Chaotic S-Box: Intertwining Logistic Map and Bacterial Foraging Optimization

Ye Tian,Zhimao Lu

doi:10.1155/2017/6969312

Abstract

As the unique nonlinear component of block ciphers, Substitution box (S-box) directly affects the safety of a cryptographic system. It is important and difficult to design strong S-box that simultaneously meets multiple cryptographic criteria such as bijection, nonlinearity, strict avalanche criterion (SAC), bit independence criterion (BIC), differential probability (DP), and linear probability (LP). Though many chaotic S-boxes have been proposed, the cryptographic performance of most of them needs to be further improved. A new chaotic S-box based on the intertwining logistic map and bacterial foraging optimization is designed in this paper. It firstly iterates the intertwining logistic map to construct many S-boxes and then applies a bacterial foraging optimization algorithm to find the optimal S-box. Moreover, bacterial foraging optimization algorithm considers the nonlinearity and differential uniformity as the fitness functions in the optimization process. We experiment that the proposed S-box can effectively resist multiple types of cryptanalysis attacks.

Highlights

The dynamic developments in the multimedia industry and the Internet lead to a considerable amount of worry regarding the security of information transmitted over open or stored channels [1,2,3]
A new chaotic Substitution box (S-box) based on the intertwining logistic map and bacterial foraging optimization is designed in this paper
This paper is concerned with developing a novel S-box generation algorithm, chaotic S-box based on the intertwining logistic map and bacterial foraging optimization

Summary

Introduction

The dynamic developments in the multimedia industry and the Internet lead to a considerable amount of worry regarding the security of information transmitted over open or stored channels [1,2,3]. Literature [6] proposed a four-step method of generating chaotic S-box based on discrete logistic map. Literature [8] proposed an S-box design approach based on iteration discrete chaotic that had high immunity to the differential cryptanalysis. A simple chaos system has many defects; for example, the implementation of the chaos on a computer is affected by the limited precision; the time series outputted by the simple chaotic system generally cannot reach the theoretically complete random, resulting in the problem that the pseudorandom sequence appears periodicity [10] To cope with these problems, many complex chaotic maps based S-boxes have been presented in recent years. Unlike other chaos-based algorithms that generate strong S-boxes by using the random distribution property of chaotic maps, we divide the process of designing an S-box into two steps. Abbreviations section shows some abbreviations of technical terms involved in this paper

Preliminary Work

Scheme of Generating of an S-Box

S-Box Evaluation Criteria

Cryptographic Criteria Analyses of Proposed S-Box

Conclusion