Chaotic Cryptosystems: Cryptanalysis and Identifiability

Floriane Anstett (1) , Gilles Millérioux (1) , Gérard Bloch (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

A general framework and a systematic methodology for the cryptanalysis of a large class of chaotic cryptosystems are proposed. More precisely, it is tested, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not. Robustness against brute force attacks is first considered. A connection between uniqueness in the parameters and identifiability 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 to retrieve the parameters in the context of a known plaintext attack. It is shown that cryptosystems involving polynomial nonlinearities, chaotic or not, are weak against this attack, called algebraic attack.

Mots clés: Chaotic cryptosystems; cryptanalysis; identifiability; brute force attack; known plaintext attack; algebraic attack

Domaines: Automatique; Dynamique Chaotique [nlin.CD]

Floriane Anstett, Gilles Millérioux, Gérard Bloch. Chaotic Cryptosystems: Cryptanalysis and Identifiability. IEEE Transactions on Circuits and Systems I: Regular Papers, 2006, 53 (12), pp.2673-2680. ⟨10.1109/TCSI.2006.885979⟩. ⟨hal-00113989⟩