Abstract
In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) based on chaotic time series of the logistic map for different carrying capacities. The use of different carrying capacities in the chaotic map leads to low computational complexity, which is desirable to get high-speed communication systems. We generate a main sequence by means of two auxiliary sequences with uniform distribution via the logistic map for different carrying capacities. The elements of the main sequence are useful for generating the elements of an S-box. The auxiliary sequences are generated by considering lag time chaotic series; this helps to hide the chaotic map used. The U-shape distribution of logistic chaotic map is also avoided, in contrast with common chaos-based schemes without considering lag time chaotic series, and uncorrelated S-box elements are obtained. The proposed algorithm guarantees the generation of strong S-boxes that fulfill the following criteria: bijection, nonlinearity, strict avalanche criterion, output bits independence criterion, criterion of equiprobable input/output XOR distribution, and maximum expected linear probability. Finally, an application premised on polyalphabetic ciphers principle is developed to obtain a uniform distribution of the plaintext via dynamical S-boxes.
Highlights
Nowadays, we are in the era of informatics, and due to a large number of attacks, it is important to adequately protect the information to be transmitted and avoid the possible misuse of it
In this work, we explore a different carrying capacity to map the interval [0, 28] to itself, i.e., f: [0, 256] ⟶ [0, 256], for this case, the logistic map is known as the extended logistic map
We present an algorithm to design n × nbits substitution boxes (S-boxes) based on a main sequence generated by mixing two auxiliary sequences using lag time chaotic series
Summary
We are in the era of informatics, and due to a large number of attacks, it is important to adequately protect the information to be transmitted and avoid the possible misuse of it. There are algorithms that consider the mixing of time series of continuous and discrete dynamical systems [7, 13], and in ref. We present an algorithm to design n × nbits S-boxes based on a main sequence generated by mixing two auxiliary sequences using lag time chaotic series. These chaotic time series are computed with the logistic map considering different carrying capacities. The rest of the work is organized as follows: in Section 2, an algorithm for generating substitution boxes based on binary sequences of the logistic map is presented.
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