CS 167  Cryptography Homework 5, 50 Points
Due: Friday, February 22, 2008
 TrappeWashington, Exercise 10 of Chapter 7.
 TrappeWashington, Exercise 11 of Chapter 7.

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.

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.
 TrappeWashington, Exercise 10 of Chapter 8.