Chaotic cryptosystems: Cryptanalysis and identifiability

A general framework based on the identiflability concept for the cryptanalysis of a large class of chaotic cryptosystems is proposed. A systematic methodology is provided, in order to test, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not. A connection between robustness against brute force attacks, uniqueness in the parameters and identiflability is pointed out. Two approaches, the outputs equality approach and the input/output relation approach, are presented to test the identifiability of the system parameters. The second approach is constructive in the sense that not only it allows to conclude on the identifiability of the parameters but it also provides a systematic technique, based on solving a set of algebraic equations, to retrieve the parameters in the context of a known plaintext attack. It turns out that cryptosystems involving polynomial nonlinearities, chaotic or not, are weak against such an attack, called algebraic attack.