# Generation of dynamical S-boxes via lag time chaotic series for cryptosystems

## TL;DR

This paper introduces a new algorithm for generating cryptographically strong S-boxes using lag time chaotic series from the logistic map, ensuring high nonlinearity and security criteria.

## Contribution

It presents a novel method for designing S-boxes based on chaotic time series that guarantees strong cryptographic properties and avoids distribution biases.

## Key findings

- Generated S-boxes meet all strong cryptographic criteria.
- The method effectively hides the logistic map used, ensuring unpredictability.
- Application demonstrates uniform plaintext distribution using the generated S-boxes.

## Abstract

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.