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173 lines
5.2 KiB
C
173 lines
5.2 KiB
C
/* mpn_sec_pi1_div_qr, mpn_sec_pi1_div_r -- Compute Q = floor(U / V), U = U
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mod V. Side-channel silent under the assumption that the used instructions
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are side-channel silent.
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Contributed to the GNU project by Torbjörn Granlund.
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2011-2013 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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#include "gmp-impl.h"
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#include "longlong.h"
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/* This side-channel silent division algorithm reduces the partial remainder by
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GMP_NUMB_BITS/2 bits at a time, compared to GMP_NUMB_BITS for the main
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division algorithm. We actually do not insist on reducing by exactly
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GMP_NUMB_BITS/2, but may leave a partial remainder that is D*B^i to 3D*B^i
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too large (B is the limb base, D is the divisor, and i is the induction
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variable); the subsequent step will handle the extra partial remainder bits.
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With that partial remainder reduction, each step generates a quotient "half
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limb". The outer loop generates two quotient half limbs, an upper (q1h) and
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a lower (q0h) which are stored sparsely in separate limb arrays. These
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arrays are added at the end; using separate arrays avoids data-dependent
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carry propagation which could else pose a side-channel leakage problem.
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The quotient half limbs may be between -3 to 0 from the accurate value
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("accurate" being the one which corresponds to a reduction to a principal
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partial remainder). Too small quotient half limbs correspond to too large
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remainders, which we reduce later, as described above.
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In order to keep quotients from getting too big, corresponding to a negative
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partial remainder, we use an inverse which is slightly smaller than usually.
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*/
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#if OPERATION_sec_pi1_div_qr
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/* Needs (dn + 1) + (nn - dn) + (nn - dn) = 2nn - dn + 1 limbs at tp. */
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#define FNAME mpn_sec_pi1_div_qr
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#define Q(q) q,
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#define RETTYPE mp_limb_t
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#endif
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#if OPERATION_sec_pi1_div_r
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/* Needs (dn + 1) limbs at tp. */
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#define FNAME mpn_sec_pi1_div_r
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#define Q(q)
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#define RETTYPE void
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#endif
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RETTYPE
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FNAME (Q(mp_ptr qp)
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mp_ptr np, mp_size_t nn,
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mp_srcptr dp, mp_size_t dn,
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mp_limb_t dinv,
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mp_ptr tp)
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{
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mp_limb_t nh, cy, q1h, q0h, dummy, cnd;
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mp_size_t i;
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mp_ptr hp;
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#if OPERATION_sec_pi1_div_qr
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mp_limb_t qh;
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mp_ptr qlp, qhp;
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#endif
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ASSERT (dn >= 1);
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ASSERT (nn >= dn);
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ASSERT ((dp[dn - 1] & GMP_NUMB_HIGHBIT) != 0);
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if (nn == dn)
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{
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cy = mpn_sub_n (np, np, dp, dn);
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mpn_cnd_add_n (cy, np, np, dp, dn);
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#if OPERATION_sec_pi1_div_qr
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return 1 - cy;
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#else
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return;
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#endif
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}
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/* Create a divisor copy shifted half a limb. */
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hp = tp; /* (dn + 1) limbs */
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hp[dn] = mpn_lshift (hp, dp, dn, GMP_NUMB_BITS / 2);
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#if OPERATION_sec_pi1_div_qr
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qlp = tp + (dn + 1); /* (nn - dn) limbs */
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qhp = tp + (nn + 1); /* (nn - dn) limbs */
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#endif
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np += nn - dn;
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nh = 0;
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for (i = nn - dn - 1; i >= 0; i--)
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{
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np--;
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nh = (nh << GMP_NUMB_BITS/2) + (np[dn] >> GMP_NUMB_BITS/2);
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umul_ppmm (q1h, dummy, nh, dinv);
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q1h += nh;
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#if OPERATION_sec_pi1_div_qr
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qhp[i] = q1h;
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#endif
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mpn_submul_1 (np, hp, dn + 1, q1h);
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nh = np[dn];
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umul_ppmm (q0h, dummy, nh, dinv);
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q0h += nh;
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#if OPERATION_sec_pi1_div_qr
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qlp[i] = q0h;
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#endif
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nh -= mpn_submul_1 (np, dp, dn, q0h);
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}
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/* 1st adjustment depends on extra high remainder limb. */
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cnd = nh != 0; /* FIXME: cmp-to-int */
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#if OPERATION_sec_pi1_div_qr
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qlp[0] += cnd;
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#endif
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nh -= mpn_cnd_sub_n (cnd, np, np, dp, dn);
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/* 2nd adjustment depends on remainder/divisor comparison as well as whether
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extra remainder limb was nullified by previous subtract. */
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cy = mpn_sub_n (np, np, dp, dn);
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cy = cy - nh;
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#if OPERATION_sec_pi1_div_qr
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qlp[0] += 1 - cy;
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#endif
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mpn_cnd_add_n (cy, np, np, dp, dn);
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/* 3rd adjustment depends on remainder/divisor comparison. */
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cy = mpn_sub_n (np, np, dp, dn);
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#if OPERATION_sec_pi1_div_qr
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qlp[0] += 1 - cy;
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#endif
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mpn_cnd_add_n (cy, np, np, dp, dn);
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#if OPERATION_sec_pi1_div_qr
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/* Combine quotient halves into final quotient. */
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qh = mpn_lshift (qhp, qhp, nn - dn, GMP_NUMB_BITS/2);
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qh += mpn_add_n (qp, qhp, qlp, nn - dn);
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return qh;
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#else
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return;
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#endif
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}
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