1. List some of the attacks on the Diffie-Hellman key exchange protocol. Present your solution for avoiding such attacks.

2a. In the Diffie-Helman protocol, g=7, p=23, x=3, and y=5.

i) What is the value of the symmetric key?

ii) What is the value of R1 and R2?

Variations of data

1) g=5, p=19, x=7, and y=3

2) g=11, p=31, x=3, and y=9

3) g=7, p=43, x=2, and y=7

b. In the Diffie-Helman protocol, what happens is x and y have the same value, that is, Alice and Bob accidentally chosen the same number? Are R1 and R2 same? Do the session key calculated by Alice and Bob have the same value? Explain what would adversary observe? Could she guess Alice's and Bob's private key? Use an example to prove your claims.

c. Suppose Fred sees your RSA signature on m1 and m2, (i.e., he sees (m1d mod n) and (m2d mod n)). How does he compute the signature on each of m1j mod n (for positive integer j), m1-1 mod n, m1 x m2 mod n, and in general m1j m2k mod n (for arbitrary j and k)?