Implementing Undeniable Signature Scheme : random e1 and e2 failed to compute correct d in verify protocol - signature

Question

First you check undeniable signature scheme verifying algorithm.
Than in that there is first step telling to chose two random x1 and x2.
But the verifying algo works sometime and sometime failed depending on two randoms. ( algo implemented in java and correctly).
For the same input if we run that algo multiple time, sometime it signature is matched and sometime not, last comparison is failed.
Plz help me. Im stuck here ( lack of math).

Answer 1

Actually it is an signature scheme and in paper it was confusing but now i've figure out solution.
Solution code is: let me know if you need me to explain this code.
import java.lang.*;
import java.util.*;
import java.math.*;
import java.security.MessageDigest;
import java.nio.file.*;
import java.io.*;
import java.security.*;
class UndeniableSignature {
int Q; // prime
int P; // prime of form P = 2Q + 1
BigInteger G; // Generator of Z*P
int D; // private key belongs to [2 ... Q-1]
BigInteger Y; // G^D (mod P)
int invD; // D^-1 (mod Q)
Random rand = new SecureRandom(); // uniform random generator
public int[] extendedEuclidean(int a, int b) {
if(b==0) {
int[] arr=new int[3];
arr[0] = a;
arr[1] = 1;
arr[2] = 0;
return arr;
}
int[] subResult = extendedEuclidean(b,a%b);
int[] arr=new int[3];
arr[0] = subResult[0];
arr[1] = subResult[2];
arr[2] = subResult[1] - (a/b) * subResult[2];
return arr;
}
public int secureRandom(int max) {
return rand.nextInt(max);
}
public BigInteger getGenerator(BigInteger p, BigInteger q){
BigInteger generator = BigInteger.ZERO;
BigInteger exp = p.subtract(BigInteger.ONE).divide(q);
for(int i=2;i<p.intValue()-1;i++) {
generator = BigInteger.valueOf(i);
generator = generator.modPow(exp, p);
if(!generator.equals(BigInteger.ONE)) return generator;
}
// do {
// generator = BigInteger.valueOf(this.secureRandom(p.intValue()));
// generator = generator.modPow(exp, p);
// } while(generator.equals(BigInteger.ONE));
return generator;
// BigInteger generator = BigInteger.ZERO;
// for(long i = 2; i < p.intValue()-1; i++)
// {
// generator = BigInteger.valueOf(i);
// if(generator.modPow(BigInteger.valueOf(2), p).equals(BigInteger.ONE)) continue;
// if(generator.modPow(q, p).equals(BigInteger.ONE)) continue;
// else return generator;
// }
// return generator;
}
public String readMessageFile(String filename) {
try {
return new String(Files.readAllBytes(Paths.get(filename)));
} catch(Exception ex) {
System.out.println("ERR: Can't read file.");
}
return null;
}
public int[] readSignatureFile(String filename) {
InputStream is=null;
DataInputStream dis=null;
try {
is = new FileInputStream(filename);
dis = new DataInputStream(is);
ArrayList intList = new ArrayList();
int count = 0;
while(dis.available()>0) {
intList.add(dis.readInt());
}
int[] data = new int[intList.size()];
for(int i=0;i<data.length;i++) {
data[i] = (int)intList.get(i);
}
dis.close();
is.close();
return data;
} catch(Exception ex) {
System.out.println("ERR: Can't read file.");
}
return null;
}
public static void writeSignatureFile(String filename, int[] contents) {
FileOutputStream fos=null;
DataOutputStream dos=null;
try {
fos = new FileOutputStream(filename);
dos = new DataOutputStream(fos);
for(int i=0;i<contents.length;i++) {
dos.writeInt(contents[i]);
}
dos.flush();
dos.close();
fos.close();
} catch(Exception ex) {
System.out.println("ERR: Can't write to file.");
}
}
public void keyGeneration() {
System.out.println("UNDENIABLE SIGNATURE SCHEME");
System.out.println("- KEY GENERATION");
System.out.print("\tEnter prime P (such that P=2Q+1) : ");
this.P = new Scanner(System.in).nextInt();
this.Q = (this.P - 1)/2;
System.out.println("\tPrime Q is "+this.Q+".");
this.G = this.getGenerator(BigInteger.valueOf(this.P),BigInteger.valueOf(this.Q));
System.out.println("\tGenerator G of group Z*("+this.P+") is "+this.G+".");
System.out.print("\tEnter private key D (belongs to Z*P) :");
this.D = new Scanner(System.in).nextInt();
while(this.D <= 0 || this.D >= this.P) {
System.out.println("\tInvalid private key selected, please try again.");
System.out.print("\tEnter private key D (belongs to Z*P) :");
this.D = new Scanner(System.in).nextInt();
}
this.Y = this.G.modPow(BigInteger.valueOf(this.D), BigInteger.valueOf(this.P));
System.out.println("\tG^D(mod P) = "+this.Y+".");
System.out.println("\tPublic Key [P, G, Y] is ["+this.P+", "+this.G+", "+this.Y+"].");
System.out.println("\tPrivate Key [D] is ["+this.D+"].");
int[] g = this.extendedEuclidean(this.D, this.Q);
this.invD = g[1];
if(this.invD < 0) {
this.invD = this.Q - Math.abs(this.invD);
System.out.println("\tInverse was negative.");
}
System.out.println("\tInverse of D (mod Q) is "+this.invD+".");
}
public void messageSigning(String message) {
int[] signatureBytes = new int[message.length()];
for(int i=0;i<message.length();i++) {
BigInteger m = BigInteger.valueOf((int)message.charAt(i));//this.H(message.charAt(i)+"");
BigInteger s = m.pow(this.D).mod(BigInteger.valueOf(this.P));
signatureBytes[i] = s.intValue();
// System.out.println("\tchar:"+message.charAt(i)+", m:"+m+", s:"+s+", S:"+signatureBytes[i]);
}
System.out.print("\tEnter signature filename : ");
String signatureFilename = new Scanner(System.in).nextLine();
this.writeSignatureFile(signatureFilename, signatureBytes);
System.out.println("\tSignature is successfully generated.");
}
// see the condition proof for w=W for solution of problem
public boolean signatureVerification(String message, int[] signature) {
for(int i=0;i<message.length();i++) {
// rand=new Random();
// int x1 = this.secureRandom(this.Q-1);
// while(x1<=1) x1 = this.secureRandom(this.Q-1);
// int x2 = this.secureRandom(this.Q-1);
// while(x2<=1) x2 = this.secureRandom(this.Q-1);
int x1 = 38, x2 = 397;
BigInteger S = BigInteger.valueOf(signature[i]);
BigInteger s = S.pow(x1);
BigInteger y = this.Y.pow(x2);
BigInteger z = s.multiply(y).mod(BigInteger.valueOf(this.P));
BigInteger w = signerChallengeForVerification(z);
BigInteger M = BigInteger.valueOf((int)message.charAt(i));//this.H(message.charAt(i)+"");
BigInteger m = M.pow(x1);
BigInteger g = this.G.pow(x2);
BigInteger mg = m.multiply(g);
BigInteger W = mg.mod(BigInteger.valueOf(this.P));
// System.out.println("\ti:"+i+", char:"+message.charAt(i)+", m:"+M+", s:"+S);
// System.out.println("\t\tz:"+z+", w:"+w+" , W:"+W);
if(!w.equals(W)) {
return false;
}
}
return true;
}
public boolean disavowalProtocol(String message, int[] signature) {
int x1 = 38, x2 = 397;
BigInteger response1 = BigInteger.ZERO;
BigInteger response2 = BigInteger.ZERO;
// verification 1
for(int i=0;i<message.length();i++) {
BigInteger S = BigInteger.valueOf(signature[i]);
BigInteger s = S.pow(x1);
BigInteger y = this.Y.pow(x2);
BigInteger z = s.multiply(y).mod(BigInteger.valueOf(this.P));
BigInteger w = signerChallengeForVerification(z);
BigInteger M = BigInteger.valueOf((int)message.charAt(i));//this.H(message.charAt(i)+"");
BigInteger m = M.pow(x1);
BigInteger g = this.G.pow(x2);
BigInteger mg = m.multiply(g);
BigInteger W = mg.mod(BigInteger.valueOf(this.P));
// System.out.println("\ti:"+i+", char:"+message.charAt(i)+", m:"+M+", s:"+S);
// System.out.println("\t\tz:"+z+", w:"+w+" , W:"+W);
if(!w.equals(W)) {
response1 = w;
break;
}
}
if(response1.equals(BigInteger.ZERO)) {
return false; // signature is not forgery bcoz signature is matched
}
// verification 2
for(int i=0;i<message.length();i++) {
BigInteger S = BigInteger.valueOf(signature[i]);
BigInteger s = S.pow(x1);
BigInteger y = this.Y.pow(x2);
BigInteger z = s.multiply(y).mod(BigInteger.valueOf(this.P));
BigInteger w = signerChallengeForVerification(z);
BigInteger M = BigInteger.valueOf((int)message.charAt(i));//this.H(message.charAt(i)+"");
BigInteger m = M.pow(x1);
BigInteger g = this.G.pow(x2);
BigInteger mg = m.multiply(g);
BigInteger W = mg.mod(BigInteger.valueOf(this.P));
// System.out.println("\ti:"+i+", char:"+message.charAt(i)+", m:"+M+", s:"+S);
// System.out.println("\t\tz:"+z+", w:"+w+" , W:"+W);
if(!w.equals(W)) {
response2 = w;
break;
}
}
if(response2.equals(BigInteger.ZERO)) {
return false; // signature is not forgery bcoz signature is matched
}
// forgery validation now it comes here only when one of above validation is failed
BigInteger A = response1.divide(this.G.pow(x2)).pow(x1).mod(BigInteger.valueOf(this.P));
BigInteger B = response2.divide(this.G.pow(x1)).pow(x2).mod(BigInteger.valueOf(this.P));
return A.equals(B); // signature is forgery if A == B
}
public BigInteger signerChallengeForVerification(BigInteger z) {
// System.out.println("\tchallange: "+z+", invD:"+this.invD+", d:"+(z.pow(this.invD).mod(BigInteger.valueOf(this.P))));
return z.pow(this.invD).mod(BigInteger.valueOf(this.P));
}
}
class Program {
public static void main(String[] args) {
String msgFilename, signatureFilename, message;
UndeniableSignature scheme = new UndeniableSignature();
scheme.keyGeneration();
int choice = 0;
do {
System.out.println();
System.out.println("- OPERATIONS");
System.out.println("\t1. Sign message");
System.out.println("\t2. Verify signature");
System.out.println("\t3. Disavowal protocal");
System.out.println("\t4. Exit");
System.out.print("\tChoice : ");
choice = new Scanner(System.in).nextInt();
System.out.println();
switch(choice) {
case 1:
System.out.println("- MESSAGE SIGNING");
System.out.print("\tEnter message filename : ");
msgFilename = new Scanner(System.in).nextLine();
message = new String(scheme.readMessageFile(msgFilename));
scheme.messageSigning(message);
break;
case 2:
System.out.println("- SIGNATURE VERIFICATION");
System.out.print("\tEnter message filename : ");
msgFilename = new Scanner(System.in).nextLine();
System.out.print("\tEnter signature filename : ");
signatureFilename = new Scanner(System.in).nextLine();
message = scheme.readMessageFile(msgFilename);
int[] signatureBytes = scheme.readSignatureFile(signatureFilename);
if(scheme.signatureVerification(message, signatureBytes)) {
System.out.println("\tSignature IS valid.");
} else {
System.out.println("\tSignature is NOT valid.");
}
break;
case 3:
System.out.println("- DISAVOWAL VERIFICATION");
System.out.print("\tEnter message filename : ");
msgFilename = new Scanner(System.in).nextLine();
System.out.print("\tEnter signature filename : ");
signatureFilename = new Scanner(System.in).nextLine();
message = scheme.readMessageFile(msgFilename);
signatureBytes = scheme.readSignatureFile(signatureFilename);
if(scheme.disavowalProtocol(message, signatureBytes)) {
System.out.println("\tSignature IS forgery.");
} else {
System.out.println("\tSignature is NOT forgery.");
}
break;
case 4:
System.out.println("- BYE BYE");
break;
}
} while(choice!=4);
}
}
thanks :D