/* 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= 240 */
void FP4_pow(FP4 *r,FP4* a,BIG b)
{
FP4 w;
BIG z,zilch;
int bt;
BIG_zero(zilch);
BIG_norm(b);
BIG_copy(z,b);
FP4_copy(&w,a);
FP4_one(r);
while(1)
{
bt=BIG_parity(z);
BIG_shr(z,1);
if (bt) FP4_mul(r,r,&w);
if (BIG_comp(z,zilch)==0) break;
FP4_sqr(&w,&w);
}
FP4_reduce(r);
}
/* SU= 8 */
void FP12_trace(FP4 *w,FP12 *x)
{
FP4_imul(w,&(x->a),3);
FP4_reduce(w);
}
/* reduce all components of w */
void FP12_reduce(FP12 *w)
{
FP4_reduce(&(w->a));
FP4_reduce(&(w->b));
FP4_reduce(&(w->c));
}
