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554 lines
20 KiB
Java
554 lines
20 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 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 MultiBulletproof
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{
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private static int N;
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private static int logMN;
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private static int M;
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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 == M*N && b.length == M*N;
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Curve25519Point Result = Curve25519Point.ZERO;
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for (int i = 0; i < M*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, int size)
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{
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Scalar[] result = new Scalar[size];
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for (int i = 0; i < size; 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]));
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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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assert a.length == b.length;
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Scalar[] result = new Scalar[a.length];
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for (int i = 0; i < a.length; 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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/* Given two curvepoint arrays, construct the Hadamard product */
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public static Curve25519Point[] Hadamard2(Curve25519Point[] A, Curve25519Point[] B)
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{
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assert A.length == B.length;
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Curve25519Point[] Result = new Curve25519Point[A.length];
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for (int i = 0; i < A.length; 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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/* Add two vectors */
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public static Scalar[] VectorAdd(Scalar[] a, Scalar[] b)
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{
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assert a.length == b.length;
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Scalar[] result = new Scalar[a.length];
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for (int i = 0; i < a.length; 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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assert a.length == b.length;
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Scalar[] result = new Scalar[a.length];
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for (int i = 0; i < a.length; 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[a.length];
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for (int i = 0; i < a.length; 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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/* Exponentiate a curve vector by a scalar */
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public static Curve25519Point[] VectorScalar2(Curve25519Point[] A, Scalar x)
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{
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Curve25519Point[] Result = new Curve25519Point[A.length];
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for (int i = 0; i < A.length; i++)
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{
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Result[i] = A[i].scalarMultiply(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 slice of a curvepoint vector */
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public static Curve25519Point[] CurveSlice(Curve25519Point[] a, int start, int stop)
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{
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Curve25519Point[] Result = new Curve25519Point[stop-start];
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for (int i = start; i < stop; i++)
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{
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Result[i-start] = a[i];
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}
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return Result;
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}
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/* Compute the slice of a scalar vector */
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public static Scalar[] ScalarSlice(Scalar[] a, int start, int stop)
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{
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Scalar[] result = new Scalar[stop-start];
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for (int i = start; i < stop; i++)
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{
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result[i-start] = a[i];
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}
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return result;
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}
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/* Construct an aggregate range proof */
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public static ProofTuple PROVE(Scalar[] v, Scalar[] gamma)
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{
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Curve25519Point[] V = new Curve25519Point[M];
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V[0] = H.scalarMultiply(v[0]).add(G.scalarMultiply(gamma[0]));
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// This hash is updated for Fiat-Shamir throughout the proof
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Scalar hashCache = hashToScalar(V[0].toBytes());
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for (int j = 1; j < M; j++)
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{
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V[j] = H.scalarMultiply(v[j]).add(G.scalarMultiply(gamma[j]));
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hashCache = hashToScalar(concat(hashCache.bytes,V[j].toBytes()));
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}
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// PAPER LINES 36-37
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Scalar[] aL = new Scalar[M*N];
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Scalar[] aR = new Scalar[M*N];
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for (int j = 0; j < M; j++)
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{
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BigInteger tempV = v[j].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[j*N+i] = Scalar.ZERO;
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}
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else
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{
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aL[j*N+i] = Scalar.ONE;
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tempV = tempV.subtract(basePow);
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}
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aR[j*N+i] = aL[j*N+i].sub(Scalar.ONE);
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}
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}
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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[M*N];
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Scalar[] sR = new Scalar[M*N];
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for (int i = 0; i < M*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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// Polynomial construction by coefficients
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Scalar[] l0;
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Scalar[] l1;
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Scalar[] r0;
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Scalar[] r1;
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l0 = VectorSubtract(aL,VectorScalar(VectorPowers(Scalar.ONE,M*N),z));
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l1 = sL;
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// This computes the ugly sum/concatenation from PAPER LINE 65
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Scalar[] zerosTwos = new Scalar[M*N];
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for (int i = 0; i < M*N; i++)
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{
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zerosTwos[i] = Scalar.ZERO;
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for (int j = 1; j <= M; j++) // note this starts from 1
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{
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Scalar temp = Scalar.ZERO;
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if (i >= (j-1)*N && i < j*N)
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temp = Scalar.TWO.pow(i-(j-1)*N); // exponent ranges from 0..N-1
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zerosTwos[i] = zerosTwos[i].add(z.pow(1+j).mul(temp));
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}
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}
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r0 = VectorAdd(aR,VectorScalar(VectorPowers(Scalar.ONE,M*N),z));
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r0 = Hadamard(r0,VectorPowers(y,M*N));
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r0 = VectorAdd(r0,zerosTwos);
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r1 = Hadamard(VectorPowers(y,M*N),sR);
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// Polynomial construction before PAPER LINE 46
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Scalar t0 = InnerProduct(l0,r0);
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Scalar t1 = InnerProduct(l0,r1).add(InnerProduct(l1,r0));
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Scalar t2 = InnerProduct(l1,r1);
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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 = tau1.mul(x);
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taux = taux.add(tau2.mul(x.sq()));
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for (int j = 1; j <= M; j++) // note this starts from 1
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{
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taux = taux.add(z.pow(1+j).mul(gamma[j-1]));
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}
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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 = l0;
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l = VectorAdd(l,VectorScalar(l1,x));
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Scalar[] r = r0;
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r = VectorAdd(r,VectorScalar(r1,x));
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Scalar t = InnerProduct(l,r);
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// PAPER LINES 32-33
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hashCache = hashToScalar(concat(hashCache.bytes,x.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,taux.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,mu.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,t.bytes));
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Scalar x_ip = hashCache;
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// These are used in the inner product rounds
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int nprime = M*N;
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Curve25519Point[] Gprime = new Curve25519Point[M*N];
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Curve25519Point[] Hprime = new Curve25519Point[M*N];
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Scalar[] aprime = new Scalar[M*N];
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Scalar[] bprime = new Scalar[M*N];
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for (int i = 0; i < M*N; i++)
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{
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Gprime[i] = Gi[i];
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Hprime[i] = Hi[i].scalarMultiply(Invert(y).pow(i));
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aprime[i] = l[i];
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bprime[i] = r[i];
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}
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Curve25519Point[] L = new Curve25519Point[logMN];
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Curve25519Point[] R = new Curve25519Point[logMN];
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int round = 0; // track the index based on number of rounds
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Scalar[] w = new Scalar[logMN]; // this is the challenge x in the inner product protocol
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// PAPER LINE 13
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while (nprime > 1)
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{
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// PAPER LINE 15
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nprime /= 2;
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// PAPER LINES 16-17
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Scalar cL = InnerProduct(ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length));
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Scalar cR = InnerProduct(ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime));
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// PAPER LINES 18-19
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L[round] = VectorExponentCustom(CurveSlice(Gprime,nprime,Gprime.length),CurveSlice(Hprime,0,nprime),ScalarSlice(aprime,0,nprime),ScalarSlice(bprime,nprime,bprime.length)).add(H.scalarMultiply(cL.mul(x_ip)));
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R[round] = VectorExponentCustom(CurveSlice(Gprime,0,nprime),CurveSlice(Hprime,nprime,Hprime.length),ScalarSlice(aprime,nprime,aprime.length),ScalarSlice(bprime,0,nprime)).add(H.scalarMultiply(cR.mul(x_ip)));
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// PAPER LINES 21-22
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hashCache = hashToScalar(concat(hashCache.bytes,L[round].toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,R[round].toBytes()));
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w[round] = hashCache;
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// PAPER LINES 24-25
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Gprime = Hadamard2(VectorScalar2(CurveSlice(Gprime,0,nprime),Invert(w[round])),VectorScalar2(CurveSlice(Gprime,nprime,Gprime.length),w[round]));
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Hprime = Hadamard2(VectorScalar2(CurveSlice(Hprime,0,nprime),w[round]),VectorScalar2(CurveSlice(Hprime,nprime,Hprime.length),Invert(w[round])));
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// PAPER LINES 28-29
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aprime = VectorAdd(VectorScalar(ScalarSlice(aprime,0,nprime),w[round]),VectorScalar(ScalarSlice(aprime,nprime,aprime.length),Invert(w[round])));
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bprime = VectorAdd(VectorScalar(ScalarSlice(bprime,0,nprime),Invert(w[round])),VectorScalar(ScalarSlice(bprime,nprime,bprime.length),w[round]));
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round += 1;
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}
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// PAPER LINE 58 (with inclusions from PAPER LINE 8 and PAPER LINE 20)
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return new ProofTuple(V,A,S,T1,T2,taux,mu,L,R,aprime[0],bprime[0],t);
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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[0].toBytes());
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for (int j = 1; j < M; j++)
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hashCache = hashToScalar(concat(hashCache.bytes,proof.V[j].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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hashCache = hashToScalar(concat(hashCache.bytes,x.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.taux.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.mu.bytes));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.t.bytes));
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Scalar x_ip = hashCache;
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// PAPER LINE 61
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Curve25519Point L61Left = G.scalarMultiply(proof.taux).add(H.scalarMultiply(proof.t));
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Scalar k = Scalar.ZERO.sub(z.sq().mul(InnerProduct(VectorPowers(Scalar.ONE,M*N),VectorPowers(y,M*N))));
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for (int j = 1; j <= M; j++) // note this starts from 1
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{
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k = k.sub(z.pow(j+2).mul(InnerProduct(VectorPowers(Scalar.ONE,N),VectorPowers(Scalar.TWO,N))));
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}
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Curve25519Point L61Right = H.scalarMultiply(k.add(z.mul(InnerProduct(VectorPowers(Scalar.ONE,M*N),VectorPowers(y,M*N)))));
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for (int j = 0; j < M; j++)
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{
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L61Right = L61Right.add(proof.V[j].scalarMultiply(z.pow(j+2)));
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}
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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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return false;
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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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// PAPER LINES 21-22
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// The inner product challenges are computed per round
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Scalar[] w = new Scalar[logMN];
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hashCache = hashToScalar(concat(hashCache.bytes,proof.L[0].toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.R[0].toBytes()));
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w[0] = hashCache;
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if (logMN > 1)
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{
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for (int i = 1; i < logMN; i++)
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{
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hashCache = hashToScalar(concat(hashCache.bytes,proof.L[i].toBytes()));
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hashCache = hashToScalar(concat(hashCache.bytes,proof.R[i].toBytes()));
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w[i] = hashCache;
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}
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}
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// Basically PAPER LINES 24-25
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// Compute the curvepoints from G[i] and H[i]
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Curve25519Point InnerProdG = Curve25519Point.ZERO;
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Curve25519Point InnerProdH = Curve25519Point.ZERO;
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for (int i = 0; i < M*N; i++)
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{
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// Convert the index to binary IN REVERSE and construct the scalar exponent
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int index = i;
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Scalar gScalar = proof.a;
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Scalar hScalar = proof.b.mul(Invert(y).pow(i));
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for (int j = logMN-1; j >= 0; j--)
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{
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int J = w.length - j - 1; // because this is done in reverse bit order
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int basePow = (int) Math.pow(2,j); // assumes we don't get too big
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if (index / basePow == 0) // bit is zero
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{
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gScalar = gScalar.mul(Invert(w[J]));
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hScalar = hScalar.mul(w[J]);
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}
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else // bit is one
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{
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gScalar = gScalar.mul(w[J]);
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hScalar = hScalar.mul(Invert(w[J]));
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index -= basePow;
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}
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}
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gScalar = gScalar.add(z);
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hScalar = hScalar.sub(z.mul(y.pow(i)).add(z.pow(2+i/N).mul(Scalar.TWO.pow(i%N))).mul(Invert(y).pow(i)));
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// Now compute the basepoint's scalar multiplication
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// Each of these could be written as a multiexp operation instead
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InnerProdG = InnerProdG.add(Gi[i].scalarMultiply(gScalar));
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InnerProdH = InnerProdH.add(Hi[i].scalarMultiply(hScalar));
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}
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// PAPER LINE 26
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Curve25519Point Pprime = P.add(G.scalarMultiply(Scalar.ZERO.sub(proof.mu)));
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for (int i = 0; i < logMN; i++)
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{
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Pprime = Pprime.add(proof.L[i].scalarMultiply(w[i].sq()));
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Pprime = Pprime.add(proof.R[i].scalarMultiply(Invert(w[i]).sq()));
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}
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Pprime = Pprime.add(H.scalarMultiply(proof.t.mul(x_ip)));
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if (!Pprime.equals(InnerProdG.add(InnerProdH).add(H.scalarMultiply(proof.a.mul(proof.b).mul(x_ip)))))
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return false;
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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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// Test parameters
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N = 64; // number of bits in amount range (so amounts are 0..2^(N-1))
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M = 4; // number of outputs (must be a power of 2)
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logMN = 8; // must be manually set to log_2(MN)
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int TRIALS = 25; // number of randomized trials to run
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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[M*N];
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Hi = new Curve25519Point[M*N];
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for (int i = 0; i < M*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 count = 0;
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Scalar[] amounts = new Scalar[M];
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Scalar[] masks = new Scalar[M];
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while (count < TRIALS)
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{
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for (int j = 0; j < M; j++)
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|
{
|
|
long amount = -1L;
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while (amount > Math.pow(2,N)-1 || amount < 0L)
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amount = rando.nextLong();
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amounts[j] = new Scalar(BigInteger.valueOf(amount));
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masks[j] = randomScalar();
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}
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ProofTuple proof = PROVE(amounts,masks);
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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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