Select points in subgroup and calculate x from y

calcpedersenbases/calcpedersenbases.js

@@ -3,6 +3,32 @@ const bigInt = require("snarkjs").bigInt;
 const createBlakeHash = require("blake-hash");
 const assert = require("assert");
 
+function addPoint(a,b, q) {
+    const cta = bigInt("168700");
+    const d = bigInt("168696");
+
+    const res = [];
+    res[0] = bigInt((a[0]*b[1] + b[0]*a[1]) *  bigInt(bigInt("1") + d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+    res[1] = bigInt((a[1]*b[1] - cta*a[0]*b[0]) * bigInt(bigInt("1") - d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+    return res;
+}
+
+function mulPointEscalar(base, e, q) {
+    let res = [bigInt("0"),bigInt("1")];
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = addPoint(res, exp, q);
+        }
+        exp = addPoint(exp, exp, q);
+        rem = rem.shr(1);
+    }
+
+    return res;
+}
+
 function getPoint(S) {
     const F = bn128.Fr;
     const h = createBlakeHash("blake256").update(S).digest();
@@ -15,26 +41,30 @@ function getPoint(S) {
         sign = true;
     }
 
-    let x = bigInt(0);
+    let y = bigInt(0);
     for (let i=0; i<32; i++) {
-        x = x.shl(8);
-        x = x.add(bigInt(h[i]));
+        y = y.shl(8);
+        y = y.add(bigInt(h[i]));
     }
 
     const a = bigInt("168700");
     const d = bigInt("168696");
 
-    const x2 = F.square(x);
+    const y2 = F.square(y);
+
+    let x = F.sqrt(F.div(
+        F.sub(F.one, y2),
+        F.sub(a, F.mul(d, y2))));
+
+    if (x == null) return null;
 
-    let y = F.sqrt(F.div(
-        F.sub(F.one, F.mul(a, x2)),
-        F.sub(F.one, F.mul(d, x2))));
+    if (sign) x = F.neg(x);
 
-    if (y == null) return null;
+    const p = [bn128.Fr.affine(x), bn128.Fr.affine(y)];
 
-    if (sign) y = F.neg(y);
+    const p8 =mulPointEscalar(p, 8, q);
 
-    return [bn128.Fr.affine(x), bn128.Fr.affine(y)];
+    return p8;
 }
 
 
@@ -47,10 +77,21 @@ function generatePoint(S) {
         p = getPoint(S+"_"+sidx);
         idx++;
     }
-    assert(inCurve(p));
+    assert(inCurve(p), "Point not in curve");
     return p;
 }
 
+
+
+
+
+const q = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+const r = bigInt("21888242871839275222246405745257275088614511777268538073601725287587578984328").shr(3);
+function isLowGrade(p, q) {
+    const res= mulPointEscalar(p, r, q);
+    return (res[0].equals(bigInt(0))) && (res[1].equals(bigInt(1)));
+}
+
 function inCurve(p) {
     const F = bn128.Fr;
 
@@ -60,15 +101,20 @@ function inCurve(p) {
     const x2 = F.square(p[0]);
     const y2 = F.square(p[1]);
 
-    return F.equals(
+    if (!F.equals(
         F.add(F.mul(a, x2), y2),
-        F.add(F.one, F.mul(F.mul(x2, y2), d)));
+        F.add(F.one, F.mul(F.mul(x2, y2), d)))) return false;
+
+    if (!isLowGrade(p, q)) return false;
+
+    return true;
 }
 
 const g = [
     bigInt("17777552123799933955779906779655732241715742912184938656739573121738514868268"),
     bigInt("2626589144620713026669568689430873010625803728049924121243784502389097019475")];
 
+
 if (!inCurve(g)) {
     throw new Error("Generator not In curve -> Some thing goes wrong...");
 }