CRYPYOGRAPHY (Suppose that Alice the encrypts same plaintext m to Bob and charles who have their RSA public keys (N,e,) and (N,C,) respectively with gcd(e 1,e 2 )=1.if you are an eves dropper observing this communication, explain how you can find m

Alice and Bob use the ElGamal scheme with a common prime q= 131 and a primitive root a=6. Let Bob's public key be Yn=3. A. What is the ciphertext of M=9 if Alice chooses the random integer k=4? B. If Alice uses the same k to encrypt two messages M₁ and M₂ as (12, 65) and (12, 64), what is the relation between M₁ and M₂?

Consider an RSA key set for Alice with p = 23, q = 17, n = 391 and e = 15.a)  Her public key is (e, n) = (15, 391). Is her private key (d, n) = (47, 391)? JusVfy your answer. b)  Suppose Bob wants to encrypt a message 90 for Alice using RSA keys for confidenVality. Whatis the corresponding cipher text?Justify your answer.

Alice and Bob use the ElGamal scheme with a common prime q= 131 and a primitive root a=6. Let Bob's public key be Yn=3. A. What is the ciphertext of M-9 if Alice chooses the random integer k=4? B. If Alice uses the same k to encrypt two messages M₁ and M₂ as (12, 65) and (12, 64), what is the relation between M₁ and M₂?