void elliptic_add(Poly2Mod& XT,Poly2Mod& XTy,Poly2Mod& YT,Poly2Mod& YTy,Poly2Mod& ZT,Poly2Mod& X,Poly2Mod& Y,Poly2Mod& Yy)
{ // add (X,Y,Z) to (XT,YT,ZT) on an elliptic curve
// The point Y is of the form A(x)+B(x).y
Poly2Mod ZT2,ZT3,W1,W2,W3,W4,W5,W5y,W6,W6y,W7,W8,W8y,W9,W9y;
ZT2=(ZT*ZT);
W3=XT+X*ZT2;
ZT3=ZT2*ZT;
W5=ZT3*Y;
W5y=ZT3*Yy;
W6=YT+W5;
W6y=YTy+W5y;
if (iszero(W3))
{
if (iszero(W6) && iszero(W6y))
{ // should have doubled!
elliptic_dup(XT,YT,YTy,ZT);
XTy=0;
return;
}
ZT.clear();
return;
}
ZT*=W3;
W8=W6*X+ZT*Y;
W8y=W6y*X+ZT*Yy;
W9=W6+ZT;
W1=ZT*ZT;
W2=W6y*W6y;
XT=A*W1+W3*W3*W3+W6*W9+W2*MFX;
XTy=W9*W6y+W6y*W6+W2*XX;
W2=W6y*XTy;
YT=W9*XT+W2*MFX+W8*W1;
YTy=XT*W6y+W9*XTy+W2*XX+W1*W8y;
}
void reduce(const Poly2& p,Poly2Mod& rem)
{
int m,d;
GF2m t;
big *G;
term2 *ptr,*pos=NULL;
int n=degree(p);
int degm=degree(Modulus);
if (n-degm < KARAT_BREAK_EVEN)
{
rem=(Poly2Mod)p;
return;
}
G=(big *)mr_alloc(2*(N+2),sizeof(big));
ptr=p.start;
while (ptr!=NULL)
{
G[ptr->n]=getbig(ptr->an);
ptr=ptr->next;
}
karmul2_poly(N,T,GRF,&G[N],W); // W=(G/x^n) * h
for (d=N-1;d<2*N;d++) copy(W[d],Q[d-N+1]);
m=N+1; if(m%2==1) m=N+2; // make sure m is even - pad if necessary
for (d=m;d<2*m;d++) copy(G[d],W[d]);
karmul2_poly_upper(m,T,GF,Q,W);
pos=NULL;
rem.clear();
for (d=N-1;d>=0;d--)
{
add2(W[d],G[d],W[d]);
t=W[d];
if (t.iszero()) continue;
pos=rem.addterm(t,d,pos);
}
mr_free(G);
}