## CS 167 - Cryptography Homework 5, 50 Points Due: Friday, February 22, 2008

1. Trappe-Washington, Exercise 10 of Chapter 7.
2. Trappe-Washington, Exercise 11 of Chapter 7.
3. Alice wants to send Bob a message M that is the price she is willing to pay for his used car (M is just an integer in binary). She uses the ElGamal algorithm to encrypt M into the ciphertext C using Bob's public key, so only he can decrypt it. But Eve has intercepted C and she doesn't even know Bob's public key. Explain how Eve can alter the ciphertext C to change it into C' so that if she sends C' to Bob (with Eve pretending to be Alice), then, after Bob has decrypted C', he will get a plaintext message that is twice the value of M.
4. Suppose Eve has captured two ciphertexts C=(a,b) and D=(c,d) for two separate message M and N, respectively, that were sent to Bob under the ElGamal encryption scheme (using the same public key for Bob). Explain how Eve can construct a valid encyption of the product MN.
5. Trappe-Washington, Exercise 10 of Chapter 8.