Highlights
Task A:
Let f(x) be a One-Way Homomorphic Function where f(kp+1)=f(1) for any integer k and a big
prime p. Given the value f(1) and the ElGamal ciphertext CT=(f(r), f(r*b)?M) where pk=f(b)
and sk=b. Here, r is a random number chosen by the encryptor and f(r*b) is a bit string. Q1: Show how to quickly compute f(111) step by step. (2 marks)
Q2a: Show how to break the ElGamal ciphertext in details. An inefficient solution is
acceptable (2 marks). This question is for CSCI471 students only. Q2b: Suppose that the output f(x) for all x has the problem that the first bit (MSB) is equal
to 1 with probability 99.9999%. Show how to break the ElGamal ciphertext in the IND-CPA
security model. (2 marks). This question is for CSCI971 students only.
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