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Mathematical Problems in Engineering
Volume 2017, Article ID 6969312, 11 pages
Research Article

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

Ye Tian1,2 and Zhimao Lu1,3

1College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
2Key Laboratory of Photonic and Electronic Bandgap Materials, Ministry of Education, School of Physics and Electronic Engineering, Harbin Normal University, Harbin 150025, China
3Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

Correspondence should be addressed to Ye Tian; moc.621@eynaitdsh

Received 16 June 2017; Revised 24 October 2017; Accepted 26 October 2017; Published 15 November 2017

Academic Editor: Maria L. Gandarias

Copyright © 2017 Ye Tian and Zhimao Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.