A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map

Substitution boxes are essential nonlinear components responsible to impart strong confusion and security in most of modern symmetric ciphers. Constructing efficient S-boxes has been a prominent topic of interest for security experts. With an aim to construct cryptographically efficient S-box, a novel scheme based on firefly (FA) optimization and chaotic map is proposed in this paper. The anticipated approach generates initial S-box using chaotic map. The meta-heuristic FA is applied to find notable configuration of S-box that satisfies the criterions by guided search for near-optimal features by minimizing fitness function. The performance of proposed approach is assessed through well-established criterions such as bijectivity, nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and linear approximation probability. The obtained experimental results are compared with some recently investigated S-boxes to demonstrate that the proposed scheme has better proficiency of constructing efficient S-boxes.

[1]  Stafford E. Tavares,et al.  An Expanded Set of S-box Design Criteria Based on Information Theory and its Relation to Differential-Like Attacks , 1991, EUROCRYPT.

[2]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[3]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[4]  Ming-Huwi Horng,et al.  Vector quantization using the firefly algorithm for image compression , 2012, Expert Syst. Appl..

[5]  Tariq Shah,et al.  A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems , 2012, Nonlinear Dynamics.

[6]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[7]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[8]  Pulak Mishra,et al.  Mergers, Acquisitions and Export Competitive- ness: Experience of Indian Manufacturing Sector , 2012 .

[9]  Musheer Ahmad,et al.  Designing chaos based strong substitution box , 2015, 2015 Eighth International Conference on Contemporary Computing (IC3).

[10]  Musheer Ahmad,et al.  A Novel Ant Colony Optimization Based Scheme for Substitution Box Design , 2015 .

[11]  Weiwei Liu,et al.  Designing S-boxes based on 3-D four-wing autonomous chaotic system , 2015 .

[12]  Tariq Shah,et al.  An efficient technique for the construction of substitution box with chaotic partial differential equation , 2013, Nonlinear Dynamics.

[13]  Slawomir Zak,et al.  Firefly Algorithm for Continuous Constrained Optimization Tasks , 2009, ICCCI.

[14]  Xin-She Yang,et al.  Firefly Algorithm, Lévy Flights and Global Optimization , 2010, SGAI Conf..

[15]  V. Mani,et al.  Clustering using firefly algorithm: Performance study , 2011, Swarm Evol. Comput..

[16]  Guo Chen,et al.  A novel heuristic method for obtaining S-boxes , 2008 .

[17]  Amir Hossein Gandomi,et al.  Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect , 2012, Appl. Soft Comput..

[18]  Ahmet Bedri Özer,et al.  A new S-box construction method based on the fractional-order chaotic Chen system , 2017, Signal Image Video Process..

[19]  Xin-She Yang,et al.  Firefly Algorithm: Recent Advances and Applications , 2013, ArXiv.

[20]  Tariq Shah,et al.  Construction of S-box based on chaotic Boolean functions and its application in image encryption , 2015, Neural Computing and Applications.

[21]  Stafford E. Tavares,et al.  On the Design of S-Boxes , 1985, CRYPTO.

[22]  I. Pehlivan,et al.  A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system , 2017 .

[23]  Mohammad Reza Meybodi,et al.  A Gaussian Firefly Algorithm , 2011 .

[24]  Xin-She Yang,et al.  Attraction and diffusion in nature-inspired optimization algorithms , 2015, Neural Computing and Applications.

[25]  Amrit Pal Singh,et al.  Comparative Study of Firefly Algorithm and Particle Swarm Optimization for Noisy Non- Linear Optimization Problems , 2012 .

[26]  Zeeshan Asghar,et al.  A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation , 2016, Neural Computing and Applications.

[27]  Ahmet Bedri Ozer,et al.  A method for designing strong S-Boxes based on chaotic Lorenz system , 2010 .

[28]  Janez Brest,et al.  A comprehensive review of firefly algorithms , 2013, Swarm Evol. Comput..

[29]  Ling-guo Cui,et al.  A NEW S-BOX STRUCTURE NAMED AFFINE-POWER-AFFINE , 2007 .

[30]  Faiz Ul Islam,et al.  Designing S-Box Based on 4D-4Wing Hyperchaotic System , 2017 .

[31]  Tariq Shah,et al.  An efficient construction of substitution box with fractional chaotic system , 2015, Signal Image Video Process..

[32]  Josef Pieprzyk,et al.  Towards effective nonlinear cryptosystem design , 1988 .

[33]  Dragan Lambić,et al.  A novel method of S-box design based on discrete chaotic map , 2017 .

[34]  Tariq Shah,et al.  A Watermarking Technique with Chaotic Fractional S-Box Transformation , 2016, Wirel. Pers. Commun..

[35]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[36]  Farookh Khadeer Hussain,et al.  Support vector regression with chaos-based firefly algorithm for stock market price forecasting , 2013, Appl. Soft Comput..

[37]  Sirma Yavuz,et al.  Designing chaotic S-boxes based on time-delay chaotic system , 2013 .

[38]  X. Liao,et al.  An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps , 2007 .

[39]  D. H. Lehmer.  Teaching combinatorial tricks to a computer , 1960 .

[40]  Tariq Shah,et al.  A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm , 2012, Nonlinear Dynamics.

[41]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[42]  Zeeshan Ahmed,et al.  A Technique for Designing Substitution Box Based on Van der Pol Oscillator , 2015, Wirel. Pers. Commun..

[43]  Xin-She Yang,et al.  Cuckoo Search and Firefly Algorithm , 2014 .

[44]  Xin-She Yang,et al.  Analysis of firefly algorithms and automatic parameter tuning , 2014 .

[45]  Safya Belghith,et al.  A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization , 2016, Nonlinear Dynamics.

[46]  Fatih Özkaynak.  A novel method to improve the performance of chaos based evolutionary algorithms , 2015 .

[47]  Ahmed A. Abd El-Latif,et al.  A simple yet efficient S-box method based on chaotic sine map , 2017 .

[48]  Xiaofeng Liao,et al.  A novel method for designing S-boxes based on chaotic maps , 2005 .

[49]  Fatih Özkaynak,et al.  Construction of robust substitution boxes based on chaotic systems , 2019, Neural Computing and Applications.

[50]  Dragan Lambić,et al.  Pseudo-random number generator based on discrete-space chaotic map , 2017 .

[51]  Yong Wang,et al.  A Software for S-box Performance Analysis and Test , 2009, 2009 International Conference on Electronic Commerce and Business Intelligence.

[52]  Yang Li,et al.  A novel method to design S-box based on chaotic map and genetic algorithm , 2012 .

[53]  Tariq Shah,et al.  A group theoretic approach to construct cryptographically strong substitution boxes , 2012, Neural Computing and Applications.

[54]  L. Kocarev,et al.  Chaos and cryptography: block encryption ciphers based on chaotic maps , 2001 .

[55]  Xin-She Yang,et al.  Multiobjective firefly algorithm for continuous optimization , 2012, Engineering with Computers.

[56]  Dragan Lambić,et al.  A novel method of S-box design based on chaotic map and composition method , 2014 .

[57]  Joan Daemen,et al.  AES Proposal : Rijndael , 1998 .

[58]  Iztok Fister,et al.  Memetic firefly algorithm for combinatorial optimization , 2012, 1204.5165.

[59]  Dragan Lambić.  A new discrete chaotic map based on the composition of permutations , 2015 .

[60]  Xin-She Yang,et al.  Firefly algorithm with chaos , 2013, Commun. Nonlinear Sci. Numer. Simul..