Question

Write a program in JAVA using the BigInteger library that can be used to check a RSA signature, based on the signer's RSA public key pair. To test your program, take the following information about a message Alice signed and use the verify signature to reproduce the message Alice signed and convert it back to String format.

n = 68236588817658935156357212288430888402056854883696767622850112840388111129987

e = 65537

signature = 46612763171375975923246342580942010388414761162366281695045830390867474569531

Answer 1

ANSWER::

JAVA language using the BigInteger library that can be used to check a RSA signature is as follows:--

import java.security.SecureRandom;

import java.util.Random;

import java.math.BigInteger;

int bit = 1024;

Random r = new SecureRandom();

BigInteger x = BigInteger.probablePrime(bit/ 2, r);

BigInteger y = BigInteger.probablePrime(bit/ 2, r);

BigInteger a = x.multiply(y);

BigInteger c = x.subtract(BigInteger.ONE)

    .multiply(y.subtract(BigInteger.ONE));

BigInteger i;

do i = new BigInteger(c.bitLength(), r);

while (i.compareTo(BigInteger.ONE) <= 0

    i.compareTo(c) >= 0

    !i.gcd(c).equals(BigInteger.ONE));

BigInteger j = i.modInverse(c);

BigInteger m = (“write your message:”);

BigInteger encoding = m.modPow(i, a);

BigInteger decoding = encoding.modPow(j, a);

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