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https://github.com/monero-project/research-lab.git
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372 lines
12 KiB
Java
372 lines
12 KiB
Java
// NOTE: this interchanges the roles of G and H to match other code's behavior
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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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/* Compute the value of k(y,z) */
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public static Scalar ComputeK(Scalar y, Scalar z)
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{
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Scalar result = Scalar.ZERO;
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result = result.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(y))));
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result = result.sub(z.pow(3).mul(InnerProduct(VectorPowers(Scalar.ONE),VectorPowers(Scalar.TWO))));
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return result;
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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 = H.scalarMultiply(v).add(G.scalarMultiply(gamma));
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// This hash is updated for Fiat-Shamir throughout the proof
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Scalar hashCache = hashToScalar(V.toBytes());
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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(G.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(G.scalarMultiply(rho));
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// PAPER LINES 43-45
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hashCache = hashToScalar(concat(hashCache.bytes,A.toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,S.toBytes()));
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Scalar y = hashCache;
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hashCache = hashToScalar(hashCache.bytes);
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Scalar z = hashCache;
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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 = ComputeK(y,z);
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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 = H.scalarMultiply(t1).add(G.scalarMultiply(tau1));
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Curve25519Point T2 = H.scalarMultiply(t2).add(G.scalarMultiply(tau2));
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// PAPER LINES 49-51
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hashCache = hashToScalar(concat(hashCache.bytes,z.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,T1.toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,T2.toBytes()));
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Scalar x = hashCache;
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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 hashCache = hashToScalar(proof.V.toBytes());
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hashCache = hashToScalar(concat(hashCache.bytes,proof.A.toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.S.toBytes()));
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Scalar y = hashCache;
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hashCache = hashToScalar(hashCache.bytes);
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Scalar z = hashCache;
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hashCache = hashToScalar(concat(hashCache.bytes,z.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.T1.toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.T2.toBytes()));
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Scalar x = hashCache;
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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 = G.scalarMultiply(proof.taux).add(H.scalarMultiply(t));
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Scalar k = ComputeK(y,z);
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Curve25519Point L61Right = H.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(G.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(2*i);
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Hi[i] = getHpnGLookup(2*i+1);
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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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