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

Abstract

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.

Studying the Properties of Pixels Permutations Based on Discretized Standard Map

“…As noted above, in [5] was introduced discretized standard map for pixels permutations, that is given by the following iterative equations: Properties of the discretized map (1) are not as perfect as the original [3], but it can be implemented in the integer i x and i y values of intervals, which reduce the computational complexity and are more convenient to encryption data applications [5].…”

“…For the diffusion step typically is used PRNG based on one, two or multi-dimensional maps. Along with the new encryption algorithms based on deterministic chaos, the works dedicated to cryptanalysis have been presented [1,3,10,12]. In [10] was proposed one of the earliest chaotic image encryption algorithms which uses discretized version of Chirikov standard map for pixels permutations [4].…”

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

“…Many analysis methods success with additive perturbation [ 46 , 47 , 48 ]. With the development of analysis methods, analysis of chaotic dynamics can used as a powerful tool to attack chaos-based cryptosystems [ 53 ]. However, to date, there has not been any report about a successful attack to a chaotic block cipher by means of analysis of chaotic dynamics.…”