We investigate the effectiveness of a Hidden Markov Model (HMM) with random restarts as a mean of breaking a homophonic substitution cipher. Based on extensive experiments, we find that such an HMM-based attack outperforms a previously de- veloped nested hill climb approach, particularly when the ciphertext message is short. We then consider a combination cipher, consisting of a homophonic substitution and a column transposition. We develop and analyze an attack on such a cipher. This attack employs an HMM (with random restarts), together with a hill climb to recover the column permutation. We show that this attack can succeed on relatively short ci- phertext messages. Finally, we test this combined attack on the unsolved Zodiac 340 cipher
