I’m working on a cyber security question and need guidance to help me learn.

1. Assume that Schnorr digital signature uses prime number p = 4637. Answer the following questions:

(a) Find q which is the greatest prime factor of p ? 1.

(b) Find some positive integer a so that 1 < a < p and a q ?p 1.

(c) Assuming that s = 53 is a random private key, find the public key v corresponding to s.

(d) Assuming that we use hash function H(µ) = µ mod 43 to digest messages for signing, find the signature of message M = “hi” = 3334 (you must pick a random number between zero and q before finding the signature).

(e) Illustrate how receiver will verify the obtained signature of part 1.d using global public key, the hash function H and the sender’s public key v.

2. Assume that ElGamal digital signature uses prime number q = 7919 and its primitive root ? = 1239. Answer the following questions:

(a) Given the random private key XA = 4321, find its corresponding public key YA.

(b) Assuming that ElGamal digital signature uses the hash function H(µ) = µ mod q, find the signature of message M = “hello”.

(c) Illustrate how receiver will verify the obtained signature of part 2.b using sender’s public key.

3. List and compare the security of four classes of techniques for public key distribution.