/**************** * RES = BASE ^ EXPO mod MOD */ void gcry_mpi_powm( gcry_mpi_t res, gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod) { mpi_ptr_t rp, ep, mp, bp; mpi_size_t esize, msize, bsize, rsize; int esign, msign, bsign, rsign; int esec, msec, bsec, rsec; mpi_size_t size; int mod_shift_cnt; int negative_result; mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL; mpi_ptr_t xp_marker=NULL; unsigned int mp_nlimbs = 0, bp_nlimbs = 0, ep_nlimbs = 0; unsigned int xp_nlimbs = 0; int assign_rp = 0; mpi_ptr_t tspace = NULL; mpi_size_t tsize=0; /* to avoid compiler warning */ /* fixme: we should check that the warning is void*/ esize = expo->nlimbs; msize = mod->nlimbs; size = 2 * msize; esign = expo->sign; msign = mod->sign; esec = mpi_is_secure(expo); msec = mpi_is_secure(mod); bsec = mpi_is_secure(base); rsec = mpi_is_secure(res); rp = res->d; ep = expo->d; if( !msize ) msize = 1 / msize; /* provoke a signal */ if( !esize ) { /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 * depending on if MOD equals 1. */ rp[0] = 1; res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 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; } if( res->alloced < size ) { /* We have to allocate more space for RES. If any of the input * parameters are identical to RES, defer deallocation of the old * space. */ if( rp == ep || rp == mp || rp == bp ) { rp = mpi_alloc_limb_space( size, rsec ); assign_rp = 1; } else { mpi_resize( res, size ); rp = res->d; } } else { /* Make BASE, EXPO and MOD not overlap with RES. */ if( rp == bp ) { /* RES and BASE are identical. Allocate temp. space for BASE. */ 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.*/ assert( !mp_marker ); mp_nlimbs = msec?msize:0; mp = mp_marker = mpi_alloc_limb_space( msize, msec ); MPN_COPY(mp, rp, msize); } } MPN_COPY( rp, bp, bsize ); rsize = bsize; rsign = bsign; { mpi_size_t i; mpi_ptr_t xp; int c; mpi_limb_t e; mpi_limb_t carry_limb; struct karatsuba_ctx karactx; 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) && base->sign; i = esize - 1; e = ep[i]; count_leading_zeros (c, e); e = (e << c) << 1; /* shift the expo bits to the left, lose msb */ c = BITS_PER_MPI_LIMB - 1 - c; /* 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. */ for(;;) { while( c ) { mpi_ptr_t tp; mpi_size_t xsize; /*mpih_mul_n(xp, rp, rp, rsize);*/ if( rsize < KARATSUBA_THRESHOLD ) _gcry_mpih_sqr_n_basecase( xp, rp, rsize ); else { if( !tspace ) { tsize = 2 * rsize; tspace = mpi_alloc_limb_space( tsize, 0 ); } else if( tsize < (2*rsize) ) { _gcry_mpi_free_limb_space (tspace, 0); tsize = 2 * rsize; tspace = mpi_alloc_limb_space( tsize, 0 ); } _gcry_mpih_sqr_n( xp, rp, rsize, tspace ); } xsize = 2 * rsize; if( xsize > msize ) { _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize); xsize = msize; } tp = rp; rp = xp; xp = tp; rsize = xsize; if( (mpi_limb_signed_t)e < 0 ) { /*mpih_mul( xp, rp, rsize, bp, bsize );*/ if( bsize < KARATSUBA_THRESHOLD ) { _gcry_mpih_mul( xp, rp, rsize, bp, bsize ); } else { _gcry_mpih_mul_karatsuba_case( xp, rp, rsize, bp, bsize, &karactx ); } xsize = rsize + bsize; if( xsize > msize ) { _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize); xsize = msize; } tp = rp; rp = xp; xp = tp; rsize = xsize; } e <<= 1; c--; } i--; if( i < 0 ) break; e = ep[i]; c = BITS_PER_MPI_LIMB; } /* 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 { 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 ); } 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); } res->nlimbs = rsize; res->sign = rsign; leave: if( assign_rp ) _gcry_mpi_assign_limb_space( res, rp, size ); 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 ); if( tspace ) _gcry_mpi_free_limb_space( tspace, 0 ); }
/**************** * RES = BASE ^ EXPO mod MOD */ 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 tspace = NULL; mpi_size_t tsize = 0; esize = expo->nlimbs; msize = mod->nlimbs; size = 2 * msize; msign = mod->sign; esec = mpi_is_secure(expo); msec = mpi_is_secure(mod); bsec = mpi_is_secure(base); rp = res->d; ep = expo->d; if (!msize) grub_fatal ("mpi division 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; } MPN_COPY ( rp, bp, bsize ); rsize = bsize; rsign = bsign; /* Main processing. */ { mpi_size_t i; mpi_ptr_t xp; int c; mpi_limb_t e; mpi_limb_t carry_limb; struct karatsuba_ctx karactx; 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) && base->sign; i = esize - 1; e = ep[i]; count_leading_zeros (c, e); e = (e << c) << 1; /* Shift the expo bits to the left, lose msb. */ c = BITS_PER_MPI_LIMB - 1 - c; /* 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. */ for (;;) { while (c) { mpi_ptr_t tp; mpi_size_t xsize; /*mpih_mul_n(xp, rp, rp, rsize);*/ if ( rsize < KARATSUBA_THRESHOLD ) _gcry_mpih_sqr_n_basecase( xp, rp, rsize ); else { if ( !tspace ) { tsize = 2 * rsize; tspace = mpi_alloc_limb_space( tsize, 0 ); } else if ( tsize < (2*rsize) ) { _gcry_mpi_free_limb_space (tspace, 0); tsize = 2 * rsize; tspace = mpi_alloc_limb_space (tsize, 0 ); } _gcry_mpih_sqr_n (xp, rp, rsize, tspace); } xsize = 2 * rsize; if ( xsize > msize ) { _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize); xsize = msize; } tp = rp; rp = xp; xp = tp; rsize = xsize; /* To mitigate the Yarom/Falkner flush+reload cache * side-channel attack on the RSA secret exponent, we do * the multiplication regardless of the value of the * high-bit of E. But to avoid this performance penalty * we do it only if the exponent has been stored in secure * memory and we can thus assume it is a secret exponent. */ if (esec || (mpi_limb_signed_t)e < 0) { /*mpih_mul( xp, rp, rsize, bp, bsize );*/ if( bsize < KARATSUBA_THRESHOLD ) _gcry_mpih_mul ( xp, rp, rsize, bp, bsize ); else _gcry_mpih_mul_karatsuba_case (xp, rp, rsize, bp, bsize, &karactx); xsize = rsize + bsize; if ( xsize > msize ) { _gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize); xsize = msize; } } if ( (mpi_limb_signed_t)e < 0 ) { tp = rp; rp = xp; xp = tp; rsize = xsize; } e <<= 1; c--; } i--; if ( i < 0 ) break; e = ep[i]; c = BITS_PER_MPI_LIMB; } /* 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 ); } /* 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 ); if (tspace) _gcry_mpi_free_limb_space( tspace, 0 ); }
void _gcry_mpi_tdiv_qr( gcry_mpi_t quot, gcry_mpi_t rem, gcry_mpi_t num, gcry_mpi_t den) { mpi_ptr_t np, dp; mpi_ptr_t qp, rp; mpi_size_t nsize = num->nlimbs; mpi_size_t dsize = den->nlimbs; mpi_size_t qsize, rsize; mpi_size_t sign_remainder = num->sign; mpi_size_t sign_quotient = num->sign ^ den->sign; unsigned normalization_steps; mpi_limb_t q_limb; mpi_ptr_t marker[5]; unsigned int marker_nlimbs[5]; int markidx=0; /* Ensure space is enough for quotient and remainder. * We need space for an extra limb in the remainder, because it's * up-shifted (normalized) below. */ rsize = nsize + 1; mpi_resize( rem, rsize); qsize = rsize - dsize; /* qsize cannot be bigger than this. */ if( qsize <= 0 ) { if( num != rem ) { rem->nlimbs = num->nlimbs; rem->sign = num->sign; MPN_COPY(rem->d, num->d, nsize); } if( quot ) { /* This needs to follow the assignment to rem, in case the * numerator and quotient are the same. */ quot->nlimbs = 0; quot->sign = 0; } return; } if( quot ) mpi_resize( quot, qsize); /* Read pointers here, when reallocation is finished. */ np = num->d; dp = den->d; rp = rem->d; /* Optimize division by a single-limb divisor. */ if( dsize == 1 ) { mpi_limb_t rlimb; if( quot ) { qp = quot->d; rlimb = _gcry_mpih_divmod_1( qp, np, nsize, dp[0] ); qsize -= qp[qsize - 1] == 0; quot->nlimbs = qsize; quot->sign = sign_quotient; } else rlimb = _gcry_mpih_mod_1( np, nsize, dp[0] ); rp[0] = rlimb; rsize = rlimb != 0?1:0; rem->nlimbs = rsize; rem->sign = sign_remainder; return; } if( quot ) { qp = quot->d; /* Make sure QP and NP point to different objects. Otherwise the * numerator would be gradually overwritten by the quotient limbs. */ if(qp == np) { /* Copy NP object to temporary space. */ marker_nlimbs[markidx] = nsize; np = marker[markidx++] = mpi_alloc_limb_space(nsize, mpi_is_secure(quot)); MPN_COPY(np, qp, nsize); } } else /* Put quotient at top of remainder. */ qp = rp + dsize; count_leading_zeros( normalization_steps, dp[dsize - 1] ); /* Normalize the denominator, i.e. make its most significant bit set by * shifting it NORMALIZATION_STEPS bits to the left. Also shift the * numerator the same number of steps (to keep the quotient the same!). */ if( normalization_steps ) { mpi_ptr_t tp; mpi_limb_t nlimb; /* Shift up the denominator setting the most significant bit of * the most significant word. Use temporary storage not to clobber * the original contents of the denominator. */ marker_nlimbs[markidx] = dsize; tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den)); _gcry_mpih_lshift( tp, dp, dsize, normalization_steps ); dp = tp; /* Shift up the numerator, possibly introducing a new most * significant word. Move the shifted numerator in the remainder * meanwhile. */ nlimb = _gcry_mpih_lshift(rp, np, nsize, normalization_steps); if( nlimb ) { rp[nsize] = nlimb; rsize = nsize + 1; } else rsize = nsize; } else { /* The denominator is already normalized, as required. Copy it to * temporary space if it overlaps with the quotient or remainder. */ if( dp == rp || (quot && (dp == qp))) { mpi_ptr_t tp; marker_nlimbs[markidx] = dsize; tp = marker[markidx++] = mpi_alloc_limb_space(dsize, mpi_is_secure(den)); MPN_COPY( tp, dp, dsize ); dp = tp; } /* Move the numerator to the remainder. */ if( rp != np ) MPN_COPY(rp, np, nsize); rsize = nsize; } q_limb = _gcry_mpih_divrem( qp, 0, rp, rsize, dp, dsize ); if( quot ) { qsize = rsize - dsize; if(q_limb) { qp[qsize] = q_limb; qsize += 1; } quot->nlimbs = qsize; quot->sign = sign_quotient; } rsize = dsize; MPN_NORMALIZE (rp, rsize); if( normalization_steps && rsize ) { _gcry_mpih_rshift(rp, rp, rsize, normalization_steps); rsize -= rp[rsize - 1] == 0?1:0; } rem->nlimbs = rsize; rem->sign = sign_remainder; while( markidx ) { markidx--; _gcry_mpi_free_limb_space (marker[markidx], marker_nlimbs[markidx]); } }