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BP Code
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This commit is contained in:
Brandon Goodell
GitHub
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3 changed files with 1332 additions and 0 deletions
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package how.monero.hodl.bulletproof;
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import how.monero.hodl.crypto.Curve25519Point;
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import how.monero.hodl.crypto.Scalar;
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import how.monero.hodl.crypto.CryptoUtil;
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import how.monero.hodl.util.ByteUtil;
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import java.math.BigInteger;
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import how.monero.hodl.util.VarInt;
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import java.util.Random;
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import static how.monero.hodl.crypto.Scalar.randomScalar;
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import static how.monero.hodl.crypto.CryptoUtil.*;
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import static how.monero.hodl.util.ByteUtil.*;
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public class LinearBulletproof
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{
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private static int N;
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private static Curve25519Point G;
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private static Curve25519Point H;
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private static Curve25519Point[] Gi;
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private static Curve25519Point[] Hi;
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public static class ProofTuple
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{
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private Curve25519Point V;
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private Curve25519Point A;
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private Curve25519Point S;
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private Curve25519Point T1;
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private Curve25519Point T2;
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private Scalar taux;
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private Scalar mu;
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private Scalar[] l;
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private Scalar[] r;
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public ProofTuple(Curve25519Point V, Curve25519Point A, Curve25519Point S, Curve25519Point T1, Curve25519Point T2, Scalar taux, Scalar mu, Scalar[] l, Scalar[] r)
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{
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this.V = V;
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this.A = A;
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this.S = S;
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this.T1 = T1;
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this.T2 = T2;
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this.taux = taux;
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this.mu = mu;
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this.l = l;
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this.r = r;
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}
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}
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/* Given two scalar arrays, construct a vector commitment */
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public static Curve25519Point VectorExponent(Scalar[] a, Scalar[] b)
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{
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Curve25519Point Result = Curve25519Point.ZERO;
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for (int i = 0; i < N; i++)
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{
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Result = Result.add(Gi[i].scalarMultiply(a[i]));
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Result = Result.add(Hi[i].scalarMultiply(b[i]));
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}
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return Result;
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}
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/* Given a scalar, construct a vector of powers */
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public static Scalar[] VectorPowers(Scalar x)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = x.pow(i);
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}
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return result;
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}
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/* Given two scalar arrays, construct the inner product */
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public static Scalar InnerProduct(Scalar[] a, Scalar[] b)
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{
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Scalar result = Scalar.ZERO;
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for (int i = 0; i < N; i++)
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{
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result = result.add(a[i].mul(b[i]));
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}
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return result;
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}
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/* Given two scalar arrays, construct the Hadamard product */
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public static Scalar[] Hadamard(Scalar[] a, Scalar[] b)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = a[i].mul(b[i]);
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}
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return result;
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}
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/* Add two vectors */
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public static Scalar[] VectorAdd(Scalar[] a, Scalar[] b)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = a[i].add(b[i]);
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}
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return result;
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}
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/* Subtract two vectors */
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public static Scalar[] VectorSubtract(Scalar[] a, Scalar[] b)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = a[i].sub(b[i]);
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}
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return result;
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}
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/* Multiply a scalar and a vector */
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public static Scalar[] VectorScalar(Scalar[] a, Scalar x)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = a[i].mul(x);
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}
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return result;
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}
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/* Compute the inverse of a scalar, the stupid way */
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public static Scalar Invert(Scalar x)
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{
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Scalar inverse = new Scalar(x.toBigInteger().modInverse(CryptoUtil.l));
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assert x.mul(inverse).equals(Scalar.ONE);
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return inverse;
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}
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/* Given a value v (0..2^N-1) and a mask gamma, construct a range proof */
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public static ProofTuple PROVE(Scalar v, Scalar gamma)
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{
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Curve25519Point V = G.scalarMultiply(v).add(H.scalarMultiply(gamma));
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// PAPER LINES 36-37
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Scalar[] aL = new Scalar[N];
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Scalar[] aR = new Scalar[N];
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BigInteger tempV = v.toBigInteger();
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for (int i = N-1; i >= 0; i--)
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{
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BigInteger basePow = BigInteger.valueOf(2).pow(i);
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if (tempV.divide(basePow).equals(BigInteger.ZERO))
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{
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aL[i] = Scalar.ZERO;
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}
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else
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{
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aL[i] = Scalar.ONE;
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tempV = tempV.subtract(basePow);
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}
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aR[i] = aL[i].sub(Scalar.ONE);
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}
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// DEBUG: Test to ensure this recovers the value
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BigInteger test_aL = BigInteger.ZERO;
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BigInteger test_aR = BigInteger.ZERO;
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for (int i = 0; i < N; i++)
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{
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if (aL[i].equals(Scalar.ONE))
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test_aL = test_aL.add(BigInteger.valueOf(2).pow(i));
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if (aR[i].equals(Scalar.ZERO))
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test_aR = test_aR.add(BigInteger.valueOf(2).pow(i));
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}
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assert test_aL.equals(v.toBigInteger());
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assert test_aR.equals(v.toBigInteger());
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// PAPER LINES 38-39
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Scalar alpha = randomScalar();
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Curve25519Point A = VectorExponent(aL,aR).add(H.scalarMultiply(alpha));
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// PAPER LINES 40-42
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Scalar[] sL = new Scalar[N];
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Scalar[] sR = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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sL[i] = randomScalar();
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sR[i] = randomScalar();
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}
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Scalar rho = randomScalar();
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Curve25519Point S = VectorExponent(sL,sR).add(H.scalarMultiply(rho));
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// PAPER LINES 43-45
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Scalar y = hashToScalar(concat(A.toBytes(),S.toBytes()));
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Scalar z = hashToScalar(y.bytes);
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Scalar t0 = Scalar.ZERO;
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Scalar t1 = Scalar.ZERO;
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Scalar t2 = Scalar.ZERO;
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t0 = t0.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
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t0 = t0.add(z.sq().mul(v));
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Scalar k = Scalar.ZERO;
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k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
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k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
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t0 = t0.add(k);
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// DEBUG: Test the value of t0 has the correct form
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Scalar test_t0 = Scalar.ZERO;
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test_t0 = test_t0.add(InnerProduct(aL,Hadamard(aR,VectorPowers(y))));
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test_t0 = test_t0.add(z.mul(InnerProduct(VectorSubtract(aL,aR),VectorPowers(y))));
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test_t0 = test_t0.add(z.sq().mul(InnerProduct(VectorPowers(Scalar.TWO),aL)));
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test_t0 = test_t0.add(k);
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assert test_t0.equals(t0);
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t1 = t1.add(InnerProduct(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),Hadamard(VectorPowers(y),sR)));
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t1 = t1.add(InnerProduct(sL,VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorScalar(VectorPowers(Scalar.ONE),z))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()))));
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t2 = t2.add(InnerProduct(sL,Hadamard(VectorPowers(y),sR)));
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// PAPER LINES 47-48
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Scalar tau1 = randomScalar();
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Scalar tau2 = randomScalar();
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Curve25519Point T1 = G.scalarMultiply(t1).add(H.scalarMultiply(tau1));
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Curve25519Point T2 = G.scalarMultiply(t2).add(H.scalarMultiply(tau2));
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// PAPER LINES 49-51
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Scalar x = hashToScalar(concat(z.bytes,T1.toBytes(),T2.toBytes()));
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// PAPER LINES 52-53
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Scalar taux = Scalar.ZERO;
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taux = tau1.mul(x);
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taux = taux.add(tau2.mul(x.sq()));
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taux = taux.add(gamma.mul(z.sq()));
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Scalar mu = x.mul(rho).add(alpha);
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// PAPER LINES 54-57
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Scalar[] l = new Scalar[N];
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Scalar[] r = new Scalar[N];
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l = VectorAdd(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),VectorScalar(sL,x));
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r = VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorAdd(VectorScalar(VectorPowers(Scalar.ONE),z),VectorScalar(sR,x)))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()));
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// DEBUG: Test if the l and r vectors match the polynomial forms
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Scalar test_t = Scalar.ZERO;
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test_t = test_t.add(t0).add(t1.mul(x));
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test_t = test_t.add(t2.mul(x.sq()));
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assert test_t.equals(InnerProduct(l,r));
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// PAPER LINE 58
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return new ProofTuple(V,A,S,T1,T2,taux,mu,l,r);
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}
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/* Given a range proof, determine if it is valid */
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public static boolean VERIFY(ProofTuple proof)
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{
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// Reconstruct the challenges
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Scalar y = hashToScalar(concat(proof.A.toBytes(),proof.S.toBytes()));
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Scalar z = hashToScalar(y.bytes);
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Scalar x = hashToScalar(concat(z.bytes,proof.T1.toBytes(),proof.T2.toBytes()));
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// PAPER LINE 60
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Scalar t = InnerProduct(proof.l,proof.r);
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// PAPER LINE 61
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Curve25519Point L61Left = H.scalarMultiply(proof.taux).add(G.scalarMultiply(t));
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Scalar k = Scalar.ZERO;
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k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
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k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
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Curve25519Point L61Right = G.scalarMultiply(k.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y)))));
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L61Right = L61Right.add(proof.V.scalarMultiply(z.sq()));
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L61Right = L61Right.add(proof.T1.scalarMultiply(x));
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L61Right = L61Right.add(proof.T2.scalarMultiply(x.sq()));
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if (!L61Right.equals(L61Left))
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{
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return false;
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}
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// PAPER LINE 62
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Curve25519Point P = Curve25519Point.ZERO;
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P = P.add(proof.A);
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P = P.add(proof.S.scalarMultiply(x));
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Scalar[] Gexp = new Scalar[N];
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for (int i = 0; i < N; i++)
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Gexp[i] = Scalar.ZERO.sub(z);
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Scalar[] Hexp = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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Hexp[i] = Scalar.ZERO;
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Hexp[i] = Hexp[i].add(z.mul(y.pow(i)));
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Hexp[i] = Hexp[i].add(z.sq().mul(Scalar.TWO.pow(i)));
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Hexp[i] = Hexp[i].mul(Invert(y).pow(i));
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}
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P = P.add(VectorExponent(Gexp,Hexp));
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// PAPER LINE 63
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for (int i = 0; i < N; i++)
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{
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Hexp[i] = Scalar.ZERO;
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Hexp[i] = Hexp[i].add(proof.r[i]);
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Hexp[i] = Hexp[i].mul(Invert(y).pow(i));
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}
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Curve25519Point L63Right = VectorExponent(proof.l,Hexp).add(H.scalarMultiply(proof.mu));
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if (!L63Right.equals(P))
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{
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return false;
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}
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return true;
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}
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public static void main(String[] args)
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{
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// Number of bits in the range
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N = 64;
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// Set the curve base points
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G = Curve25519Point.G;
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H = Curve25519Point.hashToPoint(G);
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Gi = new Curve25519Point[N];
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Hi = new Curve25519Point[N];
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for (int i = 0; i < N; i++)
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{
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Gi[i] = getHpnGLookup(i);
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Hi[i] = getHpnGLookup(N+i);
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}
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// Run a bunch of randomized trials
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Random rando = new Random();
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int TRIALS = 250;
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int count = 0;
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while (count < TRIALS)
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{
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long amount = rando.nextLong();
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if (amount > Math.pow(2,N)-1 || amount < 0)
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continue;
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ProofTuple proof = PROVE(new Scalar(BigInteger.valueOf(amount)),randomScalar());
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if (!VERIFY(proof))
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System.out.println("Test failed");
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count += 1;
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}
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}
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}
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@ -0,0 +1,497 @@
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package how.monero.hodl.bulletproof;
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import how.monero.hodl.crypto.Curve25519Point;
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import how.monero.hodl.crypto.Scalar;
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import how.monero.hodl.crypto.CryptoUtil;
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import java.math.BigInteger;
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import java.util.Random;
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import static how.monero.hodl.crypto.Scalar.randomScalar;
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import static how.monero.hodl.crypto.CryptoUtil.*;
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import static how.monero.hodl.util.ByteUtil.*;
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public class LogBulletproof
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{
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private static int N;
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private static int logN;
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private static Curve25519Point G;
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private static Curve25519Point H;
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private static Curve25519Point[] Gi;
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private static Curve25519Point[] Hi;
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public static class ProofTuple
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{
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private Curve25519Point V;
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private Curve25519Point A;
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private Curve25519Point S;
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private Curve25519Point T1;
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private Curve25519Point T2;
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private Scalar taux;
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private Scalar mu;
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private Curve25519Point[] L;
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private Curve25519Point[] R;
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private Scalar a;
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private Scalar b;
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private Scalar t;
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public ProofTuple(Curve25519Point V, Curve25519Point A, Curve25519Point S, Curve25519Point T1, Curve25519Point T2, Scalar taux, Scalar mu, Curve25519Point[] L, Curve25519Point[] R, Scalar a, Scalar b, Scalar t)
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{
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this.V = V;
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this.A = A;
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this.S = S;
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this.T1 = T1;
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this.T2 = T2;
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this.taux = taux;
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this.mu = mu;
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this.L = L;
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this.R = R;
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this.a = a;
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this.b = b;
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this.t = t;
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}
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}
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/* Given two scalar arrays, construct a vector commitment */
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public static Curve25519Point VectorExponent(Scalar[] a, Scalar[] b)
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{
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assert a.length == N && b.length == N;
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Curve25519Point Result = Curve25519Point.ZERO;
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for (int i = 0; i < N; i++)
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{
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Result = Result.add(Gi[i].scalarMultiply(a[i]));
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Result = Result.add(Hi[i].scalarMultiply(b[i]));
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}
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return Result;
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}
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/* Compute a custom vector-scalar commitment */
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public static Curve25519Point VectorExponentCustom(Curve25519Point[] A, Curve25519Point[] B, Scalar[] a, Scalar[] b)
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{
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assert a.length == A.length && b.length == B.length && a.length == b.length;
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Curve25519Point Result = Curve25519Point.ZERO;
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for (int i = 0; i < a.length; i++)
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{
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Result = Result.add(A[i].scalarMultiply(a[i]));
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Result = Result.add(B[i].scalarMultiply(b[i]));
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}
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return Result;
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}
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/* Given a scalar, construct a vector of powers */
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public static Scalar[] VectorPowers(Scalar x)
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{
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Scalar[] result = new Scalar[N];
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for (int i = 0; i < N; i++)
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{
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result[i] = x.pow(i);
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}
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return result;
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}
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/* Given two scalar arrays, construct the inner product */
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public static Scalar InnerProduct(Scalar[] a, Scalar[] b)
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{
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assert a.length == b.length;
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Scalar result = Scalar.ZERO;
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for (int i = 0; i < a.length; i++)
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{
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result = result.add(a[i].mul(b[i]));
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given two scalar arrays, construct the Hadamard product */
|
||||
public static Scalar[] Hadamard(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].mul(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given two curvepoint arrays, construct the Hadamard product */
|
||||
public static Curve25519Point[] Hadamard2(Curve25519Point[] A, Curve25519Point[] B)
|
||||
{
|
||||
assert A.length == B.length;
|
||||
|
||||
Curve25519Point[] Result = new Curve25519Point[A.length];
|
||||
for (int i = 0; i < A.length; i++)
|
||||
{
|
||||
Result[i] = A[i].add(B[i]);
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Add two vectors */
|
||||
public static Scalar[] VectorAdd(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].add(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Subtract two vectors */
|
||||
public static Scalar[] VectorSubtract(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].sub(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Multiply a scalar and a vector */
|
||||
public static Scalar[] VectorScalar(Scalar[] a, Scalar x)
|
||||
{
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].mul(x);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Exponentiate a curve vector by a scalar */
|
||||
public static Curve25519Point[] VectorScalar2(Curve25519Point[] A, Scalar x)
|
||||
{
|
||||
Curve25519Point[] Result = new Curve25519Point[A.length];
|
||||
for (int i = 0; i < A.length; i++)
|
||||
{
|
||||
Result[i] = A[i].scalarMultiply(x);
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Compute the inverse of a scalar, the stupid way */
|
||||
public static Scalar Invert(Scalar x)
|
||||
{
|
||||
Scalar inverse = new Scalar(x.toBigInteger().modInverse(CryptoUtil.l));
|
||||
|
||||
assert x.mul(inverse).equals(Scalar.ONE);
|
||||
return inverse;
|
||||
}
|
||||
|
||||
/* Compute the slice of a curvepoint vector */
|
||||
public static Curve25519Point[] CurveSlice(Curve25519Point[] a, int start, int stop)
|
||||
{
|
||||
Curve25519Point[] Result = new Curve25519Point[stop-start];
|
||||
for (int i = start; i < stop; i++)
|
||||
{
|
||||
Result[i-start] = a[i];
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Compute the slice of a scalar vector */
|
||||
public static Scalar[] ScalarSlice(Scalar[] a, int start, int stop)
|
||||
{
|
||||
Scalar[] result = new Scalar[stop-start];
|
||||
for (int i = start; i < stop; i++)
|
||||
{
|
||||
result[i-start] = a[i];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given a value v (0..2^N-1) and a mask gamma, construct a range proof */
|
||||
public static ProofTuple PROVE(Scalar v, Scalar gamma)
|
||||
{
|
||||
Curve25519Point V = G.scalarMultiply(v).add(H.scalarMultiply(gamma));
|
||||
|
||||
// PAPER LINES 36-37
|
||||
Scalar[] aL = new Scalar[N];
|
||||
Scalar[] aR = new Scalar[N];
|
||||
|
||||
BigInteger tempV = v.toBigInteger();
|
||||
for (int i = N-1; i >= 0; i--)
|
||||
{
|
||||
BigInteger basePow = BigInteger.valueOf(2).pow(i);
|
||||
if (tempV.divide(basePow).equals(BigInteger.ZERO))
|
||||
{
|
||||
aL[i] = Scalar.ZERO;
|
||||
}
|
||||
else
|
||||
{
|
||||
aL[i] = Scalar.ONE;
|
||||
tempV = tempV.subtract(basePow);
|
||||
}
|
||||
|
||||
aR[i] = aL[i].sub(Scalar.ONE);
|
||||
}
|
||||
|
||||
// PAPER LINES 38-39
|
||||
Scalar alpha = randomScalar();
|
||||
Curve25519Point A = VectorExponent(aL,aR).add(H.scalarMultiply(alpha));
|
||||
|
||||
// PAPER LINES 40-42
|
||||
Scalar[] sL = new Scalar[N];
|
||||
Scalar[] sR = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
sL[i] = randomScalar();
|
||||
sR[i] = randomScalar();
|
||||
}
|
||||
Scalar rho = randomScalar();
|
||||
Curve25519Point S = VectorExponent(sL,sR).add(H.scalarMultiply(rho));
|
||||
|
||||
// PAPER LINES 43-45
|
||||
Scalar y = hashToScalar(concat(A.toBytes(),S.toBytes()));
|
||||
Scalar z = hashToScalar(y.bytes);
|
||||
|
||||
// Polynomial construction before PAPER LINE 46
|
||||
Scalar t0 = Scalar.ZERO;
|
||||
Scalar t1 = Scalar.ZERO;
|
||||
Scalar t2 = Scalar.ZERO;
|
||||
|
||||
t0 = t0.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
t0 = t0.add(z.sq().mul(v));
|
||||
Scalar k = Scalar.ZERO;
|
||||
k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
|
||||
t0 = t0.add(k);
|
||||
|
||||
t1 = t1.add(InnerProduct(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),Hadamard(VectorPowers(y),sR)));
|
||||
t1 = t1.add(InnerProduct(sL,VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorScalar(VectorPowers(Scalar.ONE),z))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()))));
|
||||
|
||||
t2 = t2.add(InnerProduct(sL,Hadamard(VectorPowers(y),sR)));
|
||||
|
||||
// PAPER LINES 47-48
|
||||
Scalar tau1 = randomScalar();
|
||||
Scalar tau2 = randomScalar();
|
||||
Curve25519Point T1 = G.scalarMultiply(t1).add(H.scalarMultiply(tau1));
|
||||
Curve25519Point T2 = G.scalarMultiply(t2).add(H.scalarMultiply(tau2));
|
||||
|
||||
// PAPER LINES 49-51
|
||||
Scalar x = hashToScalar(concat(z.bytes,T1.toBytes(),T2.toBytes()));
|
||||
|
||||
// PAPER LINES 52-53
|
||||
Scalar taux = Scalar.ZERO;
|
||||
taux = tau1.mul(x);
|
||||
taux = taux.add(tau2.mul(x.sq()));
|
||||
taux = taux.add(gamma.mul(z.sq()));
|
||||
Scalar mu = x.mul(rho).add(alpha);
|
||||
|
||||
// PAPER LINES 54-57
|
||||
Scalar[] l = new Scalar[N];
|
||||
Scalar[] r = new Scalar[N];
|
||||
|
||||
l = VectorAdd(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),VectorScalar(sL,x));
|
||||
r = VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorAdd(VectorScalar(VectorPowers(Scalar.ONE),z),VectorScalar(sR,x)))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()));
|
||||
|
||||
Scalar t = InnerProduct(l,r);
|
||||
|
||||
// PAPER LINES 32-33
|
||||
Scalar x_ip = hashToScalar(concat(x.bytes,taux.bytes,mu.bytes,t.bytes));
|
||||
|
||||
// These are used in the inner product rounds
|
||||
int nprime = N;
|
||||
Curve25519Point[] Gprime = new Curve25519Point[N];
|
||||
Curve25519Point[] Hprime = new Curve25519Point[N];
|
||||
Scalar[] aprime = new Scalar[N];
|
||||
Scalar[] bprime = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Gprime[i] = Gi[i];
|
||||
Hprime[i] = Hi[i].scalarMultiply(Invert(y).pow(i));
|
||||
aprime[i] = l[i];
|
||||
bprime[i] = r[i];
|
||||
}
|
||||
Curve25519Point[] L = new Curve25519Point[logN];
|
||||
Curve25519Point[] R = new Curve25519Point[logN];
|
||||
int round = 0; // track the index based on number of rounds
|
||||
Scalar[] w = new Scalar[logN]; // this is the challenge x in the inner product protocol
|
||||
|
||||
// PAPER LINE 13
|
||||
while (nprime > 1)
|
||||
{
|
||||
// PAPER LINE 15
|
||||
nprime /= 2;
|
||||
|
||||
// PAPER LINES 16-17
|
||||
Scalar cL = InnerProduct(ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length));
|
||||
Scalar cR = InnerProduct(ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime));
|
||||
|
||||
// PAPER LINES 18-19
|
||||
L[round] = VectorExponentCustom(CurveSlice(Gprime,nprime,Gprime.length),CurveSlice(Hprime,0,nprime),ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length)).add(G.scalarMultiply(cL.mul(x_ip)));
|
||||
R[round] = VectorExponentCustom(CurveSlice(Gprime,0,nprime),CurveSlice(Hprime,nprime,Hprime.length),ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime)).add(G.scalarMultiply(cR.mul(x_ip)));
|
||||
|
||||
// PAPER LINES 21-22
|
||||
if (round == 0)
|
||||
w[0] = hashToScalar(concat(L[0].toBytes(),R[0].toBytes()));
|
||||
else
|
||||
w[round] = hashToScalar(concat(w[round-1].bytes,L[round].toBytes(),R[round].toBytes()));
|
||||
|
||||
// PAPER LINES 24-25
|
||||
Gprime = Hadamard2(VectorScalar2(CurveSlice(Gprime,0,nprime),Invert(w[round])),VectorScalar2(CurveSlice(Gprime,nprime,Gprime.length),w[round]));
|
||||
Hprime = Hadamard2(VectorScalar2(CurveSlice(Hprime,0,nprime),w[round]),VectorScalar2(CurveSlice(Hprime,nprime,Hprime.length),Invert(w[round])));
|
||||
|
||||
// PAPER LINES 28-29
|
||||
aprime = VectorAdd(VectorScalar(ScalarSlice(aprime,0,nprime),w[round]),VectorScalar(ScalarSlice(aprime,nprime,aprime.length),Invert(w[round])));
|
||||
bprime = VectorAdd(VectorScalar(ScalarSlice(bprime,0,nprime),Invert(w[round])),VectorScalar(ScalarSlice(bprime,nprime,bprime.length),w[round]));
|
||||
|
||||
round += 1;
|
||||
}
|
||||
|
||||
// PAPER LINE 58 (with inclusions from PAPER LINE 8 and PAPER LINE 20)
|
||||
return new ProofTuple(V,A,S,T1,T2,taux,mu,L,R,aprime[0],bprime[0],t);
|
||||
}
|
||||
|
||||
/* Given a range proof, determine if it is valid */
|
||||
public static boolean VERIFY(ProofTuple proof)
|
||||
{
|
||||
// Reconstruct the challenges
|
||||
Scalar y = hashToScalar(concat(proof.A.toBytes(),proof.S.toBytes()));
|
||||
Scalar z = hashToScalar(y.bytes);
|
||||
Scalar x = hashToScalar(concat(z.bytes,proof.T1.toBytes(),proof.T2.toBytes()));
|
||||
Scalar x_ip = hashToScalar(concat(x.bytes,proof.taux.bytes,proof.mu.bytes,proof.t.bytes));
|
||||
|
||||
// PAPER LINE 61
|
||||
Curve25519Point L61Left = H.scalarMultiply(proof.taux).add(G.scalarMultiply(proof.t));
|
||||
|
||||
Scalar k = Scalar.ZERO;
|
||||
k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
|
||||
|
||||
Curve25519Point L61Right = G.scalarMultiply(k.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y)))));
|
||||
L61Right = L61Right.add(proof.V.scalarMultiply(z.sq()));
|
||||
L61Right = L61Right.add(proof.T1.scalarMultiply(x));
|
||||
L61Right = L61Right.add(proof.T2.scalarMultiply(x.sq()));
|
||||
|
||||
if (!L61Right.equals(L61Left))
|
||||
return false;
|
||||
|
||||
// PAPER LINE 62
|
||||
Curve25519Point P = Curve25519Point.ZERO;
|
||||
P = P.add(proof.A);
|
||||
P = P.add(proof.S.scalarMultiply(x));
|
||||
|
||||
Scalar[] Gexp = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
Gexp[i] = Scalar.ZERO.sub(z);
|
||||
|
||||
Scalar[] Hexp = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Hexp[i] = Scalar.ZERO;
|
||||
Hexp[i] = Hexp[i].add(z.mul(y.pow(i)));
|
||||
Hexp[i] = Hexp[i].add(z.sq().mul(Scalar.TWO.pow(i)));
|
||||
Hexp[i] = Hexp[i].mul(Invert(y).pow(i));
|
||||
}
|
||||
P = P.add(VectorExponent(Gexp,Hexp));
|
||||
|
||||
// Compute the number of rounds for the inner product
|
||||
int rounds = proof.L.length;
|
||||
|
||||
// PAPER LINES 21-22
|
||||
// The inner product challenges are computed per round
|
||||
Scalar[] w = new Scalar[rounds];
|
||||
w[0] = hashToScalar(concat(proof.L[0].toBytes(),proof.R[0].toBytes()));
|
||||
if (rounds > 1)
|
||||
{
|
||||
for (int i = 1; i < rounds; i++)
|
||||
{
|
||||
w[i] = hashToScalar(concat(w[i-1].bytes,proof.L[i].toBytes(),proof.R[i].toBytes()));
|
||||
}
|
||||
}
|
||||
|
||||
// Basically PAPER LINES 24-25
|
||||
// Compute the curvepoints from G[i] and H[i]
|
||||
Curve25519Point InnerProdG = Curve25519Point.ZERO;
|
||||
Curve25519Point InnerProdH = Curve25519Point.ZERO;
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
// Convert the index to binary IN REVERSE and construct the scalar exponent
|
||||
int index = i;
|
||||
Scalar gScalar = Scalar.ONE;
|
||||
Scalar hScalar = Invert(y).pow(i);
|
||||
|
||||
for (int j = rounds-1; j >= 0; j--)
|
||||
{
|
||||
int J = w.length - j - 1; // because this is done in reverse bit order
|
||||
int basePow = (int) Math.pow(2,j); // assumes we don't get too big
|
||||
if (index / basePow == 0) // bit is zero
|
||||
{
|
||||
gScalar = gScalar.mul(Invert(w[J]));
|
||||
hScalar = hScalar.mul(w[J]);
|
||||
}
|
||||
else // bit is one
|
||||
{
|
||||
gScalar = gScalar.mul(w[J]);
|
||||
hScalar = hScalar.mul(Invert(w[J]));
|
||||
index -= basePow;
|
||||
}
|
||||
}
|
||||
|
||||
// Now compute the basepoint's scalar multiplication
|
||||
// Each of these could be written as a multiexp operation instead
|
||||
InnerProdG = InnerProdG.add(Gi[i].scalarMultiply(gScalar));
|
||||
InnerProdH = InnerProdH.add(Hi[i].scalarMultiply(hScalar));
|
||||
}
|
||||
|
||||
// PAPER LINE 26
|
||||
Curve25519Point Pprime = P.add(H.scalarMultiply(Scalar.ZERO.sub(proof.mu)));
|
||||
|
||||
for (int i = 0; i < rounds; i++)
|
||||
{
|
||||
Pprime = Pprime.add(proof.L[i].scalarMultiply(w[i].sq()));
|
||||
Pprime = Pprime.add(proof.R[i].scalarMultiply(Invert(w[i]).sq()));
|
||||
}
|
||||
Pprime = Pprime.add(G.scalarMultiply(proof.t.mul(x_ip)));
|
||||
|
||||
if (!Pprime.equals(InnerProdG.scalarMultiply(proof.a).add(InnerProdH.scalarMultiply(proof.b)).add(G.scalarMultiply(proof.a.mul(proof.b).mul(x_ip)))))
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
public static void main(String[] args)
|
||||
{
|
||||
// Number of bits in the range
|
||||
N = 64;
|
||||
logN = 6; // its log, manually
|
||||
|
||||
// Set the curve base points
|
||||
G = Curve25519Point.G;
|
||||
H = Curve25519Point.hashToPoint(G);
|
||||
Gi = new Curve25519Point[N];
|
||||
Hi = new Curve25519Point[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Gi[i] = getHpnGLookup(i);
|
||||
Hi[i] = getHpnGLookup(N+i);
|
||||
}
|
||||
|
||||
// Run a bunch of randomized trials
|
||||
Random rando = new Random();
|
||||
int TRIALS = 250;
|
||||
int count = 0;
|
||||
|
||||
while (count < TRIALS)
|
||||
{
|
||||
long amount = rando.nextLong();
|
||||
if (amount > Math.pow(2,N)-1 || amount < 0)
|
||||
continue;
|
||||
|
||||
ProofTuple proof = PROVE(new Scalar(BigInteger.valueOf(amount)),randomScalar());
|
||||
if (!VERIFY(proof))
|
||||
System.out.println("Test failed");
|
||||
|
||||
count += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,487 @@
|
|||
package how.monero.hodl.bulletproof;
|
||||
|
||||
import how.monero.hodl.crypto.Curve25519Point;
|
||||
import how.monero.hodl.crypto.Scalar;
|
||||
import how.monero.hodl.crypto.CryptoUtil;
|
||||
import java.math.BigInteger;
|
||||
import java.util.Random;
|
||||
|
||||
import static how.monero.hodl.crypto.Scalar.randomScalar;
|
||||
import static how.monero.hodl.crypto.CryptoUtil.*;
|
||||
import static how.monero.hodl.util.ByteUtil.*;
|
||||
|
||||
public class OptimizedLogBulletproof
|
||||
{
|
||||
private static int N;
|
||||
private static int logN;
|
||||
private static Curve25519Point G;
|
||||
private static Curve25519Point H;
|
||||
private static Curve25519Point[] Gi;
|
||||
private static Curve25519Point[] Hi;
|
||||
|
||||
public static class ProofTuple
|
||||
{
|
||||
private Curve25519Point V;
|
||||
private Curve25519Point A;
|
||||
private Curve25519Point S;
|
||||
private Curve25519Point T1;
|
||||
private Curve25519Point T2;
|
||||
private Scalar taux;
|
||||
private Scalar mu;
|
||||
private Curve25519Point[] L;
|
||||
private Curve25519Point[] R;
|
||||
private Scalar a;
|
||||
private Scalar b;
|
||||
private Scalar t;
|
||||
|
||||
public ProofTuple(Curve25519Point V, Curve25519Point A, Curve25519Point S, Curve25519Point T1, Curve25519Point T2, Scalar taux, Scalar mu, Curve25519Point[] L, Curve25519Point[] R, Scalar a, Scalar b, Scalar t)
|
||||
{
|
||||
this.V = V;
|
||||
this.A = A;
|
||||
this.S = S;
|
||||
this.T1 = T1;
|
||||
this.T2 = T2;
|
||||
this.taux = taux;
|
||||
this.mu = mu;
|
||||
this.L = L;
|
||||
this.R = R;
|
||||
this.a = a;
|
||||
this.b = b;
|
||||
this.t = t;
|
||||
}
|
||||
}
|
||||
|
||||
/* Given two scalar arrays, construct a vector commitment */
|
||||
public static Curve25519Point VectorExponent(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == N && b.length == N;
|
||||
|
||||
Curve25519Point Result = Curve25519Point.ZERO;
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Result = Result.add(Gi[i].scalarMultiply(a[i]));
|
||||
Result = Result.add(Hi[i].scalarMultiply(b[i]));
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Compute a custom vector-scalar commitment */
|
||||
public static Curve25519Point VectorExponentCustom(Curve25519Point[] A, Curve25519Point[] B, Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == A.length && b.length == B.length && a.length == b.length;
|
||||
|
||||
Curve25519Point Result = Curve25519Point.ZERO;
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
Result = Result.add(A[i].scalarMultiply(a[i]));
|
||||
Result = Result.add(B[i].scalarMultiply(b[i]));
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Given a scalar, construct a vector of powers */
|
||||
public static Scalar[] VectorPowers(Scalar x)
|
||||
{
|
||||
Scalar[] result = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
result[i] = x.pow(i);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given two scalar arrays, construct the inner product */
|
||||
public static Scalar InnerProduct(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar result = Scalar.ZERO;
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result = result.add(a[i].mul(b[i]));
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given two scalar arrays, construct the Hadamard product */
|
||||
public static Scalar[] Hadamard(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].mul(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given two curvepoint arrays, construct the Hadamard product */
|
||||
public static Curve25519Point[] Hadamard2(Curve25519Point[] A, Curve25519Point[] B)
|
||||
{
|
||||
assert A.length == B.length;
|
||||
|
||||
Curve25519Point[] Result = new Curve25519Point[A.length];
|
||||
for (int i = 0; i < A.length; i++)
|
||||
{
|
||||
Result[i] = A[i].add(B[i]);
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Add two vectors */
|
||||
public static Scalar[] VectorAdd(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].add(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Subtract two vectors */
|
||||
public static Scalar[] VectorSubtract(Scalar[] a, Scalar[] b)
|
||||
{
|
||||
assert a.length == b.length;
|
||||
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].sub(b[i]);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Multiply a scalar and a vector */
|
||||
public static Scalar[] VectorScalar(Scalar[] a, Scalar x)
|
||||
{
|
||||
Scalar[] result = new Scalar[a.length];
|
||||
for (int i = 0; i < a.length; i++)
|
||||
{
|
||||
result[i] = a[i].mul(x);
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Exponentiate a curve vector by a scalar */
|
||||
public static Curve25519Point[] VectorScalar2(Curve25519Point[] A, Scalar x)
|
||||
{
|
||||
Curve25519Point[] Result = new Curve25519Point[A.length];
|
||||
for (int i = 0; i < A.length; i++)
|
||||
{
|
||||
Result[i] = A[i].scalarMultiply(x);
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Compute the inverse of a scalar, the stupid way */
|
||||
public static Scalar Invert(Scalar x)
|
||||
{
|
||||
Scalar inverse = new Scalar(x.toBigInteger().modInverse(CryptoUtil.l));
|
||||
|
||||
assert x.mul(inverse).equals(Scalar.ONE);
|
||||
return inverse;
|
||||
}
|
||||
|
||||
/* Compute the slice of a curvepoint vector */
|
||||
public static Curve25519Point[] CurveSlice(Curve25519Point[] a, int start, int stop)
|
||||
{
|
||||
Curve25519Point[] Result = new Curve25519Point[stop-start];
|
||||
for (int i = start; i < stop; i++)
|
||||
{
|
||||
Result[i-start] = a[i];
|
||||
}
|
||||
return Result;
|
||||
}
|
||||
|
||||
/* Compute the slice of a scalar vector */
|
||||
public static Scalar[] ScalarSlice(Scalar[] a, int start, int stop)
|
||||
{
|
||||
Scalar[] result = new Scalar[stop-start];
|
||||
for (int i = start; i < stop; i++)
|
||||
{
|
||||
result[i-start] = a[i];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Given a value v (0..2^N-1) and a mask gamma, construct a range proof */
|
||||
public static ProofTuple PROVE(Scalar v, Scalar gamma)
|
||||
{
|
||||
Curve25519Point V = G.scalarMultiply(v).add(H.scalarMultiply(gamma));
|
||||
|
||||
// PAPER LINES 36-37
|
||||
Scalar[] aL = new Scalar[N];
|
||||
Scalar[] aR = new Scalar[N];
|
||||
|
||||
BigInteger tempV = v.toBigInteger();
|
||||
for (int i = N-1; i >= 0; i--)
|
||||
{
|
||||
BigInteger basePow = BigInteger.valueOf(2).pow(i);
|
||||
if (tempV.divide(basePow).equals(BigInteger.ZERO))
|
||||
{
|
||||
aL[i] = Scalar.ZERO;
|
||||
}
|
||||
else
|
||||
{
|
||||
aL[i] = Scalar.ONE;
|
||||
tempV = tempV.subtract(basePow);
|
||||
}
|
||||
|
||||
aR[i] = aL[i].sub(Scalar.ONE);
|
||||
}
|
||||
|
||||
// PAPER LINES 38-39
|
||||
Scalar alpha = randomScalar();
|
||||
Curve25519Point A = VectorExponent(aL,aR).add(H.scalarMultiply(alpha));
|
||||
|
||||
// PAPER LINES 40-42
|
||||
Scalar[] sL = new Scalar[N];
|
||||
Scalar[] sR = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
sL[i] = randomScalar();
|
||||
sR[i] = randomScalar();
|
||||
}
|
||||
Scalar rho = randomScalar();
|
||||
Curve25519Point S = VectorExponent(sL,sR).add(H.scalarMultiply(rho));
|
||||
|
||||
// PAPER LINES 43-45
|
||||
Scalar y = hashToScalar(concat(A.toBytes(),S.toBytes()));
|
||||
Scalar z = hashToScalar(y.bytes);
|
||||
|
||||
// Polynomial construction before PAPER LINE 46
|
||||
Scalar t0 = Scalar.ZERO;
|
||||
Scalar t1 = Scalar.ZERO;
|
||||
Scalar t2 = Scalar.ZERO;
|
||||
|
||||
t0 = t0.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
t0 = t0.add(z.sq().mul(v));
|
||||
Scalar k = Scalar.ZERO;
|
||||
k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
|
||||
t0 = t0.add(k);
|
||||
|
||||
t1 = t1.add(InnerProduct(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),Hadamard(VectorPowers(y),sR)));
|
||||
t1 = t1.add(InnerProduct(sL,VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorScalar(VectorPowers(Scalar.ONE),z))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()))));
|
||||
|
||||
t2 = t2.add(InnerProduct(sL,Hadamard(VectorPowers(y),sR)));
|
||||
|
||||
// PAPER LINES 47-48
|
||||
Scalar tau1 = randomScalar();
|
||||
Scalar tau2 = randomScalar();
|
||||
Curve25519Point T1 = G.scalarMultiply(t1).add(H.scalarMultiply(tau1));
|
||||
Curve25519Point T2 = G.scalarMultiply(t2).add(H.scalarMultiply(tau2));
|
||||
|
||||
// PAPER LINES 49-51
|
||||
Scalar x = hashToScalar(concat(z.bytes,T1.toBytes(),T2.toBytes()));
|
||||
|
||||
// PAPER LINES 52-53
|
||||
Scalar taux = Scalar.ZERO;
|
||||
taux = tau1.mul(x);
|
||||
taux = taux.add(tau2.mul(x.sq()));
|
||||
taux = taux.add(gamma.mul(z.sq()));
|
||||
Scalar mu = x.mul(rho).add(alpha);
|
||||
|
||||
// PAPER LINES 54-57
|
||||
Scalar[] l = new Scalar[N];
|
||||
Scalar[] r = new Scalar[N];
|
||||
|
||||
l = VectorAdd(VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE),z)),VectorScalar(sL,x));
|
||||
r = VectorAdd(Hadamard(VectorPowers(y),VectorAdd(aR,VectorAdd(VectorScalar(VectorPowers(Scalar.ONE),z),VectorScalar(sR,x)))),VectorScalar(VectorPowers(Scalar.TWO),z.sq()));
|
||||
|
||||
Scalar t = InnerProduct(l,r);
|
||||
|
||||
// PAPER LINES 32-33
|
||||
Scalar x_ip = hashToScalar(concat(x.bytes,taux.bytes,mu.bytes,t.bytes));
|
||||
|
||||
// These are used in the inner product rounds
|
||||
int nprime = N;
|
||||
Curve25519Point[] Gprime = new Curve25519Point[N];
|
||||
Curve25519Point[] Hprime = new Curve25519Point[N];
|
||||
Scalar[] aprime = new Scalar[N];
|
||||
Scalar[] bprime = new Scalar[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Gprime[i] = Gi[i];
|
||||
Hprime[i] = Hi[i].scalarMultiply(Invert(y).pow(i));
|
||||
aprime[i] = l[i];
|
||||
bprime[i] = r[i];
|
||||
}
|
||||
Curve25519Point[] L = new Curve25519Point[logN];
|
||||
Curve25519Point[] R = new Curve25519Point[logN];
|
||||
int round = 0; // track the index based on number of rounds
|
||||
Scalar[] w = new Scalar[logN]; // this is the challenge x in the inner product protocol
|
||||
|
||||
// PAPER LINE 13
|
||||
while (nprime > 1)
|
||||
{
|
||||
// PAPER LINE 15
|
||||
nprime /= 2;
|
||||
|
||||
// PAPER LINES 16-17
|
||||
Scalar cL = InnerProduct(ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length));
|
||||
Scalar cR = InnerProduct(ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime));
|
||||
|
||||
// PAPER LINES 18-19
|
||||
L[round] = VectorExponentCustom(CurveSlice(Gprime,nprime,Gprime.length),CurveSlice(Hprime,0,nprime),ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length)).add(G.scalarMultiply(cL.mul(x_ip)));
|
||||
R[round] = VectorExponentCustom(CurveSlice(Gprime,0,nprime),CurveSlice(Hprime,nprime,Hprime.length),ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime)).add(G.scalarMultiply(cR.mul(x_ip)));
|
||||
|
||||
// PAPER LINES 21-22
|
||||
if (round == 0)
|
||||
w[0] = hashToScalar(concat(L[0].toBytes(),R[0].toBytes()));
|
||||
else
|
||||
w[round] = hashToScalar(concat(w[round-1].bytes,L[round].toBytes(),R[round].toBytes()));
|
||||
|
||||
// PAPER LINES 24-25
|
||||
Gprime = Hadamard2(VectorScalar2(CurveSlice(Gprime,0,nprime),Invert(w[round])),VectorScalar2(CurveSlice(Gprime,nprime,Gprime.length),w[round]));
|
||||
Hprime = Hadamard2(VectorScalar2(CurveSlice(Hprime,0,nprime),w[round]),VectorScalar2(CurveSlice(Hprime,nprime,Hprime.length),Invert(w[round])));
|
||||
|
||||
// PAPER LINES 28-29
|
||||
aprime = VectorAdd(VectorScalar(ScalarSlice(aprime,0,nprime),w[round]),VectorScalar(ScalarSlice(aprime,nprime,aprime.length),Invert(w[round])));
|
||||
bprime = VectorAdd(VectorScalar(ScalarSlice(bprime,0,nprime),Invert(w[round])),VectorScalar(ScalarSlice(bprime,nprime,bprime.length),w[round]));
|
||||
|
||||
round += 1;
|
||||
}
|
||||
|
||||
// PAPER LINE 58 (with inclusions from PAPER LINE 8 and PAPER LINE 20)
|
||||
return new ProofTuple(V,A,S,T1,T2,taux,mu,L,R,aprime[0],bprime[0],t);
|
||||
}
|
||||
|
||||
/* Given a range proof, determine if it is valid */
|
||||
public static boolean VERIFY(ProofTuple proof)
|
||||
{
|
||||
// Reconstruct the challenges
|
||||
Scalar y = hashToScalar(concat(proof.A.toBytes(),proof.S.toBytes()));
|
||||
Scalar z = hashToScalar(y.bytes);
|
||||
Scalar x = hashToScalar(concat(z.bytes,proof.T1.toBytes(),proof.T2.toBytes()));
|
||||
Scalar x_ip = hashToScalar(concat(x.bytes,proof.taux.bytes,proof.mu.bytes,proof.t.bytes));
|
||||
|
||||
// PAPER LINE 61
|
||||
Curve25519Point L61Left = H.scalarMultiply(proof.taux).add(G.scalarMultiply(proof.t));
|
||||
|
||||
Scalar k = Scalar.ZERO;
|
||||
k = k.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
|
||||
k = k.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
|
||||
|
||||
Curve25519Point L61Right = G.scalarMultiply(k.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y)))));
|
||||
L61Right = L61Right.add(proof.V.scalarMultiply(z.sq()));
|
||||
L61Right = L61Right.add(proof.T1.scalarMultiply(x));
|
||||
L61Right = L61Right.add(proof.T2.scalarMultiply(x.sq()));
|
||||
|
||||
if (!L61Right.equals(L61Left))
|
||||
return false;
|
||||
|
||||
// PAPER LINE 62
|
||||
Curve25519Point P = Curve25519Point.ZERO;
|
||||
P = P.add(proof.A);
|
||||
P = P.add(proof.S.scalarMultiply(x));
|
||||
|
||||
// Compute the number of rounds for the inner product
|
||||
int rounds = proof.L.length;
|
||||
|
||||
// PAPER LINES 21-22
|
||||
// The inner product challenges are computed per round
|
||||
Scalar[] w = new Scalar[rounds];
|
||||
w[0] = hashToScalar(concat(proof.L[0].toBytes(),proof.R[0].toBytes()));
|
||||
if (rounds > 1)
|
||||
{
|
||||
for (int i = 1; i < rounds; i++)
|
||||
{
|
||||
w[i] = hashToScalar(concat(w[i-1].bytes,proof.L[i].toBytes(),proof.R[i].toBytes()));
|
||||
}
|
||||
}
|
||||
|
||||
// Basically PAPER LINES 24-25
|
||||
// Compute the curvepoints from G[i] and H[i]
|
||||
Curve25519Point InnerProdG = Curve25519Point.ZERO;
|
||||
Curve25519Point InnerProdH = Curve25519Point.ZERO;
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
// Convert the index to binary IN REVERSE and construct the scalar exponent
|
||||
int index = i;
|
||||
Scalar gScalar = proof.a;
|
||||
Scalar hScalar = proof.b.mul(Invert(y).pow(i));
|
||||
|
||||
for (int j = rounds-1; j >= 0; j--)
|
||||
{
|
||||
int J = w.length - j - 1; // because this is done in reverse bit order
|
||||
int basePow = (int) Math.pow(2,j); // assumes we don't get too big
|
||||
if (index / basePow == 0) // bit is zero
|
||||
{
|
||||
gScalar = gScalar.mul(Invert(w[J]));
|
||||
hScalar = hScalar.mul(w[J]);
|
||||
}
|
||||
else // bit is one
|
||||
{
|
||||
gScalar = gScalar.mul(w[J]);
|
||||
hScalar = hScalar.mul(Invert(w[J]));
|
||||
index -= basePow;
|
||||
}
|
||||
}
|
||||
|
||||
// Adjust the scalars using the exponents from PAPER LINE 62
|
||||
gScalar = gScalar.add(z);
|
||||
hScalar = hScalar.sub(z.mul(y.pow(i)).add(z.sq().mul(Scalar.TWO.pow(i))).mul(Invert(y).pow(i)));
|
||||
|
||||
// Now compute the basepoint's scalar multiplication
|
||||
// Each of these could be written as a multiexp operation instead
|
||||
InnerProdG = InnerProdG.add(Gi[i].scalarMultiply(gScalar));
|
||||
InnerProdH = InnerProdH.add(Hi[i].scalarMultiply(hScalar));
|
||||
}
|
||||
|
||||
// PAPER LINE 26
|
||||
Curve25519Point Pprime = P.add(H.scalarMultiply(Scalar.ZERO.sub(proof.mu)));
|
||||
|
||||
for (int i = 0; i < rounds; i++)
|
||||
{
|
||||
Pprime = Pprime.add(proof.L[i].scalarMultiply(w[i].sq()));
|
||||
Pprime = Pprime.add(proof.R[i].scalarMultiply(Invert(w[i]).sq()));
|
||||
}
|
||||
Pprime = Pprime.add(G.scalarMultiply(proof.t.mul(x_ip)));
|
||||
|
||||
if (!Pprime.equals(InnerProdG.add(InnerProdH).add(G.scalarMultiply(proof.a.mul(proof.b).mul(x_ip)))))
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
public static void main(String[] args)
|
||||
{
|
||||
// Number of bits in the range
|
||||
N = 64;
|
||||
logN = 6; // its log, manually
|
||||
|
||||
// Set the curve base points
|
||||
G = Curve25519Point.G;
|
||||
H = Curve25519Point.hashToPoint(G);
|
||||
Gi = new Curve25519Point[N];
|
||||
Hi = new Curve25519Point[N];
|
||||
for (int i = 0; i < N; i++)
|
||||
{
|
||||
Gi[i] = getHpnGLookup(i);
|
||||
Hi[i] = getHpnGLookup(N+i);
|
||||
}
|
||||
|
||||
// Run a bunch of randomized trials
|
||||
Random rando = new Random();
|
||||
int TRIALS = 250;
|
||||
int count = 0;
|
||||
|
||||
while (count < TRIALS)
|
||||
{
|
||||
long amount = rando.nextLong();
|
||||
if (amount > Math.pow(2,N)-1 || amount < 0)
|
||||
continue;
|
||||
|
||||
ProofTuple proof = PROVE(new Scalar(BigInteger.valueOf(amount)),randomScalar());
|
||||
if (!VERIFY(proof))
|
||||
System.out.println("Test failed");
|
||||
|
||||
count += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in a new issue