This paper introduces a method of generating a strong S-box by using combined chaotic system and fitness function. Our method presents an algorithm which has two stages: static S-box generation and dynamic S-box optimization. Chaotic sequences generation, sequences discretization are involved in the first stage. Moreover, the proposed static S-box is converted into a dynamic S-box with the help of fitness function. The optimal S-box satisfies the following criteria: bijectivity, nonlinearity, strict avalanche criteria, output bits independence criterion, equiprobable inputs/outputs XOR distribution. Extensive experiments demonstrate that the proposed algorithm has excellent performance in cryptography and attacks resistance.
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Belazi A, Khan M, Abd El-Latif AA, Belghith S (2016) Efficient cryptosystem approaches: S-boxes and permutationsubstitution-based encryption. Nonlinear Dyn. 87(1):1–25
Biham E, Shamir A (1991) Differential cryptanalysis of des-like cryptosystems. J Cryptol 4(1):3–72
Chen X, Hu CJ (2017) Adaptive medical image encryption algorithm based on multiple chaotic mapping. Saudi J. Biol. Sci. 24(8):1821–1827
Daor J (1998) Joan Daemen, and Vincent Rijmen. AES proposal, Rijndael
Tarek Farah, Rhouma Rhouma, and Safya Belghith. A novel method for designing S-box based on chaotic map and TeachingLearning-Based Optimization. Nonlinear Dyn. 88(2):1059–1074, 2017.
Guo C (2008) A novel heuristic method for obtaining sboxes. Chaos Solitons and Fractals. 36(4):1028–1036
Hua Z, Zhou Y (2016) Image encryption using 2D logistic-adjusted-sine map. Inform. Sci. 339:237–253
Jakimoski G, Kocarev L (2001) Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. 48(2):163–169
Khan M (2015) A novel image encryption scheme based on multiple chaotic S-boxes. Nonlinear Dyn. 82(1–2):527–533
Khan M, Asghar Z (2018) A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8permutation. Neural Comput. Applic. 29(4):993–999
Khan M, Shah T, Mahmood H, Gondal MA (2013) An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3):489–492
P. A. W. Lewis, A. S. Goodman, and J. M. Miller (1969) A pseudo-random number generator for the system/360. IBM Syst. J. 8(2):136-146.
Matsui M (1994) Linear cryptanalysis method for DES Cipher. Advances in Cryptology — EUROCRYPT ’93. Springer Berlin Heidelberg. 386–397
Ozkaynak F, Ḉelik V, Özer AB (2017) A new S-box construction method based on the fractionalorder chaotic Chen system. Signal Image Video P. 11(4):659–664
Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process. 138:129–137
Tong XJ (2012) The novel bilateral diffusion image encryption algorithm with dynamical compound chaos. J Syst Software. 85(4):850–858
Tong X, Liu Y, Zhang M et al (2012) A novel image encryption scheme based on dynamical multiple Chaos and baker map[C]// international symposium on distributed Computing & Applications to business. IEEE Computer Society
Ullah A, Jamal SS, Shah T (2017) A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dyn. 88(4):2757–2769
Ullah A, Jamal SS, Shah T (2018) A novel scheme for image encryption using substitution box and chaotic system. Nonlinear Dyn. 91(1):359–370
Wang Y, Wong KW, Li C, Li Y (2012) A novel method to design s-box based on chaotic map and genetic algorithm. Physics Letters A 376(67):827–833
Webster AF, Tavares SE (1986) On the design of S-Boxes. Springer, Berlin Heidelberg
Wu D, Weihong X (2011) Study on the relationship between S-box differential analysis and nonlinearity. Journal of Changsha University 25(5)
XiangYang X (2010) A new genetic algorithm and tabu search for S-box optimization. In International Conference on Computer Design and Applications. V4–492-V4–495
Zaibi G, Peyrard F, Kachouri A et al (2014) Efficient and secure chaotic S-box for wireless sensor network[J]. Secur Commun Netw. 7(2):279–292
Zhang T, Li S, Ge R, Yuan M, Ma Y (2016) A novel 1D hybrid chaotic map-basedimage compression and encryption using compressed sensing and fibonacci-lucas transform. Math. Probl. Eng.
Zhou Y, Bao L, Chen CLP (2014) A new 1D chaotic system for image encryption. Signal Process. 97:172–182
This work was supported by the following projects and foundations: project ZR2019MF054 supported by Shandong Provincial Natural Science Foundation, the Foundation of Science and Technology on Information Assurance Laboratory (No.KJ-17-004), 2017 Weihai University Co-construction Project, Equip Pre-research Projects of 2018, Foundation of China Academy of Space Technology (No. WT-TXYY/ WLZDFHJY003).
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Zhu, H., Tong, X., Wang, Z. et al. A novel method of dynamic S-box design based on combined chaotic map and fitness function. Multimed Tools Appl (2020) doi:10.1007/s11042-019-08478-0
- Combined chaotic system
- Substitution box
- Fitness function
- Dynamic S-box