Requirements: 1. Generate key pair using RSA Implement method (p and q can be parameters of this method or class fields, by your choice. 2. Use the key pair to encrypt and decrypt a message Implement...

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Requirements: 1. Generate key pair using RSA Implement method (p and q can be parameters of this method or class fields, by your choice. 2. Use the key pair to encrypt and decrypt a message Implement encrypt and decrypt methods 3. Using key pair to generate the verify digital signature Implement digital signature generation and verification methods. 4. Prove the homomorphic property of RSA E(m1).E(m2) = E(m1.m2) (where E is encryption of a message) 5. In main method: Message can be randomly generated or chosen by your choice RSA Algorithm: To generate key pair: · -  Pick large primes p and q · -  Let n = p*q, keep p and q to yourself. · -  For public key, choose e that is relatively prime to ø(n) =(p-1)(q-1), let pub = · -  For private key, find d that is the multiplicative inverse of e mod ø(n), i.e., e*d =1 mod ø(n), let pri = . How does RSA work? Key Generation ● Input: none ● Computation: -Select two prime integers p,q - compute integers n = p * q - phi = (p-1) * (q-1) - Select small odd integer e such that gcd(e, phi) = 1 - compute integer d such that (e * d) %phi = 1 ● Output: n, e, and d · ●  How to find big primes p and q? · ●  Hoe to compute gcd? · ●  How to find mod inverse? · ●  How to manipulate big numbers ○ Java integers are of limited size Java BigInteger Class · ●  Import java.math.BigInteger · ●  Common operations · -  Add, subtract, multiply, divide · -  Equals, compareTo · ●  Useful constants -BigInteger.ONE -BigInteger.ZERO · ●  Useful Constructor -BigInteger(int numBits, int certainty, Random rnd) -Need to generate a random number beforehand - Could use 100 for certainty More useful operations: -probablePrime(int bitLength, Random rnd) ● Could use this one instead of the constructor -gcd(BigInteger val) -modInverse(BigInteger m) -modPow(BigInteger exponent, BigInteger m) Questions.... Greatest Common Divisor // greatest common divisor Int gcd(int a, int b){ If (b == 0) return(a); Else