrem. This will make the intermediate values + in the calculation slightly larger, but the correct result is + obtained after a final reduction using the original MOD value. */ + mp_nlimbs = msec? msize:0; + mp = mp_marker = mpi_alloc_limb_space(msize, msec); + count_leading_zeros (mod_shift_cnt, mod->d[msize-1]); + if (mod_shift_cnt) + _gcry_mpih_lshift (mp, mod->d, msize, mod_shift_cnt); + else + MPN_COPY( mp, mod->d, msize ); + + bsize = base->nlimbs; + bsign = base->sign; + if (bsize > msize) + { + /* The base is larger than the module. Reduce it. + + Allocate (BSIZE + 1) with space for remainder and quotient. + (The quotient is (bsize - msize + 1) limbs.) */ + bp_nlimbs = bsec ? (bsize + 1):0; + bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec ); + MPN_COPY ( bp, base->d, bsize ); + /* We don't care about the quotient, store it above the + * remainder, at BP + MSIZE. */ + _gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize ); + bsize = msize; + /* Canonicalize the base, since we are going to multiply with it + quite a few times. */ + MPN_NORMALIZE( bp, bsize ); + } + else + bp = base->d; + + if (!bsize) + { + res->nlimbs = 0; + res->sign = 0; + goto leave; + } + + + /* Make BASE, EXPO and MOD not overlap with RES. */ + if ( rp == bp ) + { + /* RES and BASE are identical. Allocate temp. space for BASE. */ + gcry_assert (!bp_marker); + bp_nlimbs = bsec? bsize:0; + bp = bp_marker = mpi_alloc_limb_space( bsize, bsec ); + MPN_COPY(bp, rp, bsize); + } + if ( rp == ep ) + { + /* RES and EXPO are identical. Allocate temp. space for EXPO. */ + ep_nlimbs = esec? esize:0; + ep = ep_marker = mpi_alloc_limb_space( esize, esec ); + MPN_COPY(ep, rp, esize); + } + if ( rp == mp ) + { + /* RES and MOD are identical. Allocate temporary space for MOD.*/ + gcry_assert (!mp_marker); + mp_nlimbs = msec?msize:0; + mp = mp_marker = mpi_alloc_limb_space( msize, msec ); + MPN_COPY(mp, rp, msize); + } + + /* Copy base to the result. */ + if (res->alloced < size) + { + mpi_resize (res, size); + rp = res->d; + } + + /* Main processing. */ + { + mpi_size_t i, j; + mpi_ptr_t xp; + mpi_size_t xsize; + int c; + mpi_limb_t e; + mpi_limb_t carry_limb; + struct karatsuba_ctx karactx; + mpi_ptr_t tp; + + xp_nlimbs = msec? (2 * (msize + 1)):0; + xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec ); + + memset( &karactx, 0, sizeof karactx ); + negative_result = (ep[0] & 1) && bsign; + + /* Precompute B_2I3[], BASE^(2 * i + 3), BASE^3, ^5, ^7, ... */ + if (W > 1) /* X := BASE^2 */ + mul_mod (xp, &xsize, bp, bsize, bp, bsize, mp, msize, &karactx); + for (i = 0; i < (1 << (W - 1)) - 1; i++) + { /* B_2I3[i] = BASE^(2 * i + 3) */ + if (i == 0) + { + base_u = bp; + base_u_size = bsize; + } + else + { + base_u = b_2i3[i-1]; + base_u_size = b_2i3size[i-1]; + } + + if (xsize >= base_u_size) + mul_mod (rp, &rsize, xp, xsize, base_u, base_u_size, + mp, msize, &karactx); + else + mul_mod (rp, &rsize, base_u, base_u_size, xp, xsize, + mp, msize, &karactx); + b_2i3[i] = mpi_alloc_limb_space (rsize, esec); + b_2i3size[i] = rsize; + MPN_COPY (b_2i3[i], rp, rsize); + } + + i = esize - 1; + + /* Main loop. + + Make the result be pointed to alternately by XP and RP. This + helps us avoid block copying, which would otherwise be + necessary with the overlap restrictions of + _gcry_mpih_divmod. With 50% probability the result after this + loop will be in the area originally pointed by RP (==RES->d), + and with 50% probability in the area originally pointed to by XP. */ + rsign = 0; + if (W == 1) + { + rsize = bsize; + } + else + { + rsize = msize; + MPN_ZERO (rp, rsize); + } + MPN_COPY ( rp, bp, bsize ); + + e = ep[i]; + count_leading_zeros (c, e); + e = (e << c) << 1; + c = BITS_PER_MPI_LIMB - 1 - c; + + j = 0; + + for (;;) + if (e == 0) + { + j += c; + i--; + if ( i < 0 ) + { + c = 0; + break; + } + + e = ep[i]; + c = BITS_PER_MPI_LIMB; + } + else + { + int c0; + mpi_limb_t e0; + + count_leading_zeros (c0, e); + e = (e << c0); + c -= c0; + j += c0; + + if (c >= W) + { + e0 = (e >> (BITS_PER_MPI_LIMB - W)); + e = (e << W); + c -= W; + } + else + { + i--; + if ( i < 0 ) + { + e = (e >> (BITS_PER_MPI_LIMB - c)); + break; + } + + c0 = c; + e0 = (e >> (BITS_PER_MPI_LIMB - W)) + | (ep[i] >> (BITS_PER_MPI_LIMB - W + c0)); + e = (ep[i] << (W - c0)); + c = BITS_PER_MPI_LIMB - W + c0; + } + + count_trailing_zeros (c0, e0); + e0 = (e0 >> c0) >> 1; + + for (j += W - c0; j; j--) + { + mul_mod (xp, &xsize, rp, rsize, rp, rsize, mp, msize, &karactx); + tp = rp; rp = xp; xp = tp; + rsize = xsize; + } + + if (e0 == 0) + { + base_u = bp; + base_u_size = bsize; + } + else + { + base_u = b_2i3[e0 - 1]; + base_u_size = b_2i3size[e0 -1]; + } + + mul_mod (xp, &xsize, rp, rsize, base_u, base_u_size, + mp, msize, &karactx); + tp = rp; rp = xp; xp = tp; + rsize = xsize; + + j = c0; + } + + if (c != 0) + { + j += c; + count_trailing_zeros (c, e); + e = (e >> c); + j -= c; + } + + while (j--) + { + mul_mod (xp, &xsize, rp, rsize, rp, rsize, mp, msize, &karactx); + tp = rp; rp = xp; xp = tp; + rsize = xsize; + } + + if (e != 0) + { + if ((e>>1) == 0) + { + base_u = bp; + base_u_size = bsize; + } + else + { + base_u = b_2i3[(e>>1) - 1]; + base_u_size = b_2i3size[(e>>1) -1]; + } + + mul_mod (xp, &xsize, rp, rsize, base_u, base_u_size, + mp, msize, &karactx); + tp = rp; rp = xp; xp = tp; + rsize = xsize; + + for (; c; c--) + { + mul_mod (xp, &xsize, rp, rsize, rp, rsize, mp, msize, &karactx); + tp = rp; rp = xp; xp = tp; + rsize = xsize; + } + } + + /* We shifted MOD, the modulo reduction argument, left + MOD_SHIFT_CNT steps. Adjust the result by reducing it with the + original MOD. + + Also make sure the result is put in RES->d (where it already + might be, see above). */ + if ( mod_shift_cnt ) + { + carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt); + rp = res->d; + if ( carry_limb ) + { + rp[rsize] = carry_limb; + rsize++; + } + } + else if (res->d != rp) + { + MPN_COPY (res->d, rp, rsize); + rp = res->d; + } + + if ( rsize >= msize ) + { + _gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize); + rsize = msize; + } + + /* Remove any leading zero words from the result. */ + if ( mod_shift_cnt ) + _gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt); + MPN_NORMALIZE (rp, rsize); + + _gcry_mpih_release_karatsuba_ctx (&karactx ); + for (i = 0; i < (1 << (W - 1)) - 1; i++) + _gcry_mpi_free_limb_space( b_2i3[i], esec ? b_2i3size[i] : 0 ); + } + + /* Fixup for negative results. */ + if ( negative_result && rsize ) + { + if ( mod_shift_cnt ) + _gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt); + _gcry_mpih_sub( rp, mp, msize, rp, rsize); + rsize = msize; + rsign = msign; + MPN_NORMALIZE(rp, rsize); + } + gcry_assert (res->d == rp); + res->nlimbs = rsize; + res->sign = rsign; + + leave: + if (mp_marker) + _gcry_mpi_free_limb_space( mp_marker, mp_nlimbs ); + if (bp_marker) + _gcry_mpi_free_limb_space( bp_marker, bp_nlimbs ); + if (ep_marker) + _gcry_mpi_free_limb_space( ep_marker, ep_nlimbs ); + if (xp_marker) + _gcry_mpi_free_limb_space( xp_marker, xp_nlimbs ); +} +#endif |