| /* |
| Licensed to the Apache Software Foundation (ASF) under one |
| or more contributor license agreements. See the NOTICE file |
| distributed with this work for additional information |
| regarding copyright ownership. The ASF licenses this file |
| to you 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. |
| */ |
| |
| /* AMCL Fp^12 functions */ |
| /* SU=m, m is Stack Usage (no lazy )*/ |
| /* FP48 elements are of the form a+i.b+i^2.c */ |
| |
| #include "fp48_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 FP48_select(YYY::FP48 *f,YYY::FP48 g[],sign32 b) |
| { |
| YYY::FP48 invf; |
| sign32 m=b>>31; |
| sign32 babs=(b^m)-m; |
| |
| babs=(babs-1)/2; |
| |
| FP48_cmove(f,&g[0],teq(babs,0)); // conditional move |
| FP48_cmove(f,&g[1],teq(babs,1)); |
| FP48_cmove(f,&g[2],teq(babs,2)); |
| FP48_cmove(f,&g[3],teq(babs,3)); |
| FP48_cmove(f,&g[4],teq(babs,4)); |
| FP48_cmove(f,&g[5],teq(babs,5)); |
| FP48_cmove(f,&g[6],teq(babs,6)); |
| FP48_cmove(f,&g[7],teq(babs,7)); |
| |
| FP48_copy(&invf,f); |
| FP48_conj(&invf,&invf); // 1/f |
| FP48_cmove(f,&invf,(int)(m&1)); |
| } |
| |
| |
| /* test x==0 ? */ |
| /* SU= 8 */ |
| int YYY::FP48_iszilch(FP48 *x) |
| { |
| if (FP16_iszilch(&(x->a)) && FP16_iszilch(&(x->b)) && FP16_iszilch(&(x->c))) return 1; |
| return 0; |
| } |
| |
| /* test x==1 ? */ |
| /* SU= 8 */ |
| int YYY::FP48_isunity(FP48 *x) |
| { |
| if (FP16_isunity(&(x->a)) && FP16_iszilch(&(x->b)) && FP16_iszilch(&(x->c))) return 1; |
| return 0; |
| } |
| |
| /* FP48 copy w=x */ |
| /* SU= 16 */ |
| void YYY::FP48_copy(FP48 *w,FP48 *x) |
| { |
| if (x==w) return; |
| FP16_copy(&(w->a),&(x->a)); |
| FP16_copy(&(w->b),&(x->b)); |
| FP16_copy(&(w->c),&(x->c)); |
| w->type=x->type; |
| } |
| |
| /* FP48 w=1 */ |
| /* SU= 8 */ |
| void YYY::FP48_one(FP48 *w) |
| { |
| FP16_one(&(w->a)); |
| FP16_zero(&(w->b)); |
| FP16_zero(&(w->c)); |
| w->type=FP_UNITY; |
| } |
| |
| void YYY::FP48_zero(FP48 *w) |
| { |
| FP16_zero(&(w->a)); |
| FP16_zero(&(w->b)); |
| FP16_zero(&(w->c)); |
| w->type=FP_ZERO; |
| } |
| |
| /* return 1 if x==y, else 0 */ |
| /* SU= 16 */ |
| int YYY::FP48_equals(FP48 *x,FP48 *y) |
| { |
| if (FP16_equals(&(x->a),&(y->a)) && FP16_equals(&(x->b),&(y->b)) && FP16_equals(&(x->b),&(y->b))) |
| return 1; |
| return 0; |
| } |
| |
| /* Set w=conj(x) */ |
| /* SU= 8 */ |
| void YYY::FP48_conj(FP48 *w,FP48 *x) |
| { |
| FP48_copy(w,x); |
| FP16_conj(&(w->a),&(w->a)); |
| FP16_nconj(&(w->b),&(w->b)); |
| FP16_conj(&(w->c),&(w->c)); |
| } |
| |
| /* Create FP48 from FP16 */ |
| /* SU= 8 */ |
| void YYY::FP48_from_FP16(FP48 *w,FP16 *a) |
| { |
| FP16_copy(&(w->a),a); |
| FP16_zero(&(w->b)); |
| FP16_zero(&(w->c)); |
| w->type=FP_SPARSER; |
| } |
| |
| /* Create FP48 from 3 FP16's */ |
| /* SU= 16 */ |
| void YYY::FP48_from_FP16s(FP48 *w,FP16 *a,FP16 *b,FP16 *c) |
| { |
| FP16_copy(&(w->a),a); |
| FP16_copy(&(w->b),b); |
| FP16_copy(&(w->c),c); |
| w->type=FP_DENSE; |
| } |
| |
| /* Granger-Scott Unitary Squaring. This does not benefit from lazy reduction */ |
| /* SU= 600 */ |
| void YYY::FP48_usqr(FP48 *w,FP48 *x) |
| { |
| FP16 A,B,C,D; |
| |
| FP16_copy(&A,&(x->a)); |
| |
| FP16_sqr(&(w->a),&(x->a)); |
| FP16_add(&D,&(w->a),&(w->a)); |
| FP16_add(&(w->a),&D,&(w->a)); |
| |
| FP16_norm(&(w->a)); |
| FP16_nconj(&A,&A); |
| |
| FP16_add(&A,&A,&A); |
| FP16_add(&(w->a),&(w->a),&A); |
| FP16_sqr(&B,&(x->c)); |
| FP16_times_i(&B); |
| |
| FP16_add(&D,&B,&B); |
| FP16_add(&B,&B,&D); |
| FP16_norm(&B); |
| |
| FP16_sqr(&C,&(x->b)); |
| |
| FP16_add(&D,&C,&C); |
| FP16_add(&C,&C,&D); |
| |
| FP16_norm(&C); |
| FP16_conj(&(w->b),&(x->b)); |
| FP16_add(&(w->b),&(w->b),&(w->b)); |
| FP16_nconj(&(w->c),&(x->c)); |
| |
| FP16_add(&(w->c),&(w->c),&(w->c)); |
| FP16_add(&(w->b),&B,&(w->b)); |
| FP16_add(&(w->c),&C,&(w->c)); |
| w->type=FP_DENSE; |
| |
| FP48_reduce(w); /* reduce here as in pow function repeated squarings would trigger multiple reductions */ |
| } |
| |
| /* FP48 squaring w=x^2 */ |
| /* SU= 600 */ |
| void YYY::FP48_sqr(FP48 *w,FP48 *x) |
| { |
| /* Use Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */ |
| |
| FP16 A,B,C,D; |
| |
| if (x->type<=FP_UNITY) |
| { |
| FP48_copy(w,x); |
| return; |
| } |
| |
| FP16_sqr(&A,&(x->a)); |
| FP16_mul(&B,&(x->b),&(x->c)); |
| FP16_add(&B,&B,&B); |
| FP16_norm(&B); |
| FP16_sqr(&C,&(x->c)); |
| |
| FP16_mul(&D,&(x->a),&(x->b)); |
| FP16_add(&D,&D,&D); |
| |
| FP16_add(&(w->c),&(x->a),&(x->c)); |
| FP16_add(&(w->c),&(x->b),&(w->c)); |
| FP16_norm(&(w->c)); |
| |
| FP16_sqr(&(w->c),&(w->c)); |
| |
| FP16_copy(&(w->a),&A); |
| FP16_add(&A,&A,&B); |
| |
| FP16_norm(&A); |
| |
| FP16_add(&A,&A,&C); |
| FP16_add(&A,&A,&D); |
| |
| FP16_norm(&A); |
| |
| FP16_neg(&A,&A); |
| FP16_times_i(&B); |
| FP16_times_i(&C); |
| |
| FP16_add(&(w->a),&(w->a),&B); |
| FP16_add(&(w->b),&C,&D); |
| FP16_add(&(w->c),&(w->c),&A); |
| |
| if (x->type==FP_SPARSER) |
| w->type=FP_SPARSE; |
| else |
| w->type=FP_DENSE; |
| |
| FP48_norm(w); |
| } |
| |
| /* FP48 full multiplication w=w*y */ |
| |
| |
| /* SU= 896 */ |
| /* FP48 full multiplication w=w*y */ |
| void YYY::FP48_mul(FP48 *w,FP48 *y) |
| { |
| FP16 z0,z1,z2,z3,t0,t1; |
| |
| FP16_mul(&z0,&(w->a),&(y->a)); |
| FP16_mul(&z2,&(w->b),&(y->b)); // |
| |
| FP16_add(&t0,&(w->a),&(w->b)); |
| FP16_add(&t1,&(y->a),&(y->b)); // |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&z1,&t0,&t1); |
| FP16_add(&t0,&(w->b),&(w->c)); |
| FP16_add(&t1,&(y->b),&(y->c)); // |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&z3,&t0,&t1); |
| |
| FP16_neg(&t0,&z0); |
| FP16_neg(&t1,&z2); |
| |
| FP16_add(&z1,&z1,&t0); // z1=z1-z0 |
| FP16_add(&(w->b),&z1,&t1); // z1=z1-z2 |
| FP16_add(&z3,&z3,&t1); // z3=z3-z2 |
| FP16_add(&z2,&z2,&t0); // z2=z2-z0 |
| |
| FP16_add(&t0,&(w->a),&(w->c)); |
| FP16_add(&t1,&(y->a),&(y->c)); |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&t0,&t1,&t0); |
| FP16_add(&z2,&z2,&t0); |
| |
| FP16_mul(&t0,&(w->c),&(y->c)); |
| FP16_neg(&t1,&t0); |
| |
| FP16_add(&(w->c),&z2,&t1); |
| FP16_add(&z3,&z3,&t1); |
| FP16_times_i(&t0); |
| FP16_add(&(w->b),&(w->b),&t0); |
| FP16_norm(&z3); |
| FP16_times_i(&z3); |
| FP16_add(&(w->a),&z0,&z3); |
| |
| FP48_norm(w); |
| w->type=FP_DENSE; |
| } |
| |
| /* FP48 full multiplication w=w*y */ |
| /* Supports sparse multiplicands */ |
| /* Usually w is denser than y */ |
| void YYY::FP48_ssmul(FP48 *w,FP48 *y) |
| { |
| FP16 z0,z1,z2,z3,t0,t1; |
| if (w->type==FP_UNITY) |
| { |
| FP48_copy(w,y); |
| return; |
| } |
| if (y->type==FP_UNITY) |
| return; |
| |
| if (y->type >= FP_SPARSE) |
| { |
| FP16_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) |
| { |
| FP8_mul(&z2.b,&(w->b).b,&(y->b).b); |
| FP8_zero(&z2.a); |
| if (y->type!=FP_SPARSE) |
| FP8_mul(&z2.a,&(w->b).b,&(y->b).a); |
| if (w->type!=FP_SPARSE) |
| FP8_mul(&z2.a,&(w->b).a,&(y->b).b); |
| FP16_times_i(&z2); |
| } |
| else |
| #endif |
| FP16_mul(&z2,&(w->b),&(y->b)); // xb.yb could be 00x00 or 01x01 or or 10x10 or 11x00 or 11x10 or 11x01 or 11x11 |
| |
| FP16_add(&t0,&(w->a),&(w->b)); // (xa+xb) |
| FP16_add(&t1,&(y->a),&(y->b)); // (ya+yb) |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&z1,&t0,&t1); // (xa+xb)(ya+yb) always 11x11 |
| FP16_add(&t0,&(w->b),&(w->c)); // (xb+xc) |
| FP16_add(&t1,&(y->b),&(y->c)); // (yb+yc) |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&z3,&t0,&t1); // (xb+xc)(yb+yc) could be anything... |
| FP16_neg(&t0,&z0); // -(xa.ya) |
| FP16_neg(&t1,&z2); // -(xb.yb) |
| |
| FP16_add(&z1,&z1,&t0); |
| FP16_add(&(w->b),&z1,&t1); // /wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) = xa.yb + xb.ya |
| |
| FP16_add(&z3,&z3,&t1); // (xb+xc)(yb+yc) -(xb.yb) |
| FP16_add(&z2,&z2,&t0); // (xb.yb) - (xa.ya) |
| |
| FP16_add(&t0,&(w->a),&(w->c)); // (xa+xc) |
| FP16_add(&t1,&(y->a),&(y->c)); // (ya+yc) |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&t0,&t1,&t0); // (xa+xc)(ya+yc) always 11x11 |
| FP16_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) |
| { |
| FP8_mul(&t0.a,&(w->c).a,&(y->c).a); |
| FP8_zero(&t0.b); |
| if (y->type!=FP_SPARSE) |
| FP8_mul(&t0.b,&(w->c).a,&(y->c).b); |
| if (w->type!=FP_SPARSE) |
| FP8_mul(&t0.b,&(w->c).b,&(y->c).a); |
| } |
| else |
| #endif |
| FP16_mul(&t0,&(w->c),&(y->c)); // (xc.yc) could be anything |
| |
| FP16_neg(&t1,&t0); // -(xc.yc) |
| |
| FP16_add(&(w->c),&z2,&t1); // wc = (xb.yb) - (xa.ya) + (xa+xc)(ya+yc) - (xc.yc) = xb.yb + xc.ya + xa.yc |
| FP16_add(&z3,&z3,&t1); // (xb+xc)(yb+yc) -(xb.yb) - (xc.yc) = xb.yc + xc.yb |
| FP16_times_i(&t0); // i.(xc.yc) |
| FP16_add(&(w->b),&(w->b),&t0); // wb = (xa+xb)(ya+yb) -(xa.ya) -(xb.yb) +i(xc.yc) |
| FP16_norm(&z3); |
| FP16_times_i(&z3); // i[(xb+xc)(yb+yc) -(xb.yb) - (xc.yc)] = i(xb.yc + xc.yb) |
| FP16_add(&(w->a),&z0,&z3); // wa = xa.ya + i(xb.yc + xc.yb) |
| } else { |
| if (w->type==FP_SPARSER) |
| { |
| FP48_smul(w,y); |
| return; |
| } |
| // dense by sparser - 13m |
| #if SEXTIC_TWIST_ZZZ == D_TYPE |
| FP16_copy(&z3,&(w->b)); |
| FP16_mul(&z0,&(w->a),&(y->a)); |
| |
| FP16_pmul(&z2,&(w->b),&(y->b).a); |
| FP16_add(&(w->b),&(w->a),&(w->b)); |
| FP16_copy(&t1,&(y->a)); |
| FP8_add(&t1.a,&t1.a,&(y->b).a); |
| |
| FP16_norm(&t1); |
| FP16_norm(&(w->b)); |
| |
| FP16_mul(&(w->b),&(w->b),&t1); |
| FP16_add(&z3,&z3,&(w->c)); |
| FP16_norm(&z3); |
| FP16_pmul(&z3,&z3,&(y->b).a); |
| FP16_neg(&t0,&z0); |
| FP16_neg(&t1,&z2); |
| |
| FP16_add(&(w->b),&(w->b),&t0); // z1=z1-z0 |
| FP16_add(&(w->b),&(w->b),&t1); // z1=z1-z2 |
| |
| FP16_add(&z3,&z3,&t1); // z3=z3-z2 |
| FP16_add(&z2,&z2,&t0); // z2=z2-z0 |
| |
| FP16_add(&t0,&(w->a),&(w->c)); |
| FP16_norm(&t0); |
| FP16_norm(&z3); |
| |
| FP16_mul(&t0,&(y->a),&t0); |
| FP16_add(&(w->c),&z2,&t0); |
| |
| FP16_times_i(&z3); |
| FP16_add(&(w->a),&z0,&z3); |
| #endif |
| #if SEXTIC_TWIST_ZZZ == M_TYPE |
| FP16_mul(&z0,&(w->a),&(y->a)); |
| FP16_add(&t0,&(w->a),&(w->b)); |
| FP16_norm(&t0); |
| |
| FP16_mul(&z1,&t0,&(y->a)); |
| FP16_add(&t0,&(w->b),&(w->c)); |
| FP16_norm(&t0); |
| |
| FP16_pmul(&z3,&t0,&(y->c).b); |
| FP16_times_i(&z3); |
| |
| FP16_neg(&t0,&z0); |
| FP16_add(&z1,&z1,&t0); // z1=z1-z0 |
| |
| FP16_copy(&(w->b),&z1); |
| FP16_copy(&z2,&t0); |
| |
| FP16_add(&t0,&(w->a),&(w->c)); |
| FP16_add(&t1,&(y->a),&(y->c)); |
| |
| FP16_norm(&t0); |
| FP16_norm(&t1); |
| |
| FP16_mul(&t0,&t1,&t0); |
| FP16_add(&z2,&z2,&t0); |
| |
| FP16_pmul(&t0,&(w->c),&(y->c).b); |
| FP16_times_i(&t0); |
| FP16_neg(&t1,&t0); |
| FP16_times_i(&t0); |
| |
| FP16_add(&(w->c),&z2,&t1); |
| FP16_add(&z3,&z3,&t1); |
| |
| FP16_add(&(w->b),&(w->b),&t0); |
| FP16_norm(&z3); |
| FP16_times_i(&z3); |
| FP16_add(&(w->a),&z0,&z3); |
| #endif |
| } |
| w->type=FP_DENSE; |
| FP48_norm(w); |
| } |
| |
| /* FP48 multiplication w=w*y */ |
| /* catering for special case that arises from special form of ATE pairing line function */ |
| /* w and y are both sparser line functions - cost = 6m */ |
| void YYY::FP48_smul(FP48 *w,FP48 *y) |
| { |
| FP8 w1,w2,w3,ta,tb,tc,td,te,t; |
| |
| |
| #if SEXTIC_TWIST_ZZZ == D_TYPE |
| FP8_mul(&w1,&(w->a).a,&(y->a).a); // A1.A2 |
| FP8_mul(&w2,&(w->a).b,&(y->a).b); // B1.B2 |
| FP8_mul(&w3,&(w->b).a,&(y->b).a); // C1.C2 |
| |
| FP8_add(&ta,&(w->a).a,&(w->a).b); // A1+B1 |
| FP8_add(&tb,&(y->a).a,&(y->a).b); // A2+B2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&tc,&ta,&tb); // (A1+B1)(A2+B2) |
| FP8_add(&t,&w1,&w2); |
| FP8_neg(&t,&t); |
| FP8_add(&tc,&tc,&t); // (A1+B1)(A2+B2)-A1.A2-B1*B2 = (A1.B2+A2.B1) |
| |
| FP8_add(&ta,&(w->a).a,&(w->b).a); // A1+C1 |
| FP8_add(&tb,&(y->a).a,&(y->b).a); // A2+C2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&td,&ta,&tb); // (A1+C1)(A2+C2) |
| FP8_add(&t,&w1,&w3); |
| FP8_neg(&t,&t); |
| FP8_add(&td,&td,&t); // (A1+C1)(A2+C2)-A1.A2-C1*C2 = (A1.C2+A2.C1) |
| |
| FP8_add(&ta,&(w->a).b,&(w->b).a); // B1+C1 |
| FP8_add(&tb,&(y->a).b,&(y->b).a); // B2+C2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&te,&ta,&tb); // (B1+C1)(B2+C2) |
| FP8_add(&t,&w2,&w3); |
| FP8_neg(&t,&t); |
| FP8_add(&te,&te,&t); // (B1+C1)(B2+C2)-B1.B2-C1*C2 = (B1.C2+B2.C1) |
| |
| FP8_times_i(&w2); |
| FP8_add(&w1,&w1,&w2); |
| FP16_from_FP8s(&(w->a),&w1,&tc); |
| FP16_from_FP8s(&(w->b),&td,&te); // only norm these 2 |
| FP16_from_FP8(&(w->c),&w3); |
| |
| FP16_norm(&(w->a)); |
| FP16_norm(&(w->b)); |
| #endif |
| #if SEXTIC_TWIST_ZZZ == M_TYPE |
| FP8_mul(&w1,&(w->a).a,&(y->a).a); // A1.A2 |
| FP8_mul(&w2,&(w->a).b,&(y->a).b); // B1.B2 |
| FP8_mul(&w3,&(w->c).b,&(y->c).b); // F1.F2 |
| |
| FP8_add(&ta,&(w->a).a,&(w->a).b); // A1+B1 |
| FP8_add(&tb,&(y->a).a,&(y->a).b); // A2+B2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&tc,&ta,&tb); // (A1+B1)(A2+B2) |
| FP8_add(&t,&w1,&w2); |
| FP8_neg(&t,&t); |
| FP8_add(&tc,&tc,&t); // (A1+B1)(A2+B2)-A1.A2-B1*B2 = (A1.B2+A2.B1) |
| |
| FP8_add(&ta,&(w->a).a,&(w->c).b); // A1+F1 |
| FP8_add(&tb,&(y->a).a,&(y->c).b); // A2+F2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&td,&ta,&tb); // (A1+F1)(A2+F2) |
| FP8_add(&t,&w1,&w3); |
| FP8_neg(&t,&t); |
| FP8_add(&td,&td,&t); // (A1+F1)(A2+F2)-A1.A2-F1*F2 = (A1.F2+A2.F1) |
| |
| FP8_add(&ta,&(w->a).b,&(w->c).b); // B1+F1 |
| FP8_add(&tb,&(y->a).b,&(y->c).b); // B2+F2 |
| FP8_norm(&ta); |
| FP8_norm(&tb); |
| FP8_mul(&te,&ta,&tb); // (B1+F1)(B2+F2) |
| FP8_add(&t,&w2,&w3); |
| FP8_neg(&t,&t); |
| FP8_add(&te,&te,&t); // (B1+F1)(B2+F2)-B1.B2-F1*F2 = (B1.F2+B2.F1) |
| |
| FP8_times_i(&w2); |
| FP8_add(&w1,&w1,&w2); |
| FP16_from_FP8s(&(w->a),&w1,&tc); |
| |
| FP8_times_i(&w3); |
| FP8_norm(&w3); |
| FP16_from_FP8H(&(w->b),&w3); |
| |
| FP8_norm(&te); |
| FP8_times_i(&te); |
| FP16_from_FP8s(&(w->c),&te,&td); |
| |
| FP16_norm(&(w->a)); |
| FP16_norm(&(w->c)); |
| #endif |
| |
| w->type=FP_SPARSE; |
| } |
| |
| /* Set w=1/x */ |
| /* SU= 600 */ |
| void YYY::FP48_inv(FP48 *w,FP48 *x) |
| { |
| FP16 f0,f1,f2,f3; |
| |
| FP16_sqr(&f0,&(x->a)); |
| FP16_mul(&f1,&(x->b),&(x->c)); |
| FP16_times_i(&f1); |
| FP16_sub(&f0,&f0,&f1); /* y.a */ |
| FP16_norm(&f0); |
| |
| FP16_sqr(&f1,&(x->c)); |
| FP16_times_i(&f1); |
| FP16_mul(&f2,&(x->a),&(x->b)); |
| FP16_sub(&f1,&f1,&f2); /* y.b */ |
| FP16_norm(&f1); |
| |
| FP16_sqr(&f2,&(x->b)); |
| FP16_mul(&f3,&(x->a),&(x->c)); |
| FP16_sub(&f2,&f2,&f3); /* y.c */ |
| FP16_norm(&f2); |
| |
| FP16_mul(&f3,&(x->b),&f2); |
| FP16_times_i(&f3); |
| FP16_mul(&(w->a),&f0,&(x->a)); |
| FP16_add(&f3,&(w->a),&f3); |
| FP16_mul(&(w->c),&f1,&(x->c)); |
| FP16_times_i(&(w->c)); |
| |
| FP16_add(&f3,&(w->c),&f3); |
| FP16_norm(&f3); |
| |
| FP16_inv(&f3,&f3); |
| FP16_mul(&(w->a),&f0,&f3); |
| FP16_mul(&(w->b),&f1,&f3); |
| FP16_mul(&(w->c),&f2,&f3); |
| w->type=FP_DENSE; |
| } |
| |
| /* constant time powering by small integer of max length bts */ |
| |
| void YYY::FP48_pinpow(FP48 *r,int e,int bts) |
| { |
| int i,b; |
| FP48 R[2]; |
| |
| FP48_one(&R[0]); |
| FP48_copy(&R[1],r); |
| |
| for (i=bts-1; i>=0; i--) |
| { |
| b=(e>>i)&1; |
| FP48_mul(&R[1-b],&R[b]); |
| FP48_usqr(&R[b],&R[b]); |
| } |
| FP48_copy(r,&R[0]); |
| } |
| |
| /* Compressed powering of unitary elements y=x^(e mod r) */ |
| |
| void YYY::FP48_compow(FP16 *c,FP48 *x,BIG e,BIG r) |
| { |
| FP48 g1,g2; |
| FP16 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); |
| |
| FP48_copy(&g1,x); |
| FP48_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); |
| |
| FP48_trace(c,&g1); |
| |
| if (BIG_iszilch(b)) |
| { |
| FP16_xtr_pow(c,c,e); |
| return; |
| } |
| |
| FP48_frob(&g2,&f,1); |
| FP48_trace(&cp,&g2); |
| FP48_conj(&g1,&g1); |
| FP48_mul(&g2,&g1); |
| FP48_trace(&cpm1,&g2); |
| FP48_mul(&g2,&g1); |
| |
| FP48_trace(&cpm2,&g2); |
| |
| FP16_xtr_pow2(c,&cp,c,&cpm1,&cpm2,a,b); |
| |
| } |
| |
| /* Note this is simple square and multiply, so not side-channel safe */ |
| |
| void YYY::FP48_pow(FP48 *r,FP48 *a,BIG b) |
| { |
| FP48 w,sf; |
| BIG b1,b3; |
| int i,nb,bt; |
| BIG_copy(b1,b); |
| BIG_norm(b1); |
| BIG_pmul(b3,b1,3); |
| BIG_norm(b3); |
| |
| FP48_copy(&sf,a); |
| FP48_norm(&sf); |
| FP48_copy(&w,&sf); |
| |
| nb=BIG_nbits(b3); |
| for (i=nb-2;i>=1;i--) |
| { |
| FP48_usqr(&w,&w); |
| bt=BIG_bit(b3,i)-BIG_bit(b1,i); |
| if (bt==1) |
| FP48_mul(&w,&sf); |
| if (bt==-1) |
| { |
| FP48_conj(&sf,&sf); |
| FP48_mul(&w,&sf); |
| FP48_conj(&sf,&sf); |
| } |
| } |
| |
| FP48_copy(r,&w); |
| FP48_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::FP48_pow16(FP48 *p,FP48 *q,BIG u[16]) |
| { |
| int i,j,k,nb,pb1,pb2,pb3,pb4,bt; |
| FP48 g1[8],g2[8],g3[8],g4[8],r; |
| BIG t[16],mt; |
| sign8 w1[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 s1[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 w2[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 s2[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 w3[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 s3[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 w4[NLEN_XXX*BASEBITS_XXX+1]; |
| sign8 s4[NLEN_XXX*BASEBITS_XXX+1]; |
| FP fx,fy; |
| FP2 X; |
| |
| FP_rcopy(&fx,Fra); |
| FP_rcopy(&fy,Frb); |
| FP2_from_FPs(&X,&fx,&fy); |
| |
| for (i=0; i<16; i++) |
| BIG_copy(t[i],u[i]); |
| |
| // Precomputed table |
| FP48_copy(&g1[0],&q[0]); // q[0] |
| FP48_copy(&g1[1],&g1[0]); |
| FP48_mul(&g1[1],&q[1]); // q[0].q[1] |
| FP48_copy(&g1[2],&g1[0]); |
| FP48_mul(&g1[2],&q[2]); // q[0].q[2] |
| FP48_copy(&g1[3],&g1[1]); |
| FP48_mul(&g1[3],&q[2]); // q[0].q[1].q[2] |
| FP48_copy(&g1[4],&g1[0]); |
| FP48_mul(&g1[4],&q[3]); // q[0].q[3] |
| FP48_copy(&g1[5],&g1[1]); |
| FP48_mul(&g1[5],&q[3]); // q[0].q[1].q[3] |
| FP48_copy(&g1[6],&g1[2]); |
| FP48_mul(&g1[6],&q[3]); // q[0].q[2].q[3] |
| FP48_copy(&g1[7],&g1[3]); |
| FP48_mul(&g1[7],&q[3]); // q[0].q[1].q[2].q[3] |
| |
| // Use Frobenius |
| |
| for (i=0;i<8;i++) |
| { |
| FP48_copy(&g2[i],&g1[i]); |
| FP48_frob(&g2[i],&X,4); |
| |
| FP48_copy(&g3[i],&g2[i]); |
| FP48_frob(&g3[i],&X,4); |
| |
| FP48_copy(&g4[i],&g3[i]); |
| FP48_frob(&g4[i],&X,4); |
| } |
| |
| // Make them odd |
| pb1=1-BIG_parity(t[0]); |
| BIG_inc(t[0],pb1); |
| BIG_norm(t[0]); |
| |
| pb2=1-BIG_parity(t[4]); |
| BIG_inc(t[4],pb2); |
| BIG_norm(t[4]); |
| |
| pb3=1-BIG_parity(t[8]); |
| BIG_inc(t[8],pb3); |
| BIG_norm(t[8]); |
| |
| pb4=1-BIG_parity(t[12]); |
| BIG_inc(t[12],pb4); |
| BIG_norm(t[12]); |
| |
| // Number of bits |
| BIG_zero(mt); |
| for (i=0; i<16; i++) |
| { |
| BIG_or(mt,mt,t[i]); |
| } |
| nb=1+BIG_nbits(mt); |
| |
| // Sign pivot |
| s1[nb-1]=1; |
| s2[nb-1]=1; |
| s3[nb-1]=1; |
| s4[nb-1]=1; |
| for (i=0;i<nb-1;i++) |
| { |
| BIG_fshr(t[0],1); |
| s1[i]=2*BIG_parity(t[0])-1; |
| BIG_fshr(t[4],1); |
| s2[i]=2*BIG_parity(t[4])-1; |
| BIG_fshr(t[8],1); |
| s3[i]=2*BIG_parity(t[8])-1; |
| BIG_fshr(t[12],1); |
| s4[i]=2*BIG_parity(t[12])-1; |
| } |
| |
| // Recoded exponents |
| for (i=0; i<nb; i++) |
| { |
| w1[i]=0; |
| k=1; |
| for (j=1; j<4; j++) |
| { |
| bt=s1[i]*BIG_parity(t[j]); |
| BIG_fshr(t[j],1); |
| |
| BIG_dec(t[j],(bt>>1)); |
| BIG_norm(t[j]); |
| w1[i]+=bt*k; |
| k*=2; |
| } |
| |
| w2[i]=0; |
| k=1; |
| for (j=5; j<8; j++) |
| { |
| bt=s2[i]*BIG_parity(t[j]); |
| BIG_fshr(t[j],1); |
| |
| BIG_dec(t[j],(bt>>1)); |
| BIG_norm(t[j]); |
| w2[i]+=bt*k; |
| k*=2; |
| } |
| |
| w3[i]=0; |
| k=1; |
| for (j=9; j<12; j++) |
| { |
| bt=s3[i]*BIG_parity(t[j]); |
| BIG_fshr(t[j],1); |
| |
| BIG_dec(t[j],(bt>>1)); |
| BIG_norm(t[j]); |
| w3[i]+=bt*k; |
| k*=2; |
| } |
| |
| w4[i]=0; |
| k=1; |
| for (j=13; j<16; j++) |
| { |
| bt=s4[i]*BIG_parity(t[j]); |
| BIG_fshr(t[j],1); |
| |
| BIG_dec(t[j],(bt>>1)); |
| BIG_norm(t[j]); |
| w4[i]+=bt*k; |
| k*=2; |
| } |
| } |
| |
| // Main loop |
| FP48_select(p,g1,2*w1[nb-1]+1); |
| FP48_select(&r,g2,2*w2[nb-1]+1); |
| FP48_mul(p,&r); |
| FP48_select(&r,g3,2*w3[nb-1]+1); |
| FP48_mul(p,&r); |
| FP48_select(&r,g4,2*w4[nb-1]+1); |
| FP48_mul(p,&r); |
| for (i=nb-2; i>=0; i--) |
| { |
| FP48_usqr(p,p); |
| FP48_select(&r,g1,2*w1[i]+s1[i]); |
| FP48_mul(p,&r); |
| FP48_select(&r,g2,2*w2[i]+s2[i]); |
| FP48_mul(p,&r); |
| FP48_select(&r,g3,2*w3[i]+s3[i]); |
| FP48_mul(p,&r); |
| FP48_select(&r,g4,2*w4[i]+s4[i]); |
| FP48_mul(p,&r); |
| } |
| |
| // apply correction |
| FP48_conj(&r,&q[0]); |
| FP48_mul(&r,p); |
| FP48_cmove(p,&r,pb1); |
| FP48_conj(&r,&q[4]); |
| FP48_mul(&r,p); |
| FP48_cmove(p,&r,pb2); |
| |
| FP48_conj(&r,&q[8]); |
| FP48_mul(&r,p); |
| FP48_cmove(p,&r,pb3); |
| FP48_conj(&r,&q[12]); |
| FP48_mul(&r,p); |
| FP48_cmove(p,&r,pb4); |
| |
| FP48_reduce(p); |
| } |
| |
| /* Set w=w^p using Frobenius */ |
| /* SU= 160 */ |
| void YYY::FP48_frob(FP48 *w,FP2 *f,int n) |
| { |
| int i; |
| FP8 X2,X4; |
| FP4 F; |
| FP2 f3,f2; // f=(1+i)^(p-19)/24 |
| FP2_sqr(&f2,f); // |
| FP2_mul(&f3,&f2,f); // f3=f^3=(1+i)^(p-19)/8 |
| |
| FP2_mul_ip(&f3); |
| FP2_norm(&f3); |
| FP2_mul_ip(&f3); // f3 = (1+i)^16/8.(1+i)^(p-19)/8 = (1+i)^(p-3)/8 |
| FP2_norm(&f3); |
| |
| for (i=0;i<n;i++) |
| { |
| FP16_frob(&(w->a),&f3); // a=a^p |
| FP16_frob(&(w->b),&f3); // b=b^p |
| FP16_frob(&(w->c),&f3); // c=c^p |
| |
| FP16_qmul(&(w->b),&(w->b),f); FP16_times_i4(&(w->b)); FP16_times_i2(&(w->b)); |
| FP16_qmul(&(w->c),&(w->c),&f2); FP16_times_i4(&(w->c)); FP16_times_i4(&(w->c)); FP16_times_i4(&(w->c)); |
| } |
| w->type=FP_DENSE; |
| } |
| |
| /* SU= 8 */ |
| /* normalise all components of w */ |
| void YYY::FP48_norm(FP48 *w) |
| { |
| FP16_norm(&(w->a)); |
| FP16_norm(&(w->b)); |
| FP16_norm(&(w->c)); |
| } |
| |
| /* SU= 8 */ |
| /* reduce all components of w */ |
| void YYY::FP48_reduce(FP48 *w) |
| { |
| FP16_reduce(&(w->a)); |
| FP16_reduce(&(w->b)); |
| FP16_reduce(&(w->c)); |
| } |
| |
| /* trace function w=trace(x) */ |
| /* SU= 8 */ |
| void YYY::FP48_trace(FP16 *w,FP48 *x) |
| { |
| FP16_imul(w,&(x->a),3); |
| FP16_reduce(w); |
| } |
| |
| /* SU= 8 */ |
| /* Output w in hex */ |
| void YYY::FP48_output(FP48 *w) |
| { |
| printf("["); |
| FP16_output(&(w->a)); |
| printf(","); |
| FP16_output(&(w->b)); |
| printf(","); |
| FP16_output(&(w->c)); |
| printf("]"); |
| } |
| |
| /* Convert g to octet string w */ |
| void YYY::FP48_toOctet(octet *W,FP48 *g) |
| { |
| BIG a; |
| W->len=48*MODBYTES_XXX; |
| |
| FP_redc(a,&(g->a.a.a.a.a)); |
| BIG_toBytes(&(W->val[0]),a); |
| FP_redc(a,&(g->a.a.a.a.b)); |
| BIG_toBytes(&(W->val[MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.a.a.b.a)); |
| BIG_toBytes(&(W->val[2*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.a.a.b.b)); |
| BIG_toBytes(&(W->val[3*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.a.b.a.a)); |
| BIG_toBytes(&(W->val[4*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.a.b.a.b)); |
| BIG_toBytes(&(W->val[5*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.a.b.b.a)); |
| BIG_toBytes(&(W->val[6*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.a.b.b.b)); |
| BIG_toBytes(&(W->val[7*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.b.a.a.a)); |
| BIG_toBytes(&(W->val[8*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.b.a.a.b)); |
| BIG_toBytes(&(W->val[9*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.b.a.b.a)); |
| BIG_toBytes(&(W->val[10*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.b.a.b.b)); |
| BIG_toBytes(&(W->val[11*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.b.b.a.a)); |
| BIG_toBytes(&(W->val[12*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.b.b.a.b)); |
| BIG_toBytes(&(W->val[13*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->a.b.b.b.a)); |
| BIG_toBytes(&(W->val[14*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->a.b.b.b.b)); |
| BIG_toBytes(&(W->val[15*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.a.a.a.a)); |
| BIG_toBytes(&(W->val[16*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.a.a.a.b)); |
| BIG_toBytes(&(W->val[17*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.a.a.b.a)); |
| BIG_toBytes(&(W->val[18*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.a.a.b.b)); |
| BIG_toBytes(&(W->val[19*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.a.b.a.a)); |
| BIG_toBytes(&(W->val[20*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.a.b.a.b)); |
| BIG_toBytes(&(W->val[21*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.a.b.b.a)); |
| BIG_toBytes(&(W->val[22*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.a.b.b.b)); |
| BIG_toBytes(&(W->val[23*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.b.a.a.a)); |
| BIG_toBytes(&(W->val[24*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.b.a.a.b)); |
| BIG_toBytes(&(W->val[25*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.b.a.b.a)); |
| BIG_toBytes(&(W->val[26*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.b.a.b.b)); |
| BIG_toBytes(&(W->val[27*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.b.b.a.a)); |
| BIG_toBytes(&(W->val[28*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.b.b.a.b)); |
| BIG_toBytes(&(W->val[29*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->b.b.b.b.a)); |
| BIG_toBytes(&(W->val[30*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->b.b.b.b.b)); |
| BIG_toBytes(&(W->val[31*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.a.a.a.a)); |
| BIG_toBytes(&(W->val[32*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.a.a.a.b)); |
| BIG_toBytes(&(W->val[33*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.a.a.b.a)); |
| BIG_toBytes(&(W->val[34*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.a.a.b.b)); |
| BIG_toBytes(&(W->val[35*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.a.b.a.a)); |
| BIG_toBytes(&(W->val[36*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.a.b.a.b)); |
| BIG_toBytes(&(W->val[37*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.a.b.b.a)); |
| BIG_toBytes(&(W->val[38*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.a.b.b.b)); |
| BIG_toBytes(&(W->val[39*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.b.a.a.a)); |
| BIG_toBytes(&(W->val[40*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.b.a.a.b)); |
| BIG_toBytes(&(W->val[41*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.b.a.b.a)); |
| BIG_toBytes(&(W->val[42*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.b.a.b.b)); |
| BIG_toBytes(&(W->val[43*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.b.b.a.a)); |
| BIG_toBytes(&(W->val[44*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.b.b.a.b)); |
| BIG_toBytes(&(W->val[45*MODBYTES_XXX]),a); |
| |
| FP_redc(a,&(g->c.b.b.b.a)); |
| BIG_toBytes(&(W->val[46*MODBYTES_XXX]),a); |
| FP_redc(a,&(g->c.b.b.b.b)); |
| BIG_toBytes(&(W->val[47*MODBYTES_XXX]),a); |
| |
| } |
| |
| /* Restore g from octet string w */ |
| void YYY::FP48_fromOctet(FP48 *g,octet *W) |
| { |
| BIG b; |
| |
| BIG_fromBytes(b,&W->val[0]); |
| FP_nres(&(g->a.a.a.a.a),b); |
| BIG_fromBytes(b,&W->val[MODBYTES_XXX]); |
| FP_nres(&(g->a.a.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[2*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.a.b.a),b); |
| BIG_fromBytes(b,&W->val[3*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[4*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.b.a.a),b); |
| BIG_fromBytes(b,&W->val[5*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[6*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.b.b.a),b); |
| BIG_fromBytes(b,&W->val[7*MODBYTES_XXX]); |
| FP_nres(&(g->a.a.b.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[8*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.a.a.a),b); |
| BIG_fromBytes(b,&W->val[9*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[10*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.a.b.a),b); |
| BIG_fromBytes(b,&W->val[11*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[12*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.b.a.a),b); |
| BIG_fromBytes(b,&W->val[13*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[14*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.b.b.a),b); |
| BIG_fromBytes(b,&W->val[15*MODBYTES_XXX]); |
| FP_nres(&(g->a.b.b.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[16*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.a.a.a),b); |
| BIG_fromBytes(b,&W->val[17*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[18*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.a.b.a),b); |
| BIG_fromBytes(b,&W->val[19*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[20*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.b.a.a),b); |
| BIG_fromBytes(b,&W->val[21*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[22*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.b.b.a),b); |
| BIG_fromBytes(b,&W->val[23*MODBYTES_XXX]); |
| FP_nres(&(g->b.a.b.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[24*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.a.a.a),b); |
| BIG_fromBytes(b,&W->val[25*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[26*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.a.b.a),b); |
| BIG_fromBytes(b,&W->val[27*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[28*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.b.a.a),b); |
| BIG_fromBytes(b,&W->val[29*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[30*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.b.b.a),b); |
| BIG_fromBytes(b,&W->val[31*MODBYTES_XXX]); |
| FP_nres(&(g->b.b.b.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[32*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.a.a.a),b); |
| BIG_fromBytes(b,&W->val[33*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[34*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.a.b.a),b); |
| BIG_fromBytes(b,&W->val[35*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[36*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.b.a.a),b); |
| BIG_fromBytes(b,&W->val[37*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[38*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.b.b.a),b); |
| BIG_fromBytes(b,&W->val[39*MODBYTES_XXX]); |
| FP_nres(&(g->c.a.b.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[40*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.a.a.a),b); |
| BIG_fromBytes(b,&W->val[41*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.a.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[42*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.a.b.a),b); |
| BIG_fromBytes(b,&W->val[43*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.a.b.b),b); |
| |
| BIG_fromBytes(b,&W->val[44*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.b.a.a),b); |
| BIG_fromBytes(b,&W->val[45*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.b.a.b),b); |
| |
| BIG_fromBytes(b,&W->val[46*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.b.b.a),b); |
| BIG_fromBytes(b,&W->val[47*MODBYTES_XXX]); |
| FP_nres(&(g->c.b.b.b.b),b); |
| |
| } |
| |
| /* Move b to a if d=1 */ |
| void YYY::FP48_cmove(FP48 *f,FP48 *g,int d) |
| { |
| FP16_cmove(&(f->a),&(g->a),d); |
| FP16_cmove(&(f->b),&(g->b),d); |
| FP16_cmove(&(f->c),&(g->c),d); |
| d=~(d-1); |
| f->type^=(f->type^g->type)&d; |
| } |
| |