An analysis of an HMM-based attack on the substitution cipher with error-prone ciphertext

The classic simple substitution cipher is an elementary cipher for which many automated ciphertext-only attack algorithms have been developed. The reliable performance of these algorithms is, however, conditioned on obtaining an error-free version of the ciphertext. Although cryptosystems are designed according to Kerckhoffs's assumption, i.e., the security of the cipher resides only in the secret key, the existence of practical physical-layer security codes may provide a vehicle to restricting attackers to error-prone ciphertext, and thus enhance cryptographic secrecy by means of natural phenomena in a noisy channel. This additional layer of security, however, must be quantified to understand the possible boons to multilayer security solutions with secrecy coding at the physical layer. This paper provides an experimental analysis of the behavior of an HMM-based substitution cipher attack to quantify the enhancement in security when errors occur as the ciphertext passes through a discrete memoryless symmetric channel. Results indicate that a bound on the performance of the attack can be directly linked to the mutual information between the inputs and outputs of the channel. Rough linear approximations to the high-end performance of the attack are also presented.