/* 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); }
/* Set w=s*x, where s is int */ void FP4_imul(FP4 *w,FP4 *x,int s) { FP2_imul(&(w->a),&(x->a),s); FP2_imul(&(w->b),&(x->b),s); }