/* SU= 8 */ void 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)); }
/* XTR xtr_d function */ void FP4_xtr_D(FP4 *r,FP4 *x) { FP4 w; FP4_copy(r,x); FP4_conj(&w,r); FP4_add(&w,&w,&w); FP4_sqr(r,r); FP4_sub(r,r,&w); FP4_reduce(r); /* reduce here as multiple calls trigger automatic reductions */ }
/* r=x^n using XTR method on traces of FP12s */ void FP4_xtr_pow(FP4 *r,FP4 *x,BIG n) { int i,par,nb; BIG v; FP2 w; FP4 t,a,b,c; BIG_zero(v); BIG_inc(v,3); FP2_from_BIG(&w,v); FP4_from_FP2(&a,&w); FP4_copy(&b,x); FP4_xtr_D(&c,x); BIG_norm(n); par=BIG_parity(n); BIG_copy(v,n); BIG_shr(v,1); if (par==0) {BIG_dec(v,1); BIG_norm(v);} nb=BIG_nbits(v); for (i=nb-1;i>=0;i--) { if (!BIG_bit(v,i)) { FP4_copy(&t,&b); FP4_conj(x,x); FP4_conj(&c,&c); FP4_xtr_A(&b,&a,&b,x,&c); FP4_conj(x,x); FP4_xtr_D(&c,&t); FP4_xtr_D(&a,&a); } else { FP4_conj(&t,&a); FP4_xtr_D(&a,&b); FP4_xtr_A(&b,&c,&b,x,&t); FP4_xtr_D(&c,&c); } } if (par==0) FP4_copy(r,&c); else FP4_copy(r,&b); FP4_reduce(r); }
/* SU= 600 */ void FP12_usqr(FP12 *w,FP12 *x) { FP4 A,B,C,D; FP4_copy(&A,&(x->a)); FP4_sqr(&(w->a),&(x->a)); FP4_add(&D,&(w->a),&(w->a)); FP4_add(&(w->a),&D,&(w->a)); #if CHUNK<64 FP4_norm(&(w->a)); #endif FP4_nconj(&A,&A); FP4_add(&A,&A,&A); FP4_add(&(w->a),&(w->a),&A); FP4_sqr(&B,&(x->c)); FP4_times_i(&B); FP4_add(&D,&B,&B); FP4_add(&B,&B,&D); #if CHUNK<64 FP4_norm(&B); #endif FP4_sqr(&C,&(x->b)); FP4_add(&D,&C,&C); FP4_add(&C,&C,&D); #if CHUNK<64 FP4_norm(&C); #endif 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)); FP12_reduce(w); /* reduce here as in pow function repeated squarings would trigger multiple reductions */ }
/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */ void FP4_xtr_pow2(FP4 *r,FP4 *ck,FP4 *cl,FP4 *ckml,FP4 *ckm2l,BIG a,BIG b) { int i,f2,nb; BIG d,e,w; FP4 t,cu,cv,cumv,cum2v; BIG_norm(a); BIG_norm(b); BIG_copy(e,a); BIG_copy(d,b); FP4_copy(&cu,ck); FP4_copy(&cv,cl); FP4_copy(&cumv,ckml); FP4_copy(&cum2v,ckm2l); f2=0; while (BIG_parity(d)==0 && BIG_parity(e)==0) { BIG_shr(d,1); BIG_shr(e,1); f2++; } while (BIG_comp(d,e)!=0) { if (BIG_comp(d,e)>0) { BIG_imul(w,e,4); BIG_norm(w); if (BIG_comp(d,w)<=0) { BIG_copy(w,d); BIG_copy(d,e); BIG_sub(e,w,e); BIG_norm(e); FP4_xtr_A(&t,&cu,&cv,&cumv,&cum2v); FP4_conj(&cum2v,&cumv); FP4_copy(&cumv,&cv); FP4_copy(&cv,&cu); FP4_copy(&cu,&t); } else if (BIG_parity(d)==0) { BIG_shr(d,1); FP4_conj(r,&cum2v); FP4_xtr_A(&t,&cu,&cumv,&cv,r); FP4_xtr_D(&cum2v,&cumv); FP4_copy(&cumv,&t); FP4_xtr_D(&cu,&cu); } else if (BIG_parity(e)==1) { BIG_sub(d,d,e); BIG_norm(d); BIG_shr(d,1); FP4_xtr_A(&t,&cu,&cv,&cumv,&cum2v); FP4_xtr_D(&cu,&cu); FP4_xtr_D(&cum2v,&cv); FP4_conj(&cum2v,&cum2v); FP4_copy(&cv,&t); } else { BIG_copy(w,d); BIG_copy(d,e); BIG_shr(d,1); BIG_copy(e,w); FP4_xtr_D(&t,&cumv); FP4_conj(&cumv,&cum2v); FP4_conj(&cum2v,&t); FP4_xtr_D(&t,&cv); FP4_copy(&cv,&cu); FP4_copy(&cu,&t); } } if (BIG_comp(d,e)<0) { BIG_imul(w,d,4); BIG_norm(w); if (BIG_comp(e,w)<=0) { BIG_sub(e,e,d); BIG_norm(e); FP4_xtr_A(&t,&cu,&cv,&cumv,&cum2v); FP4_copy(&cum2v,&cumv); FP4_copy(&cumv,&cu); FP4_copy(&cu,&t); } else if (BIG_parity(e)==0) { BIG_copy(w,d); BIG_copy(d,e); BIG_shr(d,1); BIG_copy(e,w); FP4_xtr_D(&t,&cumv); FP4_conj(&cumv,&cum2v); FP4_conj(&cum2v,&t); FP4_xtr_D(&t,&cv); FP4_copy(&cv,&cu); FP4_copy(&cu,&t); } else if (BIG_parity(d)==1) { BIG_copy(w,e); BIG_copy(e,d); BIG_sub(w,w,d); BIG_norm(w); BIG_copy(d,w); BIG_shr(d,1); FP4_xtr_A(&t,&cu,&cv,&cumv,&cum2v); FP4_conj(&cumv,&cumv); FP4_xtr_D(&cum2v,&cu); FP4_conj(&cum2v,&cum2v); FP4_xtr_D(&cu,&cv); FP4_copy(&cv,&t); } else { BIG_shr(d,1); FP4_conj(r,&cum2v); FP4_xtr_A(&t,&cu,&cumv,&cv,r); FP4_xtr_D(&cum2v,&cumv); FP4_copy(&cumv,&t); FP4_xtr_D(&cu,&cu); } } } FP4_xtr_A(r,&cu,&cv,&cumv,&cum2v); for (i=0;i<f2;i++) FP4_xtr_D(r,r); FP4_xtr_pow(r,r,d); }