Generation of dynamical S-boxes via lag time chaotic series for cryptosystems
This work addresses the need for secure and efficient S-boxes in cryptography, offering a novel method for generating them, though it appears incremental as it builds on existing chaotic map techniques.
The authors tackled the problem of designing secure substitution boxes (S-boxes) for cryptosystems by developing an algorithm that uses lag time chaotic series from the logistic map to generate S-boxes that meet strong cryptographic criteria, such as high nonlinearity and strict avalanche criterion, resulting in S-boxes that avoid uniform distribution issues and are applicable in polyalphabetic ciphers.
In this work, we present an algorithm for the design of $n\times n$-bits substitution boxes (S-boxes) based on time series of a discrete dynamical system with chaotic behavior. The elements of a $n\times n$-bits substitution box are given by binary sequences generated by time series with uniform distribution. Particularly, time series with uniform distribution are generated via two lag time chaotic series of the logistic map. The aim of using these two lag time sequences is to hide the map used, and thus U-shape distribution of the logistic map is avoided and uncorrelated S-box elements are obtained. The algorithm proposed is simple and guarantees the generation of S-boxes, which are the main component in block cipher, fulfill the strong S-box criteria: bijective; nonlinearity; strict avalanche criterion; output bits independence criterion; criterion of equiprobable input/output XOR distribution and; maximum expected linear probability. The S-boxes that fulfill these criteria are commonly known as "good S-boxes". Finally, an application based on polyalphabetic ciphers principle is developed to obtain uniform distribution of the plaintext via dynamical S-boxes.