Cryptography - Week 6

1. Which of the following is a drawback of the private-key setting that is NOT addressed by the public-key setting?

• The communicating parties need the ability to generate random bits.

2. Which of the following BEST describes the security offered by the Diffie-Hellman key-exchange protocol (assuming the DDH problem is hard)?

• An attacker eavesdropping on an execution of the protocol cannot distinguish the key shared by the parties from a uniform key.

3. Assume the Diffie-Hellman protocol is run by two parties in the subgroup of ℤ∗23 generated by 2. (This subgroup has order 11.) If the first party chooses private exponent 3 and the second chooses private exponent 10, which of the following characterizes the execution of the protocol in this case?

• The first party sends 8, the second party sends 12, and they share the key 3.

4. In which of the following scenarios is public-key encryption a better choice than private-key encryption?

• A user wants to send his credit-card number to a merchant on the web.

 

5. Which of the following would NOT be a secure way for a receiver to distribute her key for a public-key encryption scheme? (Assume a passive, eavesdropping attacker here.)

• Post the private key on one's webpage.

6. Which of the following is true in the public-key setting, but NOT true in the private-key setting?

• Allowing the attacker to have access to an encryption oracle makes no difference when defining security.

7. Assume for the purposes of this question a public-key encryption scheme for which the time to encrypt a 128-bit message is 100 times slower than the time to compute one AES evaluation. Which of the following is true if we want to encrypt a 100MB message M?

• If hybrid encryption is used, then public-key encryption of M will take roughly the same time as private-key encryption of M.

8. Assume El Gamal encryption, where the group being used is ℤ∗47 with generator 5. (This group has order 46, which is not prime. But El Gamal encryption can be defined in any cyclic group.) Assume the public key contains h=10. Say an attacker sees a ciphertext (41, 18) that is the encryption of some unknown message m. Which of the following is an encryption of [5mmod47]?

• (41, 43)

9. Assume "plain RSA" encryption is used with public key (N=33,e=3). What is the encryption of the message m=2?

• 8

10. Which of the following is true about "plain RSA" encryption (assuming the RSA problem is hard)?

• If the message m is uniform in ℤ∗N, then m cannot be recovered in its entirety from the ciphertext in polynomial time.