1) Give an example of required and optional information in a digital certificate

1) Give an example of required and optional information in a digital certificate. Is it better to maximize or minimize the amount of information in a digital certificate (from the security standpoint)?

1. Public key encryption systems operate in a way analogous to ECB. Why is it not necessary to perform any chaining in this case?
2. Suppose Alice's RSA public key is (N, e) and her private key is d. Alice wants to compute [M]_Alice (sign message M). What is a mathematical formula for this operation?
3. RSA encryption can be expressed as follows: [{M}_Alice]_Alice = M. Use the same notation to express RSA signature verification and prove it is correct.
4. Briefly explain the idea of cube root attack on RSA.
5. Briefly explain the idea and possible use of the Diffie-Hellman key exchange.
6. Briefly explain the idea of a hybrid cryptosystem that uses both public and symmetric key cryptography. What ciphers would you choose for such a system?
7. Both digital signature and MAC provide data integrity. What are the advantages of a signature?
8. Define and briefly explain the principle of non-repudiation. Give an example (not from the textbook).
9. Briefly explain the man-in-the-middle attack on Diffie-Hellman.
10. Suppose that Bob's knapsack private key is (3, 5, 10, 23), multiplier is m^-1 = 6, and modulus n = 47. What is the plaintext (in hex) if the ciphertext C = 20?
11. Consider a knapsack cryptosystem with public key (18, 30, 7, 26) and n = 47. Encrypt last four bits of the first letter of your first name.
12. Suppose Alice's RSA public key is (N, e) = (33, 3) and her private key is d = 7. If Bob encrypts the message M = 19 with Alice's public key, what is the ciphertext C?
13. Suppose Alice's RSA public key is (N, e) = (33, 3) and her private key is d = 7. If Alice signs the message M = 25 with her private key, what is the signature S?
14. Consider the RSA cryptosystem with modulus N = 3127 and encryption exponent e = 17. Find a message M that encrypts to itself (M = C).