g1 curve done

src/g1curve.js

@@ -1,29 +1,147 @@
 const bigInt = require("big-integer");
-const ZnField = require("./znfield.js");
+
+const q = new bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
 
 module.eports = class G1Curve {
 
     constructor() {
-        this.F = new ZnField(bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583"));
-        this.g = [
-
-        ];
-
+        this.g = [ bigInt(1), bigInt(2), bigInt(1) ];
+        this.zero = [ bigInt(0), bigInt(1), bigInt(0) ];
     }
 
+    isZero(p) {
+        return p[2].isZero();
+    }
     add(p1, p2) {
-        // TODO
-        throw new Error("Not Implementted");
+
+        if (this.isZero(p1)) return p2;
+        if (this.isZero(p2)) return p1;
+
+        const res = new Array(3);
+
+        const Z1Z1 = p1[2].square().mod(q);
+        const Z2Z2 = p2[2].square().mod(q);
+
+        const U1 = p1[0].times(Z2Z2).mod(q);
+        const U2 = p2[0].times(Z1Z1).mod(q);
+
+        const Z1_cubed = p1[2].times(Z1Z1).mod(q);
+        const Z2_cubed = p2[2].times(Z2Z2).mod(q);
+
+        const S1 = p1[1].times(Z2_cubed).mod(q);
+        const S2 = p2[1].times(Z1_cubed).mod(q);
+
+        if (U1.equals(U2) && (S1.equals(S2))) {
+            return this.double(p1);
+        }
+
+        let H = U2.minus(U1);
+        if (H.isNegative()) H = H.add(q);
+
+        let S2_minus_S1 = S2.minus(S1);
+        if (S2_minus_S1.isNegative()) S2_minus_S1 = S2_minus_S1.add(q);
+
+        const I = H.add(H).square().mod(q);
+        const J = H.times(I).mod(q);
+
+        const r = S2_minus_S1.add(S2_minus_S1);
+        const V = U1.times(I).mod(q);
+
+        res[0] = r.square().minus(J).minus(V).minus(V).mod(q);
+        if (res[0].isNegative()) res[0] = res[0].add(q);
+
+        const S1_J = S1.times(J).mod(q);
+
+        res[1] = r.times(V.minus(res[0])).minus(S1_J).minus(S1_J).mod(q);
+        if (res[1].isNegative()) res[1] = res[1].add(q);
+
+        res[2] = p1[2].add(p2[2]).square().minus(Z1Z1).minus(Z2Z2).mod(q);
+        res[2] = res[2].times(H).mod(q);
+        if (res[2].isNegative()) res[2] = res[2].add(q);
+
+        return res;
     }
 
-    double(p1) {
-        // TODO
-        throw new Error("Not Implementted");
+    double(p) {
+        const res = new Array(3);
+
+        if (this.isZero(p)) return p;
+
+        const A = p[0].square().mod(q);
+        const B = p[1].square().mod(q);
+        const C = B.square().mod(q);
+
+        let D = p[0].add(B).square().minus(A).minus(C);
+        D = D.add(D);
+
+        const E = A.times(3);
+        const F = E.square();
+
+        res[0] = F.minus(D).minus(D).mod(q);
+        if (res[0].isNegative()) res[0] = res[0].add(q);
+
+        const eightC = C.times(8);
+
+        res[1] = E.times(D.minus(res[0])).minus(eightC).mod(q);
+        if (res[1].isNegative()) res[1] = res[1].add(q);
+
+        const Y1Z1 = p[1].times(p[2]);
+        res[2] = Y1Z1.add(Y1Z1).mod(q);
+
+        return res;
     }
 
-    mulEscalar(p1, e) {
-        // TODO
-        throw new Error("Not Implementted");
+    toAffineCoordinates(p) {
+        if (this.isZero(p)) {
+            return this.zero;
+        } else {
+            const Z_inv = p[2].modInv(q);
+            const Z2_inv = Z_inv.square().mod(q);
+            const Z3_inv = Z2_inv.times(Z_inv).mod(q);
+
+            const res = new Array(3);
+            res[0] = p[0].times(Z2_inv).mod(q);
+            res[1] = p[1].times(Z3_inv).mod(q);
+            res[2] = bigInt(1);
+
+            return res;
+        }
+    }
+
+    mulEscalar(base, e) {
+        let res = this.zero;
+        let rem = e;
+        let exp = base;
+
+        while (! rem.isZero()) {
+            if (rem.isOdd()) {
+                res = this.add(res, exp);
+            }
+            exp = this.double(exp);
+            rem = rem.shiftRight(1);
+        }
+
+        return res;
     }
 
 };
+
+const G1 = new module.eports();
+
+
+const r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+// const np = G1.mulEscalar(G1.g, bigInt(2));
+
+const np = G1.mulEscalar(G1.g, r.add(1));
+const p = G1.toAffineCoordinates(np);
+
+/*
+const np2 = G1.add(G1.g, G1.g);
+const np3 = G1.add(G1.g, np2);
+
+const p = G1.toAffineCoordinates(np3);
+*/
+
+console.log(p[0].toString() + ", " + p[1].toString() + ", " + p[2].toString());
+
+