Abstract
This article is about a criterion based on generalized fuzzy soft expert set to scrutinize the prevailing substitution boxes and learn their properties to sort out their suitability in image encryption applications. The projected criterion makes use of the results of correlation analysis, entropy analysis, contrast analysis, homogeneity analysis, energy analysis, and mean of absolute deviation analysis. These analyses are applied to Advanced Encryption Standard S-box, Affine-Power-Affine S-box, Gray S-box, \(\hbox {S}_{8}\) S-box, residue prime S-box, SKIPJACK S-box and Liu J S-box. The outcome of these analyses is additional observed and a generalized fuzzy soft expert set criterion is used to decide the suitability of an S-box to image encryption applications.
Similar content being viewed by others
References
Abuelyman, E.S., Alsehibani, A.A.S.: An optimized implementation of the S-Box using residue of prime numbers. Int. J. Comput. Sci. Netw. Secur. 8(4), 304–309 (2008)
Ahmed, F., Anees, A., Siyal, M.Y.: A noise channel tolerant image encryption scheme. Wirel. Pers. Commun. (2014). doi:10.1007/s11277-014-1667-5
Alam, G.M., Mat Kiah, M.L., Zaidan, B.B., Zaidan, A.A., Alanazi, H.O.: Using the features of mosaic image and AES cryptosystem to implement an extremely high rate and high secure data hidden: Analytical study. Int. J. Phys. Sci. 5(21), 3254–3260 (2010)
Alkhazaleh, S., Salleh, A.R.: Soft expert sets. Adv. Decis. Sci. 15 (2011)
Alkhazaleh, S., Salleh, A.R., Hassan, N.: Fuzzy parameterized interval-valued fuzzy soft set. Appl. Math. Sci. 5(67), 3335–3346 (2011)
Alkhazaleh, S., Salleh. A.R.: Fuzzy Soft Expert Sets [Ph.D. thesis], Faculty of Science and Technology, University Kebangsaan Malaysia, Selangor, Malaysia
Anees, A., Khan, W.A., Gondal, M.A., Hussain, I.: Application of mean of absolute deviation method for the selection of best nonlinear component based on video encryption, Z. Naturforsch 68a, 567–572 (2013)
Anees, A., Siddiqui, A.M., Ahmed, F.: Chaotic substitution for highly autocorrelated data in encryption algorithms. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3106–3118 (2014)
Anees, A., Siddiqui, A.M., Ahmed, J., Hussain, I.: A technique for digital steganography using chaotic maps. Nonlinear Dyn. 75, 807–816 (2014)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Atanassov, K.: Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 64, 159–174 (1994)
Avcibas, I., Memon, N., Sankur, B.: Steganalysis using image quality metrics. IEEE Trans. Image Process. 12(2), 221–229 (2003)
Chen, S.Y., Lin, W.C., Chen, C.T.: Split and merge image segmentation based on localized feature analysis and statistical tests. Graph Models Image Process. 53(5), 457–475 (1991)
Cui, L., Cao, Y.: A new S-box structure named Affine-Power-Affine. Int. J. Innov. Comput. I 3(3), 45–53 (2007)
Daemen, J., Rijmen, V.: AES Proposal: Rijndael. AES Algorithm Submission. http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf (1999)
Enayatifar, R.: Image encryption via logistic map function and heap tree. Int. J. Phys. Sci. 6(2), 221–228 (2011)
Gadelmawla, E.S.: A vision system for surface roughness characterization using the gray level co-occurrence matrix. NDT & E. Int. 37(7), 577–588 (2004)
Gondal, M.A., Anees, A.: Analysis of optimized signal processing algorithms for smart antenna systems. Neural Comput. Appl. 23(3–4), 1083–1087 (2013)
Gorzalzany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21, 1–17 (1987)
Hazaymeh, A.A., Abdullah, I.B., Balkhi, Z.T., Ibrahim, R.I.: Generalized fuzzy soft expert set, J. Appl. Math. 2012, 22 pp, Article ID 328195 (2002). doi:10.1155/2012/328195
Hussain, I.: A novel approach of audio watermarking based on S-box transformation. Math. Comput. Model. 57, 963–969 (2013)
Hussain, I., Azam, N.A., Shah, T.: Stego optical encryption based on chaotic S-box transformation. Opt. Laser Technol. 61, 50–56 (2014)
Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and S-box transformation. Nonlinear Dyn. doi:10.1007/s11071-013-1214-z
Hussain, I., Shah, T.: Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dyn. 74, 869–904 (2013)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dyn. 71, 133–140 (2013)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Efficient method for designing chaotic S-boxes based on generalized Baker’s map and TDERC chaotic sequence. Nonlinear Dyn. 74, 271–275 (2013)
Hussain, I., Shah, T., Gondal, M.A.: A group theoretic approach to construct cryptographically strong substitution boxes. Neural Comput. Appl. 23, 97–104 (2013)
Hussain, I., Shah, T., Gondal, M.A.: Application of S-box and chaotic map for image encryption. Math. Comput. Model. 57, 2576–2579 (2013)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, Hasan: A novel method for designing nonlinear component for block cipher based on TD-ERCS chaotic sequence. Nonlinear Dyn. 73, 633–637 (2013)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: A novel image encryption algorithm based on chaotic maps and GF(2\(^\wedge \)8) exponent transformation. Nonlinear Dyn. 72, 399–406 (2013)
Hussain, I., Shah, T., Mahmood, H.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. 22, 1085–1093 (2013)
Hussain, I., Shah, T., Mehmood, H.: A new algorithm to construct secure keys for AES. Int. J. Cont. Math. Sci. 5(26), 1263–1270 (2010)
Jamal, S.S., Shah, T., Hussain, I.: An efficient scheme for digital watermarking using chaotic map. Nonlinear Dyn. 73, 1469–1474 (2013)
Jing, F., Li, M., Zhang, H., Zhang, B.: Unsupervised image segmentation using local homogeneity analysis. Proc. ISCAS 2, 456–459 (2003)
Lui, J., Wai, B., Cheng, X., Wang, X.: An AES S-box to increase complexity and cryptgraphic analysis. Int. Conf. Inf. Netw. Appl. 1, 724–728 (2005)
Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)
Majumdar, P., Samanta, S.K.: Generalised fuzzy soft sets. Comput. Math. Appl. 59, 1425–1432 (2010)
Molodtsov, D.: Soft set theory first results. Comput. Math. Appl. 37, 19–31 (1999)
Pawlak, Z.: Rough sets. Int. J. Comp. Sci. 11, 341–356 (1982)
Prasadh, K., Ramar, K., Gnanajeyaraman, R.: Public key cryptosystems based on chaotic Chebyshev polynomials. Int. J. Phys. Sci. 1(7), 122–128 (2009)
Shah, T., Qamar, A., Hussain, I.: Substitution box on maximal cyclic subgroup of units of a galois ring, Z. Naturforsch. 68a, 479–482 (2013)
Shi, X.Y., Xiao, Hu, You, X.C., Lam, K.Y.: A method for obtaining cryptographically strong \(8\times 8\) S-boxes. Int. Conf. Inf. Netw. Appl. 2(3), 14–20 (2002)
SKIPJACK, KEA Algorithm. Specifications Version, vol. 2(29), pp. 1–23 (1998)
Tran, M.T., Bui, D.K., Doung, A.D.: Gray S-box for Advanced Encryption Standard. In: International Conference on Computational Intelligence and Security, pp. 253–256 (2008)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zhang, L., Liao, X., Wang, X.: An image encryption approach based on chaotic maps. Chaos Solut. Fract. 24, 759–765 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abdullah, S., Amin, N.U. Analysis of S-box image encryption based on generalized fuzzy soft expert set. Nonlinear Dyn 79, 1679–1692 (2015). https://doi.org/10.1007/s11071-014-1767-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-014-1767-5