Answer the given question with a proper explanation and step-by-step solution.  Alice and Bob are using the Diffie Hellman key exchange to establish a secret key among them. Bob sends Alice [719, 3, 191]. Alice responds with, 543. If Bob's secret number, x, is 16. What is the secret key stablished?

Exercise 1 (The RSA basics ( Alice forms a public key for the "textbook" RSA public-key encryption and signature schemes, choosing N = 1073 and e = 715. 1. Encrypt the message M = 3 for Alice. 2. What is Alice's private key, and how does she use it for decrypting the received ciphertext? 3. Generate a signature on the message M = 1234567 using the following simple hash function H: {0, 1} ZN such that H(M)= 3M + 5 (mod N). 4. Verify that the signature you generated in the previous step is a valid signature.

Let (M, C, e, d, Ke, Ka) denote the RSA cryptosystem with public key (s, n) = (5, 26051) and private key t = 5141. (a) Compute C = e(200, (5, 26051)). (b) Compute M = d(2,5141)

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?