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MastersThesis/PQ_TIIGER_TLS/sal/miracl-ubuntu22-11-04-24/includes/fp12.cpp
josi 2fb6f67e15 finale structure update
2024-04-19 14:16:07 +02:00

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/*
* Copyright (c) 2012-2020 MIRACL UK Ltd.
*
* This file is part of MIRACL Core
* (see https://github.com/miracl/core).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* CORE Fp^12 functions */
/* SU=m, m is Stack Usage (no lazy )*/
/* FP12 elements are of the form a+i.b+i^2.c */
#include "fp12_YYY.h"
#include "config_curve_ZZZ.h"
using namespace XXX;
/* return 1 if b==c, no branching */
static int teq(sign32 b, sign32 c)
{
sign32 x = b ^ c;
x -= 1; // if x=0, x now -1
return (int)((x >> 31) & 1);
}
/* Constant time select from pre-computed table */
static void FP12_select(YYY::FP12 *f, YYY::FP12 g[], sign32 b)
{
YYY::FP12 invf;
sign32 m = b >> 31;
sign32 babs = (b ^ m) - m;
babs = (babs - 1) / 2;
FP12_cmove(f, &g[0], teq(babs, 0)); // conditional move
FP12_cmove(f, &g[1], teq(babs, 1));
FP12_cmove(f, &g[2], teq(babs, 2));
FP12_cmove(f, &g[3], teq(babs, 3));
FP12_cmove(f, &g[4], teq(babs, 4));
FP12_cmove(f, &g[5], teq(babs, 5));
FP12_cmove(f, &g[6], teq(babs, 6));
FP12_cmove(f, &g[7], teq(babs, 7));
FP12_copy(&invf, f);
FP12_conj(&invf, &invf); // 1/f
FP12_cmove(f, &invf, (int)(m & 1));
}
/* test x==0 ? */
/* SU= 8 */
int YYY::FP12_iszilch(FP12 *x)
{
if (FP4_iszilch(&(x->a)) && FP4_iszilch(&(x->b)) && FP4_iszilch(&(x->c))) return 1;
return 0;
}
/* test x==1 ? */
/* SU= 8 */
int YYY::FP12_isunity(FP12 *x)
{
if (FP4_isunity(&(x->a)) && FP4_iszilch(&(x->b)) && FP4_iszilch(&(x->c))) return 1;
return 0;
}
/* FP12 copy w=x */
/* SU= 16 */
void YYY::FP12_copy(FP12 *w, FP12 *x)
{
if (x == w) return;
FP4_copy(&(w->a), &(x->a));
FP4_copy(&(w->b), &(x->b));
FP4_copy(&(w->c), &(x->c));
w->type = x->type;
}
/* FP12 w=1 */
/* SU= 8 */
void YYY::FP12_one(FP12 *w)
{
FP4_one(&(w->a));
FP4_zero(&(w->b));
FP4_zero(&(w->c));
w->type = FP_UNITY;
}
void YYY::FP12_zero(FP12 *w)
{
FP4_zero(&(w->a));
FP4_zero(&(w->b));
FP4_zero(&(w->c));
w->type = FP_ZILCH;
}
/* return 1 if x==y, else 0 */
/* SU= 16 */
int YYY::FP12_equals(FP12 *x, FP12 *y)
{
if (FP4_equals(&(x->a), &(y->a)) && FP4_equals(&(x->b), &(y->b)) && FP4_equals(&(x->c), &(y->c)))
return 1;
return 0;
}
/* Set w=conj(x) */
/* SU= 8 */
void YYY::FP12_conj(FP12 *w, FP12 *x)
{
FP12_copy(w, x);
FP4_conj(&(w->a), &(w->a));
FP4_nconj(&(w->b), &(w->b));
FP4_conj(&(w->c), &(w->c));
}
/* Create FP12 from FP4 */
/* SU= 8 */
void YYY::FP12_from_FP4(FP12 *w, FP4 *a)
{
FP4_copy(&(w->a), a);
FP4_zero(&(w->b));
FP4_zero(&(w->c));
w->type = FP_SPARSEST;
}
/* Create FP12 from 3 FP4's */
/* SU= 16 */
void YYY::FP12_from_FP4s(FP12 *w, FP4 *a, FP4 *b, FP4 *c)
{
FP4_copy(&(w->a), a);
FP4_copy(&(w->b), b);
FP4_copy(&(w->c), c);
w->type = FP_DENSE;
}
/* Granger-Scott Unitary Squaring. This does not benefit from lazy reduction */
/* SU= 600 */
void YYY::FP12_usqr(FP12 *w, FP12 *x)
{
FP4 A, B, C, D;
FP4_copy(&A, &(x->a));
FP4_sqr(&(w->a), &(x->a)); // Wa XES=2
FP4_add(&D, &(w->a), &(w->a)); // Wa XES=4
FP4_add(&(w->a), &D, &(w->a)); // Wa XES=6
FP4_norm(&(w->a));
FP4_nconj(&A, &A);
FP4_add(&A, &A, &A);
FP4_add(&(w->a), &(w->a), &A); // Wa XES=8
FP4_sqr(&B, &(x->c));
FP4_times_i(&B);
FP4_add(&D, &B, &B);
FP4_add(&B, &B, &D);
FP4_norm(&B);
FP4_sqr(&C, &(x->b));
FP4_add(&D, &C, &C);
FP4_add(&C, &C, &D);
FP4_norm(&C);
FP4_conj(&(w->b), &(x->b));
FP4_add(&(w->b), &(w->b), &(w->b));
FP4_nconj(&(w->c), &(x->c));
FP4_add(&(w->c), &(w->c), &(w->c));
FP4_add(&(w->b), &B, &(w->b));
FP4_add(&(w->c), &C, &(w->c));
w->type = FP_DENSE;
//FP12_norm(w);
FP12_reduce(w); /* reduce here as in pow function repeated squarings would trigger multiple reductions */
}
/* FP12 squaring w=x^2 */
/* SU= 600 */
void YYY::FP12_sqr(FP12 *w, FP12 *x)
{
/* Use Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */
FP4 A, B, C, D;
if (x->type <= FP_UNITY)
{
FP12_copy(w, x);
return;
}
FP4_sqr(&A, &(x->a));
FP4_mul(&B, &(x->b), &(x->c));
FP4_add(&B, &B, &B);
FP4_norm(&B);
FP4_sqr(&C, &(x->c));
FP4_mul(&D, &(x->a), &(x->b));
FP4_add(&D, &D, &D);
FP4_add(&(w->c), &(x->a), &(x->c));
FP4_add(&(w->c), &(x->b), &(w->c));
FP4_norm(&(w->c));
FP4_sqr(&(w->c), &(w->c));
FP4_copy(&(w->a), &A);
FP4_add(&A, &A, &B);
FP4_norm(&A);
FP4_add(&A, &A, &C);
FP4_add(&A, &A, &D);
FP4_norm(&A);
FP4_neg(&A, &A);
FP4_times_i(&B);
FP4_times_i(&C);
FP4_add(&(w->a), &(w->a), &B);
FP4_add(&(w->b), &C, &D);
FP4_add(&(w->c), &(w->c), &A);
if (x->type == FP_SPARSER || x->type == FP_SPARSEST)
w->type = FP_SPARSE;
else
w->type = FP_DENSE;
FP12_norm(w);
}
// Use FP12_mul when both multiplicands are dense
// Use FP12smul when it is known that both multiplicands are line functions
// Use FP12ssmul when it is suspected that one or both multiplicands could have some sparsity
/* FP12 full multiplication w=w*y */
void YYY::FP12_mul(FP12 *w, FP12 *y)
{
FP4 z0, z1, z2, z3, t0, t1;
FP4_mul(&z0, &(w->a), &(y->a)); // xa.ya always 11x11
FP4_mul(&z2, &(w->b), &(y->b)); // xb.yb could be 00x00 or 01x01 or or 10x10 or 11x00 or 11x10 or 11x01 or 11x11
FP4_add(&t0, &(w->a), &(w->b)); // (xa+xb)
FP4_add(&t1, &(y->a), &(y->b)); // (ya+yb)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&z1, &t0, &t1); // (xa+xb)(ya+yb) always 11x11
FP4_add(&t0, &(w->b), &(w->c)); // (xb+xc)
FP4_add(&t1, &(y->b), &(y->c)); // (yb+yc)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&z3, &t0, &t1); // (xb+xc)(yb+yc) could be anything...
FP4_neg(&t0, &z0); // -(xa.ya)
FP4_neg(&t1, &z2); // -(xb.yb)
FP4_add(&z1, &z1, &t0);
FP4_add(&(w->b), &z1, &t1); // /wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) = xa.yb + xb.ya
FP4_add(&z3, &z3, &t1); // (xb+xc)(yb+yc) -(xb.yb)
FP4_add(&z2, &z2, &t0); // (xb.yb) - (xa.ya)
FP4_add(&t0, &(w->a), &(w->c)); // (xa+xc)
FP4_add(&t1, &(y->a), &(y->c)); // (ya+yc)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&t0, &t1, &t0); // (xa+xc)(ya+yc) always 11x11
FP4_add(&z2, &z2, &t0); // (xb.yb) - (xa.ya) + (xa+xc)(ya+yc)
FP4_mul(&t0, &(w->c), &(y->c)); // (xc.yc) could be anything
FP4_neg(&t1, &t0); // -(xc.yc)
FP4_add(&(w->c), &z2, &t1); // wc = (xb.yb) - (xa.ya) + (xa+xc)(ya+yc) - (xc.yc) = xb.yb + xc.ya + xa.yc
FP4_add(&z3, &z3, &t1); // (xb+xc)(yb+yc) -(xb.yb) - (xc.yc) = xb.yc + xc.yb
FP4_times_i(&t0); // i.(xc.yc)
FP4_add(&(w->b), &(w->b), &t0); // wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) +i(xc.yc)
FP4_norm(&z3);
FP4_times_i(&z3); // i[(xb+xc)(yb+yc) -(xb.yb) - (xc.yc)] = i(xb.yc + xc.yb)
FP4_add(&(w->a), &z0, &z3); // wa = xa.ya + i(xb.yc + xc.yb)
FP12_norm(w);
w->type = FP_DENSE;
}
/* FP12 full multiplication w=w*y */
/* Supports sparse multiplicands */
/* Usually w is denser than y */
void YYY::FP12_ssmul(FP12 *w, FP12 *y)
{
FP4 z0, z1, z2, z3, t0, t1;
if (w->type == FP_UNITY)
{
FP12_copy(w, y);
return;
}
if (y->type == FP_UNITY)
return;
if (y->type >= FP_SPARSE)
{
FP4_mul(&z0, &(w->a), &(y->a)); // xa.ya always 11x11
#if SEXTIC_TWIST_ZZZ == M_TYPE
if (y->type == FP_SPARSE || w->type == FP_SPARSE)
{
FP2_mul(&z2.b, &(w->b).b, &(y->b).b);
FP2_zero(&z2.a);
if (y->type != FP_SPARSE)
FP2_mul(&z2.a, &(w->b).b, &(y->b).a);
if (w->type != FP_SPARSE)
FP2_mul(&z2.a, &(w->b).a, &(y->b).b);
FP4_times_i(&z2);
}
else
#endif
FP4_mul(&z2, &(w->b), &(y->b)); // xb.yb could be 00x00 or 01x01 or or 10x10 or 11x00 or 11x10 or 11x01 or 11x11
FP4_add(&t0, &(w->a), &(w->b)); // (xa+xb)
FP4_add(&t1, &(y->a), &(y->b)); // (ya+yb)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&z1, &t0, &t1); // (xa+xb)(ya+yb) always 11x11
FP4_add(&t0, &(w->b), &(w->c)); // (xb+xc)
FP4_add(&t1, &(y->b), &(y->c)); // (yb+yc)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&z3, &t0, &t1); // (xb+xc)(yb+yc) could be anything...
FP4_neg(&t0, &z0); // -(xa.ya)
FP4_neg(&t1, &z2); // -(xb.yb)
FP4_add(&z1, &z1, &t0);
FP4_add(&(w->b), &z1, &t1); // /wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) = xa.yb + xb.ya
FP4_add(&z3, &z3, &t1); // (xb+xc)(yb+yc) -(xb.yb)
FP4_add(&z2, &z2, &t0); // (xb.yb) - (xa.ya)
FP4_add(&t0, &(w->a), &(w->c)); // (xa+xc)
FP4_add(&t1, &(y->a), &(y->c)); // (ya+yc)
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&t0, &t1, &t0); // (xa+xc)(ya+yc) always 11x11
FP4_add(&z2, &z2, &t0); // (xb.yb) - (xa.ya) + (xa+xc)(ya+yc)
#if SEXTIC_TWIST_ZZZ == D_TYPE
if (y->type == FP_SPARSE || w->type == FP_SPARSE)
{
FP2_mul(&t0.a, &(w->c).a, &(y->c).a);
FP2_zero(&t0.b);
if (y->type != FP_SPARSE)
FP2_mul(&t0.b, &(w->c).a, &(y->c).b);
if (w->type != FP_SPARSE)
FP2_mul(&t0.b, &(w->c).b, &(y->c).a);
}
else
#endif
FP4_mul(&t0, &(w->c), &(y->c)); // (xc.yc) could be anything
FP4_neg(&t1, &t0); // -(xc.yc)
FP4_add(&(w->c), &z2, &t1); // wc = (xb.yb) - (xa.ya) + (xa+xc)(ya+yc) - (xc.yc) = xb.yb + xc.ya + xa.yc
FP4_add(&z3, &z3, &t1); // (xb+xc)(yb+yc) -(xb.yb) - (xc.yc) = xb.yc + xc.yb
FP4_times_i(&t0); // i.(xc.yc)
FP4_add(&(w->b), &(w->b), &t0); // wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) +i(xc.yc)
FP4_norm(&z3);
FP4_times_i(&z3); // i[(xb+xc)(yb+yc) -(xb.yb) - (xc.yc)] = i(xb.yc + xc.yb)
FP4_add(&(w->a), &z0, &z3); // wa = xa.ya + i(xb.yc + xc.yb)
} else {
if (w->type == FP_SPARSER || w->type == FP_SPARSEST)
{
FP12_smul(w, y);
return;
}
// dense by sparser or sparsest - 13m
#if SEXTIC_TWIST_ZZZ == D_TYPE
FP4_copy(&z3, &(w->b));
FP4_mul(&z0, &(w->a), &(y->a));
if (y->type == FP_SPARSEST)
FP4_qmul(&z2, &(w->b), &(y->b).a.a);
else
FP4_pmul(&z2, &(w->b), &(y->b).a);
FP4_add(&(w->b), &(w->a), &(w->b));
FP4_copy(&t1, &(y->a));
FP2_add(&t1.a, &t1.a, &(y->b).a);
FP4_norm(&t1);
FP4_norm(&(w->b));
FP4_mul(&(w->b), &(w->b), &t1);
FP4_add(&z3, &z3, &(w->c));
FP4_norm(&z3);
if (y->type == FP_SPARSEST)
FP4_qmul(&z3, &z3, &(y->b).a.a);
else
FP4_pmul(&z3, &z3, &(y->b).a);
FP4_neg(&t0, &z0);
FP4_neg(&t1, &z2);
FP4_add(&(w->b), &(w->b), &t0); // z1=z1-z0
FP4_add(&(w->b), &(w->b), &t1); // z1=z1-z2
FP4_add(&z3, &z3, &t1); // z3=z3-z2
FP4_add(&z2, &z2, &t0); // z2=z2-z0
FP4_add(&t0, &(w->a), &(w->c));
FP4_norm(&t0);
FP4_norm(&z3);
FP4_mul(&t0, &(y->a), &t0);
FP4_add(&(w->c), &z2, &t0);
FP4_times_i(&z3);
FP4_add(&(w->a), &z0, &z3);
#endif
#if SEXTIC_TWIST_ZZZ == M_TYPE
FP4_mul(&z0, &(w->a), &(y->a));
FP4_add(&t0, &(w->a), &(w->b));
FP4_norm(&t0);
FP4_mul(&z1, &t0, &(y->a));
FP4_add(&t0, &(w->b), &(w->c));
FP4_norm(&t0);
if (y->type == FP_SPARSEST)
FP4_qmul(&z3, &t0, &(y->c).b.a);
else
FP4_pmul(&z3, &t0, &(y->c).b);
FP4_times_i(&z3);
FP4_neg(&t0, &z0);
FP4_add(&z1, &z1, &t0); // z1=z1-z0
FP4_copy(&(w->b), &z1);
FP4_copy(&z2, &t0);
FP4_add(&t0, &(w->a), &(w->c));
FP4_add(&t1, &(y->a), &(y->c));
FP4_norm(&t0);
FP4_norm(&t1);
FP4_mul(&t0, &t1, &t0);
FP4_add(&z2, &z2, &t0);
if (y->type == FP_SPARSEST)
FP4_qmul(&t0, &(w->c), &(y->c).b.a);
else
FP4_pmul(&t0, &(w->c), &(y->c).b);
FP4_times_i(&t0);
FP4_neg(&t1, &t0);
FP4_times_i(&t0);
FP4_add(&(w->c), &z2, &t1);
FP4_add(&z3, &z3, &t1);
FP4_add(&(w->b), &(w->b), &t0);
FP4_norm(&z3);
FP4_times_i(&z3);
FP4_add(&(w->a), &z0, &z3);
#endif
}
w->type = FP_DENSE;
FP12_norm(w);
}
/* FP12 multiplication w=w*y */
/* catering for special case that arises from special form of ATE pairing line function */
/* w and y are both sparser or sparsest line functions - cost = 6m */
void YYY::FP12_smul(FP12 *w, FP12 *y)
{
FP2 w1, w2, w3, ta, tb, tc, td, te, t;
#if SEXTIC_TWIST_ZZZ == D_TYPE
FP2_mul(&w1, &(w->a).a, &(y->a).a); // A1.A2
FP2_mul(&w2, &(w->a).b, &(y->a).b); // B1.B2
if (y->type == FP_SPARSEST || w->type == FP_SPARSEST)
{
if (y->type == FP_SPARSEST && w->type == FP_SPARSEST)
{
FP_mul(&w3.a, &(w->b).a.a, &(y->b).a.a);
FP_zero(&w3.b);
} else {
if (y->type != FP_SPARSEST)
FP2_pmul(&w3, &(y->b).a, &(w->b).a.a);
if (w->type != FP_SPARSEST)
FP2_pmul(&w3, &(w->b).a, &(y->b).a.a);
}
}
else
FP2_mul(&w3, &(w->b).a, &(y->b).a); // C1.C2
FP2_add(&ta, &(w->a).a, &(w->a).b); // A1+B1
FP2_add(&tb, &(y->a).a, &(y->a).b); // A2+B2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&tc, &ta, &tb); // (A1+B1)(A2+B2)
FP2_add(&t, &w1, &w2);
FP2_neg(&t, &t);
FP2_add(&tc, &tc, &t); // (A1+B1)(A2+B2)-A1.A2-B1*B2 = (A1.B2+A2.B1)
FP2_add(&ta, &(w->a).a, &(w->b).a); // A1+C1
FP2_add(&tb, &(y->a).a, &(y->b).a); // A2+C2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&td, &ta, &tb); // (A1+C1)(A2+C2)
FP2_add(&t, &w1, &w3);
FP2_neg(&t, &t);
FP2_add(&td, &td, &t); // (A1+C1)(A2+C2)-A1.A2-C1*C2 = (A1.C2+A2.C1)
FP2_add(&ta, &(w->a).b, &(w->b).a); // B1+C1
FP2_add(&tb, &(y->a).b, &(y->b).a); // B2+C2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&te, &ta, &tb); // (B1+C1)(B2+C2)
FP2_add(&t, &w2, &w3);
FP2_neg(&t, &t);
FP2_add(&te, &te, &t); // (B1+C1)(B2+C2)-B1.B2-C1*C2 = (B1.C2+B2.C1)
FP2_mul_ip(&w2);
FP2_add(&w1, &w1, &w2);
FP4_from_FP2s(&(w->a), &w1, &tc);
FP4_from_FP2s(&(w->b), &td, &te); // only norm these 2
FP4_from_FP2(&(w->c), &w3);
FP4_norm(&(w->a));
FP4_norm(&(w->b));
#endif
// } else {
#if SEXTIC_TWIST_ZZZ == M_TYPE
FP2_mul(&w1, &(w->a).a, &(y->a).a); // A1.A2
FP2_mul(&w2, &(w->a).b, &(y->a).b); // B1.B2
if (y->type == FP_SPARSEST || w->type == FP_SPARSEST)
{
if (y->type == FP_SPARSEST && w->type == FP_SPARSEST)
{
FP_mul(&w3.a, &(w->c).b.a, &(y->c).b.a);
FP_zero(&w3.b);
} else {
if (y->type != FP_SPARSEST)
FP2_pmul(&w3, &(y->c).b, &(w->c).b.a);
if (w->type != FP_SPARSEST)
FP2_pmul(&w3, &(w->c).b, &(y->c).b.a);
}
}
else
FP2_mul(&w3, &(w->c).b, &(y->c).b); // F1.F2
FP2_add(&ta, &(w->a).a, &(w->a).b); // A1+B1
FP2_add(&tb, &(y->a).a, &(y->a).b); // A2+B2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&tc, &ta, &tb); // (A1+B1)(A2+B2)
FP2_add(&t, &w1, &w2);
FP2_neg(&t, &t);
FP2_add(&tc, &tc, &t); // (A1+B1)(A2+B2)-A1.A2-B1*B2 = (A1.B2+A2.B1)
FP2_add(&ta, &(w->a).a, &(w->c).b); // A1+F1
FP2_add(&tb, &(y->a).a, &(y->c).b); // A2+F2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&td, &ta, &tb); // (A1+F1)(A2+F2)
FP2_add(&t, &w1, &w3);
FP2_neg(&t, &t);
FP2_add(&td, &td, &t); // (A1+F1)(A2+F2)-A1.A2-F1*F2 = (A1.F2+A2.F1)
FP2_add(&ta, &(w->a).b, &(w->c).b); // B1+F1
FP2_add(&tb, &(y->a).b, &(y->c).b); // B2+F2
FP2_norm(&ta);
FP2_norm(&tb);
FP2_mul(&te, &ta, &tb); // (B1+F1)(B2+F2)
FP2_add(&t, &w2, &w3);
FP2_neg(&t, &t);
FP2_add(&te, &te, &t); // (B1+F1)(B2+F2)-B1.B2-F1*F2 = (B1.F2+B2.F1)
FP2_mul_ip(&w2);
FP2_add(&w1, &w1, &w2);
FP4_from_FP2s(&(w->a), &w1, &tc);
FP2_mul_ip(&w3);
FP2_norm(&w3);
FP4_from_FP2H(&(w->b), &w3);
FP2_norm(&te);
FP2_mul_ip(&te);
FP4_from_FP2s(&(w->c), &te, &td);
FP4_norm(&(w->a));
FP4_norm(&(w->c));
#endif
// }
w->type = FP_SPARSE;
}
/* Set w=1/x */
/* SU= 600 */
void YYY::FP12_inv(FP12 *w, FP12 *x)
{
FP4 f0, f1, f2, f3;
FP4_sqr(&f0, &(x->a));
FP4_mul(&f1, &(x->b), &(x->c));
FP4_times_i(&f1);
FP4_sub(&f0, &f0, &f1); /* y.a */
FP4_norm(&f0);
FP4_sqr(&f1, &(x->c));
FP4_times_i(&f1);
FP4_mul(&f2, &(x->a), &(x->b));
FP4_sub(&f1, &f1, &f2); /* y.b */
FP4_norm(&f1);
FP4_sqr(&f2, &(x->b));
FP4_mul(&f3, &(x->a), &(x->c));
FP4_sub(&f2, &f2, &f3); /* y.c */
FP4_norm(&f2);
FP4_mul(&f3, &(x->b), &f2);
FP4_times_i(&f3);
FP4_mul(&(w->a), &f0, &(x->a));
FP4_add(&f3, &(w->a), &f3);
FP4_mul(&(w->c), &f1, &(x->c));
FP4_times_i(&(w->c));
FP4_add(&f3, &(w->c), &f3);
FP4_norm(&f3);
FP4_inv(&f3, &f3, NULL);
FP4_mul(&(w->a), &f0, &f3);
FP4_mul(&(w->b), &f1, &f3);
FP4_mul(&(w->c), &f2, &f3);
w->type = FP_DENSE;
}
/* constant time powering by small integer of max length bts */
void YYY::FP12_pinpow(FP12 *r, int e, int bts)
{
int i, b;
FP12 R[2];
FP12_one(&R[0]);
FP12_copy(&R[1], r);
for (i = bts - 1; i >= 0; i--)
{
b = (e >> i) & 1;
FP12_mul(&R[1 - b], &R[b]);
FP12_usqr(&R[b], &R[b]);
}
FP12_copy(r, &R[0]);
}
/* Compressed powering of unitary elements y=x^(e mod r) */
void YYY::FP12_compow(FP4 *c, FP12 *x, BIG e, BIG r)
{
FP12 g1, g2;
FP4 cp, cpm1, cpm2;
FP2 f;
BIG q, a, b, m;
BIG_rcopy(a, Fra);
BIG_rcopy(b, Frb);
FP2_from_BIGs(&f, a, b);
BIG_rcopy(q, Modulus);
FP12_copy(&g1, x);
FP12_copy(&g2, x);
BIG_copy(m, q);
BIG_mod(m, r);
BIG_copy(a, e);
BIG_mod(a, m);
BIG_copy(b, e);
BIG_sdiv(b, m);
FP12_trace(c, &g1);
if (BIG_iszilch(b))
{
FP4_xtr_pow(c, c, e);
return;
}
FP12_frob(&g2, &f);
FP12_trace(&cp, &g2);
FP12_conj(&g1, &g1);
FP12_mul(&g2, &g1);
FP12_trace(&cpm1, &g2);
FP12_mul(&g2, &g1);
FP12_trace(&cpm2, &g2);
FP4_xtr_pow2(c, &cp, c, &cpm1, &cpm2, a, b);
}
/* Note this is simple square and multiply, so not side-channel safe */
/* But fast for final exponentiation where exponent is not a secret */
void YYY::FP12_pow(FP12 *r, FP12 *a, BIG b)
{
FP12 w, sf;
BIG b1, b3;
int i, nb, bt;
BIG_copy(b1, b);
BIG_norm(b1);
BIG_pmul(b3, b1, 3);
BIG_norm(b3);
FP12_copy(&sf, a);
FP12_norm(&sf);
FP12_copy(&w, &sf);
if (BIG_iszilch(b3))
{
FP12_one(r);
return;
}
nb = BIG_nbits(b3);
for (i = nb - 2; i >= 1; i--)
{
FP12_usqr(&w, &w);
bt = BIG_bit(b3, i) - BIG_bit(b1, i);
if (bt == 1)
FP12_mul(&w, &sf);
if (bt == -1)
{
FP12_conj(&sf, &sf);
FP12_mul(&w, &sf);
FP12_conj(&sf, &sf);
}
}
FP12_copy(r, &w);
FP12_reduce(r);
}
/* p=q0^u0.q1^u1.q2^u2.q3^u3 */
/* Side channel attack secure */
// Bos & Costello https://eprint.iacr.org/2013/458.pdf
// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf
void YYY::FP12_pow4(FP12 *p, FP12 *q, BIG u[4])
{
int i, j, k, nb, pb, bt;
FP12 g[8], r;
BIG t[4], mt;
sign8 w[NLEN_XXX * BASEBITS_XXX + 1];
sign8 s[NLEN_XXX * BASEBITS_XXX + 1];
for (i = 0; i < 4; i++)
BIG_copy(t[i], u[i]);
// Precomputed table
FP12_copy(&g[0], &q[0]); // q[0]
FP12_copy(&g[1], &g[0]);
FP12_mul(&g[1], &q[1]); // q[0].q[1]
FP12_copy(&g[2], &g[0]);
FP12_mul(&g[2], &q[2]); // q[0].q[2]
FP12_copy(&g[3], &g[1]);
FP12_mul(&g[3], &q[2]); // q[0].q[1].q[2]
FP12_copy(&g[4], &g[0]);
FP12_mul(&g[4], &q[3]); // q[0].q[3]
FP12_copy(&g[5], &g[1]);
FP12_mul(&g[5], &q[3]); // q[0].q[1].q[3]
FP12_copy(&g[6], &g[2]);
FP12_mul(&g[6], &q[3]); // q[0].q[2].q[3]
FP12_copy(&g[7], &g[3]);
FP12_mul(&g[7], &q[3]); // q[0].q[1].q[2].q[3]
// Make it odd
pb = 1 - BIG_parity(t[0]);
BIG_inc(t[0], pb);
BIG_norm(t[0]);
// Number of bits
BIG_zero(mt);
for (i = 0; i < 4; i++)
{
BIG_or(mt, mt, t[i]);
}
nb = 1 + BIG_nbits(mt);
// Sign pivot
s[nb - 1] = 1;
for (i = 0; i < nb - 1; i++)
{
BIG_fshr(t[0], 1);
s[i] = 2 * BIG_parity(t[0]) - 1;
}
// Recoded exponent
for (i = 0; i < nb; i++)
{
w[i] = 0;
k = 1;
for (j = 1; j < 4; j++)
{
bt = s[i] * BIG_parity(t[j]);
BIG_fshr(t[j], 1);
BIG_dec(t[j], (bt >> 1));
BIG_norm(t[j]);
w[i] += bt * k;
k *= 2;
}
}
// Main loop
FP12_select(p, g, 2 * w[nb - 1] + 1);
for (i = nb - 2; i >= 0; i--)
{
FP12_select(&r, g, 2 * w[i] + s[i]);
FP12_usqr(p, p);
FP12_mul(p, &r);
}
// apply correction
FP12_conj(&r, &q[0]);
FP12_mul(&r, p);
FP12_cmove(p, &r, pb);
FP12_reduce(p);
}
/* Set w=w^p using Frobenius */
/* SU= 160 */
void YYY::FP12_frob(FP12 *w, FP2 *f)
{
FP2 f2, f3;
FP2_sqr(&f2, f); /* f2=f^2 */
FP2_mul(&f3, &f2, f); /* f3=f^3 */
FP4_frob(&(w->a), &f3);
FP4_frob(&(w->b), &f3);
FP4_frob(&(w->c), &f3);
FP4_pmul(&(w->b), &(w->b), f);
FP4_pmul(&(w->c), &(w->c), &f2);
w->type = FP_DENSE;
}
/* SU= 8 */
/* normalise all components of w */
void YYY::FP12_norm(FP12 *w)
{
FP4_norm(&(w->a));
FP4_norm(&(w->b));
FP4_norm(&(w->c));
}
/* SU= 8 */
/* reduce all components of w */
void YYY::FP12_reduce(FP12 *w)
{
FP4_reduce(&(w->a));
FP4_reduce(&(w->b));
FP4_reduce(&(w->c));
}
/* trace function w=trace(x) */
/* SU= 8 */
void YYY::FP12_trace(FP4 *w, FP12 *x)
{
FP4_imul(w, &(x->a), 3);
FP4_reduce(w);
}
/* SU= 8 */
/* Output w in hex */
void YYY::FP12_output(FP12 *w)
{
printf("[");
FP4_output(&(w->a));
printf(",");
FP4_output(&(w->b));
printf(",");
FP4_output(&(w->c));
printf("]");
}
/* SU= 64 */
/* Convert g to octet string w */
void YYY::FP12_toOctet(octet *W, FP12 *g)
{
W->len = 12 * MODBYTES_XXX;
FP4_toBytes(&(W->val[0]),&(g->c));
FP4_toBytes(&(W->val[4 * MODBYTES_XXX]),&(g->b));
FP4_toBytes(&(W->val[8 * MODBYTES_XXX]),&(g->a));
}
/* SU= 24 */
/* Restore g from octet string w */
void YYY::FP12_fromOctet(FP12 *g, octet *W)
{
FP4_fromBytes(&(g->c),&(W->val[0]));
FP4_fromBytes(&(g->b),&(W->val[4 * MODBYTES_XXX]));
FP4_fromBytes(&(g->a),&(W->val[8 * MODBYTES_XXX]));
}
/* Move g to f
if d=1 */
void YYY::FP12_cmove(FP12 *f, FP12 *g, int d)
{
FP4_cmove(&(f->a), &(g->a), d);
FP4_cmove(&(f->b), &(g->b), d);
FP4_cmove(&(f->c), &(g->c), d);
d = ~(d - 1);
f->type ^= (f->type ^ g->type)&d;
}
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