[a] Alice and Bob use the Diffie-Hellman algorithm to exchange secret key. Eve intercepts the following values: q=283 a =12 Y,=77 Y, =196 Assume that Eve has decided to use brute force attack to find the private key for Alice. Find the private key for Alice using brute force attack. [4 Points [b] Consider the following security scheme: Source A Destination B M PU, Compare E.PR..HA) Redesign the above scheme to provide confidentiality alongside with authentication and digital signature. [2 Points) [] With your own words, explain how does Pretty Good Privacy (PGP) provides confidentiality. [2 Points] [d] Let G(x) = H(X)|| H'(x) where H(x) and (x) are hash functions with n- bit outputs for each. How many messages does an attacker need to generate to find a collision using a brute-force attack if G(x) is used as the hash function in the communication? [2 Points