package prover; import com.google.protobuf.ByteString; import com.google.protobuf.InvalidProtocolBufferException; import meerkat.crypto.concrete.ECElGamalEncryption; import meerkat.crypto.mixnet.Mix2ZeroKnowledgeProver; import meerkat.crypto.mixnet.Mix2ZeroKnowledgeVerifier; import meerkat.protobuf.ConcreteCrypto; import meerkat.protobuf.ConcreteCrypto.ElGamalCiphertext; import meerkat.protobuf.Crypto; import meerkat.protobuf.Mixing; import org.bouncycastle.math.ec.ECPoint; import qilin.primitives.RandomOracle; import qilin.primitives.concrete.ECGroup; import java.math.BigInteger; import java.util.List; import java.util.Random; public class Prover implements Mix2ZeroKnowledgeProver { ECGroup group; RandomOracle randomOracle; Random rand; ECElGamalEncryption ecElGamalEncryption; ECPoint g,h; public Prover(Random rand,ECElGamalEncryption encryptor,RandomOracle randomOracle) { this.rand = rand; this.ecElGamalEncryption = encryptor; this.randomOracle = randomOracle; this.group = ecElGamalEncryption.getGroup(); this.g = group.getGenerator(); this.h = ecElGamalEncryption.getElGamalPK().getPK(); } public Mixing.ZeroKnowledgeProof prove(Crypto.RerandomizableEncryptedMessage in1, Crypto.RerandomizableEncryptedMessage in2, Crypto.RerandomizableEncryptedMessage out1, Crypto.RerandomizableEncryptedMessage out2, boolean sw,int i,int j, int layer, Crypto.EncryptionRandomness r1, Crypto.EncryptionRandomness r2) throws InvalidProtocolBufferException { Mixing.ZeroKnowledgeProof.OrProof first,second,third,fourth; ProofOrganizer organizer = new ProofOrganizer(in1,in2,out1,out2,r1,r2,sw); System.out.println("first"); first = createOrProof(organizer.getOrProofInput(ProofOrganizer.OrProofOrder.first)); System.out.println("second"); second = createOrProof(organizer.getOrProofInput(ProofOrganizer.OrProofOrder.second)); System.out.println("third"); third = createOrProof(organizer.getOrProofInput(ProofOrganizer.OrProofOrder.third)); System.out.println("fourth"); fourth = createOrProof(organizer.getOrProofInput(ProofOrganizer.OrProofOrder.fourth)); Mixing.ZeroKnowledgeProof.Location location = Mixing.ZeroKnowledgeProof.Location.newBuilder() .setI(i) .setJ(j) .setLayer(layer) .build(); Mixing.ZeroKnowledgeProof result = Mixing.ZeroKnowledgeProof.newBuilder() .setFirst(first) .setSecond(second) .setThird(third) .setFourth(fourth) .setLocation(location) .build(); return result; } private Mixing.ZeroKnowledgeProof.OrProof createOrProof(ProofOrganizer.OrProofInput orProofInput) throws InvalidProtocolBufferException { ElGamalCiphertext e1ElGamal = ECElGamalEncryption.rerandomizableEncryptedMessage2ElGamalCiphertext(orProofInput.e1); ElGamalCiphertext e2ElGamal = ECElGamalEncryption.rerandomizableEncryptedMessage2ElGamalCiphertext(orProofInput.e2); ElGamalCiphertext e1TagElGamal = ECElGamalEncryption.rerandomizableEncryptedMessage2ElGamalCiphertext(orProofInput.e1New); ElGamalCiphertext e2TagElGamal = ECElGamalEncryption.rerandomizableEncryptedMessage2ElGamalCiphertext(orProofInput.e2New); return createOrProofElGamal(e1ElGamal,e2ElGamal,e1TagElGamal,e2TagElGamal,orProofInput.x,orProofInput.flag); } private ECPoint convert2ECPoint(ByteString bs){ return group.decode(bs.toByteArray()); } public BigInteger hash(Mixing.ZeroKnowledgeProof.OrProof.ForRandomOracle input) { byte[] arr = input.toByteArray(); return new BigInteger(this.randomOracle.hash(arr,arr.length)); } private Mixing.ZeroKnowledgeProof.OrProof createOrProofElGamal(ElGamalCiphertext e1, ElGamalCiphertext e2, ElGamalCiphertext e1New, ElGamalCiphertext e2New, Crypto.EncryptionRandomness x, ProofOrganizer.TrueCouple flag) { ECPoint g1 = g; ECPoint h1 = group.add(convert2ECPoint(e1New.getC1()),group.negate(convert2ECPoint(e1.getC1()))); ECPoint g2 = h; ECPoint h2 = group.add(convert2ECPoint(e1New.getC2()),group.negate(convert2ECPoint(e1.getC2()))); ECPoint g1Tag = g; ECPoint h1Tag = group.add(convert2ECPoint(e2New.getC1()),group.negate(convert2ECPoint(e2.getC1()))); ECPoint g2Tag = h; ECPoint h2Tag = group.add(convert2ECPoint(e2New.getC2()),group.negate(convert2ECPoint(e2.getC2()))); BigInteger r = new BigInteger(ecElGamalEncryption.generateRandomness(rand).getData().toByteArray()).mod(group.orderUpperBound()); BigInteger c1,c2,z,zTag; ECPoint u,v,uTag,vTag; Mixing.ZeroKnowledgeProof.OrProof.ForRandomOracle forRandomOracle; switch (flag) { case left: c2 = new BigInteger(ecElGamalEncryption.generateRandomness(rand).getData().toByteArray()).mod(group.orderUpperBound()); zTag = new BigInteger(ecElGamalEncryption.generateRandomness(rand).getData().toByteArray()).mod(group.orderUpperBound()); //step 1 u = group.multiply(g1, r); v = group.multiply(g2, r); uTag = group.add(group.multiply(g1Tag, zTag), group.negate(group.multiply(h1Tag, c2))); vTag = group.add(group.multiply(g2Tag, zTag), group.negate(group.multiply(h2Tag, c2))); //step 2 // c1 = (hash(input + step1) + group size - c2)% group size forRandomOracle = Mixing.ZeroKnowledgeProof.OrProof.ForRandomOracle.newBuilder() .setG1(ByteString.copyFrom(group.encode(g1))) .setH1(ByteString.copyFrom(group.encode(h1))) .setG2(ByteString.copyFrom(group.encode(g2))) .setH2(ByteString.copyFrom(group.encode(h2))) .setG1Tag(ByteString.copyFrom(group.encode(g1Tag))) .setH1Tag(ByteString.copyFrom(group.encode(h1Tag))) .setG2Tag(ByteString.copyFrom(group.encode(g2Tag))) .setH2Tag(ByteString.copyFrom(group.encode(h2Tag))) .setU(ByteString.copyFrom(group.encode(u))) .setV(ByteString.copyFrom(group.encode(v))) .setUTag(ByteString.copyFrom(group.encode(uTag))) .setVTag(ByteString.copyFrom(group.encode(vTag))) .build(); c1 = hash(forRandomOracle).add(group.orderUpperBound().subtract(c2)).mod(group.orderUpperBound()); //step 3 //z = (r + c1 * x) % group size; z = r.add(c1.multiply(new BigInteger(x.getData().toByteArray()))).mod(group.orderUpperBound()); break; case right: c1 = new BigInteger(ecElGamalEncryption.generateRandomness(rand).getData().toByteArray()).mod(group.orderUpperBound()); z = new BigInteger(ecElGamalEncryption.generateRandomness(rand).getData().toByteArray()).mod(group.orderUpperBound()); //step 1 uTag = group.multiply(g1Tag, r); vTag = group.multiply(g2Tag, r); u = group.add(group.multiply(g1, z), group.negate(group.multiply(h1, c1))); v = group.add(group.multiply(g2, z), group.negate(group.multiply(h2, c1))); //step 2 // c1 = (hash(input + step1) + group size - c1)% group size forRandomOracle = Mixing.ZeroKnowledgeProof.OrProof.ForRandomOracle.newBuilder() .setG1(ByteString.copyFrom(group.encode(g1))) .setH1(ByteString.copyFrom(group.encode(h1))) .setG2(ByteString.copyFrom(group.encode(g2))) .setH2(ByteString.copyFrom(group.encode(h2))) .setG1Tag(ByteString.copyFrom(group.encode(g1Tag))) .setH1Tag(ByteString.copyFrom(group.encode(h1Tag))) .setG2Tag(ByteString.copyFrom(group.encode(g2Tag))) .setH2Tag(ByteString.copyFrom(group.encode(h2Tag))) .setU(ByteString.copyFrom(group.encode(u))) .setV(ByteString.copyFrom(group.encode(v))) .setUTag(ByteString.copyFrom(group.encode(uTag))) .setVTag(ByteString.copyFrom(group.encode(vTag))) .build(); c2 = hash(forRandomOracle).add(group.orderUpperBound().subtract(c1)).mod(group.orderUpperBound()); //step 3 //zTag = (r + c2 * x) % group size; zTag = r.add(c2.multiply(new BigInteger(x.getData().toByteArray()))).mod(group.orderUpperBound()); break; default: return null; } //debugging assert (group.multiply(g1, z).equals(group.add(u, group.multiply(h1,c1)))); assert (group.multiply(g2, z).equals(group.add(v, group.multiply(h2,c1)))); assert (group.multiply(g1Tag, zTag).equals(group.add(uTag, group.multiply(h1Tag,c2)))); assert (group.multiply(g2Tag, zTag).equals(group.add(vTag, group.multiply(h2Tag,c2)))); return Mixing.ZeroKnowledgeProof.OrProof.newBuilder() .setG1(ByteString.copyFrom(group.encode(g1))) .setH1(ByteString.copyFrom(group.encode(h1))) .setG2(ByteString.copyFrom(group.encode(g2))) .setH2(ByteString.copyFrom(group.encode(h2))) .setG1Tag(ByteString.copyFrom(group.encode(g1Tag))) .setH1Tag(ByteString.copyFrom(group.encode(h1Tag))) .setG2Tag(ByteString.copyFrom(group.encode(g2Tag))) .setH2Tag(ByteString.copyFrom(group.encode(h2Tag))) .setU(ByteString.copyFrom(group.encode(u))) .setV(ByteString.copyFrom(group.encode(v))) .setUTag(ByteString.copyFrom(group.encode(uTag))) .setVTag(ByteString.copyFrom(group.encode(vTag))) .setC1(ByteString.copyFrom(c1.toByteArray())) .setC2(ByteString.copyFrom(c2.toByteArray())) .setZ(ByteString.copyFrom(z.toByteArray())) .setZTag(ByteString.copyFrom(zTag.toByteArray())) .build(); } }