1. In the Diffie-Hellman algorithm for key exchange, suppose Alice sends Bob (19, 3, 5) corresponding to (p, g, ga). Bob responds with (12). Determine the session key.
2. Consider RSA encryption with P = 7, q = 11.
a. List four legal values for e
b. Decrypt the cipher c = 321 assuming it was encrypted using the smallest value of e from the possible values (Assume the encryption is done one digit at a time).
3. In the class, we discussed the side channel attack of deriving the private key bits over a network using selected plain texts and monitoring the time to sign the text. Describe how you will continue the attack to derive the second bit of the private key (note that in class, we discussed the derivation of only the first bit).
4. Describe the difficulties in distributing keys in resource-constrained environments such as sensor networks and RFIDs. How is this problem addressed in industry?
5. Compare the complexities of elliptic curve crypto systems with the RSA scheme.