/* Line function */
static void PAIR_line(FP12 *v,ECP2 *A,ECP2 *B,BIG Qx,BIG Qy)
{
ECP2 P;
FP2 Z3,X,Y,ZZ,T,NY;
FP4 a,b,c;
int D;
ECP2_copy(&P,A);
if (A==B)
D=ECP2_dbl(A); // check these return numbers...
else
D=ECP2_add(A,B);
if (D<0)
{ /* Infinity */
FP12_one(v);
return;
}
FP2_copy(&Z3,&(A->z));
FP4_zero(&c);
FP2_sqr(&ZZ,&(P.z)); /* ZZ=Z^2 */
if (D==0)
{ /* addition */
ECP2_get(&X,&Y,B);
FP2_mul(&T,&(P.z),&Y); /* T=Z*Y2 */
FP2_mul(&ZZ,&ZZ,&T);
FP2_neg(&NY,&(P.y));
FP2_add(&ZZ,&ZZ,&NY); /* ZZ=Z^3*Y2-Y (slope numerator) */
FP2_pmul(&Z3,&Z3,Qy); /* Z3*Qy */
FP2_mul(&T,&T,&(P.x));
FP2_mul(&X,&X,&NY);
FP2_add(&T,&T,&X); /* Z*Y2*X-X2*Y */
FP4_from_FP2s(&a,&Z3,&T); /* a=[Z3*Qy,Z*Y2*X-X2*Y] */
FP2_neg(&ZZ,&ZZ);
FP2_pmul(&ZZ,&ZZ,Qx);
FP4_from_FP2(&b,&ZZ); /* b=-slope*Qx */
}
else
{ /* doubling */
FP2_sqr(&T,&(P.x));
FP2_imul(&T,&T,3); /* T=3X^2 (slope numerator) */
FP2_sqr(&Y,&(P.y));
FP2_add(&Y,&Y,&Y); /* Y=2Y^2 */
FP2_mul(&Z3,&Z3,&ZZ); /* Z3=Z3*ZZ */
FP2_pmul(&Z3,&Z3,Qy); /* Z3=Z3*ZZ*Qy */
FP2_mul(&X,&(P.x),&T);
FP2_sub(&X,&X,&Y); /* X=X*slope-2Y^2 */
FP4_from_FP2s(&a,&Z3,&X); /* a=[Z3*ZZ*Qy , X*slope-2Y^2] */
FP2_neg(&T,&T);
FP2_mul(&ZZ,&ZZ,&T);
FP2_pmul(&ZZ,&ZZ,Qx);
FP4_from_FP2(&b,&ZZ); /* b=-slope*ZZ*Qx */
}
FP12_from_FP4s(v,&a,&b,&c);
}
/* 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);
}
