G1Projective add double

Author: Hakkush-07

src/circuits/bn254/g1.rs

@@ -7,32 +7,78 @@ impl G1Projective {
 }
 
 impl G1Projective {
+    // http://koclab.cs.ucsb.edu/teaching/ccs130h/2018/09projective.pdf
     pub fn add(p: Wires, q: Wires) -> Circuit {
         assert_eq!(p.len(), Self::N_BITS);
         assert_eq!(q.len(), Self::N_BITS);
         let mut circuit = Circuit::empty();
 
-        let px = p[0..Fq::N_BITS].to_vec();
-        let py = p[Fq::N_BITS..2*Fq::N_BITS].to_vec();
-        let pz = p[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
-        let qx = q[0..Fq::N_BITS].to_vec();
-        let qy = q[Fq::N_BITS..2*Fq::N_BITS].to_vec();
-        let qz = q[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
+        let x1 = p[0..Fq::N_BITS].to_vec();
+        let y1 = p[Fq::N_BITS..2*Fq::N_BITS].to_vec();
+        let z1 = p[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
+        let x2 = q[0..Fq::N_BITS].to_vec();
+        let y2 = q[Fq::N_BITS..2*Fq::N_BITS].to_vec();
+        let z2 = q[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
 
-        todo!();
+        let z1s = circuit.extend(Fq::square(z1.clone()));
+        let z2s = circuit.extend(Fq::square(z2.clone()));
+        let u1 = circuit.extend(Fq::mul(x1.clone(), z2s.clone()));
+        let u2 = circuit.extend(Fq::mul(x2.clone(), z1s.clone()));
+        let s1 = circuit.extend(Fq::mul(y1.clone(), z2s.clone()));
+        let s2 = circuit.extend(Fq::mul(y2.clone(), z1s.clone()));
+        let r = circuit.extend(Fq::sub(s1.clone(), s2.clone()));
+        let h = circuit.extend(Fq::sub(u1.clone(), u2.clone()));
+        let h2 = circuit.extend(Fq::square(h.clone()));
+        let g = circuit.extend(Fq::mul(h.clone(), h2.clone()));
+        let v = circuit.extend(Fq::mul(u1.clone(), h2.clone()));
+        let r2 = circuit.extend(Fq::square(r.clone()));
+        let r2g = circuit.extend(Fq::add(r2.clone(), g.clone()));
+        let vd = circuit.extend(Fq::double(v.clone()));
+        let x3 = circuit.extend(Fq::sub(r2g.clone(), vd.clone()));
+        let vx3 = circuit.extend(Fq::sub(v.clone(), x3.clone()));
+        let w = circuit.extend(Fq::mul(r.clone(), vx3.clone()));
+        let s1g = circuit.extend(Fq::mul(s1.clone(), g.clone()));
+        let y3 = circuit.extend(Fq::sub(w.clone(), s1g.clone()));
+        let z1z2 = circuit.extend(Fq::mul(z1.clone(), z2.clone()));
+        let z3 = circuit.extend(Fq::mul(z1z2.clone(), h.clone()));
 
+        circuit.add_wires(x3);
+        circuit.add_wires(y3);
+        circuit.add_wires(z3);
+    
         circuit
     }
 
     pub fn double(p: Wires) -> Circuit {
         assert_eq!(p.len(), Self::N_BITS);
         let mut circuit = Circuit::empty();
 
-        let px = p[0..Fq::N_BITS].to_vec();
-        let py = p[Fq::N_BITS..2*Fq::N_BITS].to_vec();
-        let pz = p[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
+        let x = p[0..Fq::N_BITS].to_vec();
+        let y = p[Fq::N_BITS..2*Fq::N_BITS].to_vec();
+        let z = p[2*Fq::N_BITS..3*Fq::N_BITS].to_vec();
 
-        todo!();
+        let x2 = circuit.extend(Fq::square(x.clone()));
+        let y2 = circuit.extend(Fq::square(y.clone()));
+        let m = circuit.extend(Fq::triple(x2.clone()));
+        let t = circuit.extend(Fq::square(y2.clone()));
+        let xy2 = circuit.extend(Fq::mul(x.clone(), y2.clone()));
+        let xy2d = circuit.extend(Fq::double(xy2.clone()));
+        let s = circuit.extend(Fq::double(xy2d.clone()));
+        let m2 = circuit.extend(Fq::square(m.clone()));
+        let sd = circuit.extend(Fq::double(s.clone()));
+        let xr = circuit.extend(Fq::sub(m2.clone(), sd.clone()));
+        let sxr = circuit.extend(Fq::sub(s.clone(), xr.clone()));
+        let msxr = circuit.extend(Fq::mul(m.clone(), sxr.clone()));
+        let td = circuit.extend(Fq::double(t.clone()));
+        let tdd = circuit.extend(Fq::double(td.clone()));
+        let tddd = circuit.extend(Fq::double(tdd.clone()));
+        let yr = circuit.extend(Fq::sub(msxr.clone(), tddd.clone()));
+        let yz = circuit.extend(Fq::mul(y.clone(), z.clone()));
+        let zr = circuit.extend(Fq::double(yz.clone()));
+
+        circuit.add_wires(xr);
+        circuit.add_wires(yr);
+        circuit.add_wires(zr);
 
         circuit
     }