1- Symmetric Key Cryptography and Cryptanalysis Assignment: Differential Cryptanalysis Problem 1 Using a 3-round S-DES system someone has generated the following four pairs of plaintexts and ciphertexts: [011011001011, 010001010100] [111011001011, 001001010111] [011111001011, 110010001101] [011010001011, 010101110100] Use differential cryptanalaysis to find the key.

2- Consider the following DES-like encryption method. Start with a message of 2n bits. Divide it into two blocks of length n (a left half and a right half): L0R0. The key K consists of k bits, for some integer k. There is a function f(K, M) that takes an input of k bits and n bits and gives an output of n bits. One round of encryption starts with the pair LjRj . The output is the pair Lj+1Rj+1, where Rj+1 = Lj Lf(K, Rj ) and Lj+1 = Rj . This is done for m rounds.

a) If you have m-round encryption, how would you decrypt the ciphertext LmRm using the same key K? Prove that your decryption works.

b) Suppose K has n bits and f(K, M) = K LM, and suppose the encryption consists of 2 rounds (m=2). If you have only a ciphertext, can you deduce the plaintext and the key? If you have the ciphertext and the corresponding plaintext, can you deduce the key? Justify your answer. 1