A basic framework for the cryptanalysis of digital chaos-based cryptography

Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and efficient use of chaos in the context of cryptography requires a thorough knowledge about the dynamics of the selected chaotic system. Indeed, if the final encryption system reveals enough information about the underlying chaotic system it could be possible for a cryptanalyst to get the key, part of the key or some information somehow equivalent to the key just analyzing those dynamical properties leaked by the cryptosystem. This paper shows what those dynamical properties are and how a cryptanalyst can use them to prove the inadequacy of an encryption system for the secure exchange of information. This study is performed through the introduction of a series of mathematical tools which should be the basic framework of cryptanalysis in the context of digital chaos-based cryptography.