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26 7u83 1 
# Elliptic curve group operations in jacobian coordinates:
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#	x=X/Z^2
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#	x=Y/Z^3
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jacobian_new(x,y,z, X,Y,Z) {
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	X = x;
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	Y = y;
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	Z = z;
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}
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jacobian_inf(X,Y,Z) {
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	X,Y,Z = jacobian_new(0,1,0);
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}
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jacobian_affine(p, X,Y,Z) mod(p) {
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	if(Z != 0) {
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		ZZ = Z^2;
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		ZZZ = ZZ*Z;
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		X = X / ZZ;
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		Y = Y / ZZZ;
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		Z = 1;
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	}
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}
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jacobian_dbl(p,a, X1,Y1,Z1, X3,Y3,Z3) mod(p) {
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	if(Y1 == 0) {
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		X3,Y3,Z3 = jacobian_inf();
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	} else {
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		XX = X1^2;
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		YY = Y1^2;
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		YYYY = YY^2;
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		ZZ = Z1^2;
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		S = 2*((X1+YY)^2-XX-YYYY);
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		M = 3*XX+a*ZZ^2;
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		Z3 = (Y1+Z1)^2-YY-ZZ;
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		X3 = M^2-2*S;
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		Y3 = M*(S-X3)-8*YYYY;
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	}
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}
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jacobian_add(p,a, X1,Y1,Z1, X2,Y2,Z2, X3,Y3,Z3) mod(p) {
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	Z1Z1 = Z1^2;
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	Z2Z2 = Z2^2;
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	U1 = X1*Z2Z2;
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	U2 = X2*Z1Z1;
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	S1 = Y1*Z2*Z2Z2;
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	S2 = Y2*Z1*Z1Z1;
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	if(U1 == U2) {
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		if(S1 != S2) {
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			X3,Y3,Z3 = jacobian_inf();
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		} else {
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			X3,Y3,Z3 = jacobian_dbl(p,a, X1,Y1,Z1);
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		}
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	} else {
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		H = U2-U1;
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		I = (2*H)^2;
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		J = H*I;
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		r = 2*(S2-S1);
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		V = U1*I;
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		X3 = r^2-J-2*V;
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		Y3 = r*(V-X3)-2*S1*J;
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		Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H;
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	}
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}