This paper carries out the image encryption with a revised and modified cryptosystem based on a rule-90 cellular automaton. For this purpose, we used an appropriate and convenient matrix approach to implement the main components of the encryption system, two indexed families of permutations and a pseudo-random bit generator. Furthermore, we modify the encryption scheme for improving its security. This makes our encryption proposal resist some common attacks, e.g. chosen plain-text attack, and the encryption and decryption processes are performed in a flexible way. Also, some security aspects of the cryptosystem are evaluated with a series of statistical tests exhibiting good results. It is believed that this proposal fits naturally in the present digital technology and is capable of achieving high levels of performance.

The main components of an encryption system based on rule 90 cellular automata, i.e., two indexed families of permutations and a pseudo-random bit generator are implemented in a very flexible way through a convenient matrix approach.

The technique of detrended fluctuation analysis (DFA) has been widely used to unveil scaling properties of many different signals. In this paper, we determine scaling properties in the encrypted images by means of a two-dimensional DFA approach. To carry out the image encryption, we use an enhanced cryptosystem based on a rule-90 cellular automaton and we compare the results obtained with its unmodified version and the encryption system AES. The numerical results show that the encrypted images present a persistent behavior which is close to that of the 1/f-noise. These results point to the possibility that the DFA scaling exponent can be used to measure the quality of the encrypted image content.

In this paper, we implement a revised pseudo random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix H N with the aim of calculating the pseudo random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix H N is revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST).

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