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Wireless Personal Communications
Published in: Wireless Personal Communications 1/2018

09-04-2018

A Method of Generating 8 × 8 Substitution Boxes Based on Elliptic Curves

Authors: Umar Hayat, Naveed Ahmed Azam, Muhammad Asif

Published in: Wireless Personal Communications | Issue 1/2018

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Abstract

Elliptic curve cryptography provides better security and is more efficient as compared to other public key cryptosystems with identical key size. In this article, we present a new method for the construction of substitution boxes(S-boxes) based on points on elliptic curve over prime field. The resistance of the newly generated S-box against common attacks such as linear, differential and algebraic attacks is analyzed by calculating their non-linearity, linear approximation, strict avalanche, bit independence, differential approximation and algebraic complexity. The experimental results are further compared with some of the prevailing S-boxes presented in Shi et al. (Int Conf Inf Netw Appl 2:689–693, 1997), Jakimoski and Kocarev (IEEE Trans Circuits Syst I 48:163–170, 2001), Guoping et al. (Chaos, Solitons Fractals 23:413–419, 2005), Guo (Chaos, Solitons Fractals 36:1028–1036, 2008), Kim and Phan (Cryptologia 33: 246–270, 2009), Neural et al. (2010 sixth international conference on natural computation (ICNC 2010), 2010), Hussain et al. (Neural Comput Appl. https://​doi.​org/​10.​1007/​s00521-012-0914-5, 2012). Comparison reveals that the proposed algorithm generates cryptographically strong S-boxes as compared to some of the other exiting techniques.
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Literature
1.
Shi, X. Y., Xiao, H., You, X. C., & Lam, K. Y. (1997). A method for obtaining cryptographically strong 8 × 8 S-boxes. International Conference on Information Network and Application, 2, 689–693.
2.
Jakimoski, G., & Kocarev, L. (2001). Chaos and cryptography: block encryption ciphers. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48, 163–170.MathSciNetCrossRefMATH
3.
Guoping, T., Xiaofeng, L., & Yong, C. (2005). A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals, 23, 413–419.CrossRefMATH
4.
5.
Kim, J., & Phan, R. C. W. (2009). Advanced differential-style cryptanalysis of the NSA’s skipjack block cipher. Cryptologia, 33, 246–270.CrossRefMATH
6.
Neural, Y. W., Li, Y., Min, L., & Sihong, S. A method for designing S-box based on chaotic neural network. In 2010 Sixth international conference on natural computation (ICNC 2010).
7.
8.
Hussain, I., Azam, N. A., & Shah, T. (2014). Stego optical encryption based on chaotic S-box transformation. Optics & Laser Technology, 61, 50–56.CrossRef
9.
10.
Willi, M., & Othmar, S. (1990). Nonlinearity criteria for cryptographic functions. Advances in Cryptology–EUROCRYPT ’89 LNCS, 434, 549–562.MathSciNetMATH
11.
Mitsuru, M. (1994). Linear cryptanalysis method for DES cipher. Advances in Cryptology–EUROCRYPT ‘93 LNCS, 765, 386–397.MATH
12.
Eli, B., & Adi, S. (1991). Differential crypt analysis of DES-like cryptosystems. Advances in Cryptology - CRYPTO ‘90 LNCS, 537, 2–21.MATH
13.
Thomas, J., & Knudsen, L, R. (1997). The interpolation attack on block ciphers. In International workshop on fast software encription (FSE), Fast Software Encription (pp. 28–40).
14.
Nicolas, C., Alexander, K., Jacques, P., & Adi, S. (2000). Effcient algorithms for solving overdefined systems of multivariate polynomial equations. In International conference on the theory and application of cryptographic techniques EUROCRYPT 2000: advances in cryptology-EUROCRYPT (pp. 392–407).
15.
Courtois, N. T., & Josef, P. (2002). Cryptanalysis of block ciphers with overdefined systems of equations. ASIACRYPT 2002 LNCS, 2501, 267–287.MathSciNetCrossRefMATH
16.
Daemen, J., & Rijmen, V. (1999). AES proposal: Rijndael (Version 2). NIST AES, csrc.nist.gov/encryption/aes.
17.
Ferguson, N., Schroeppel, R., & Whiting, D. A. (2001). Simple algebraic representation of Rijndael. In Selected areas in cryptography SAC 01, LNCS 2259 (pp. 103–111).
18.
Murphy, S., & Robshaw, M. J. (2002). Essential algebraic structure within the AES. In Proceedings of the 22th annual international cryptology (pp. 1–16). Berlin: Springer.
19.
Rosenthal, J. (2003). A polynomial description of the Rijndael advanced encryption standard. Journal of Algebra and its Applications, 2, 223–236.MathSciNetCrossRefMATH
20.
Liu, J., Wai, B., Cheng, X., & Wang, X. (2005). An AES S-box to increase complexity and cryptographic analysis. In Proceedings of the 19th international conference on advanced information networking and applications, Taiwan (pp. 724–728).
21.
Cui, L., & Cao, Y. (2007). A new S-box structure named affine power-affine. International Journal of Innovative Computing, Information and Control, 3, 751–759.
22.
Tran, M. T., Bui, D. K., & Doung, A. D. (2008). Gray S-box for advanced encryption standard. International Conference on Computational Intelligence and Security, 1, 253–258.
23.
24.
25.
Hao, Y., Longyan, L., & Yong, W. (2010). An S-box construction algorithm based on spatiotemporal chaos. In International conference on communications and mobile computing.
26.
Yong, W., Kwok, W., Changbing, L., & Yang, L. (2012). A novel method to design S-box based on chaotic map and genetic algorithm. Physics Letters A, 376, 827–833.CrossRefMATH
27.
Wang, Y., Wong, K. W., Li, C., & Li, Y. (2012). A novel method to design S-box based on chaotic map and genetic algorithm. Physics Letters A, 376(376), 827–833.CrossRefMATH
28.
Hussain, I., Azam, N. A., & Shah, T. (2014). Stego optical encryption based on chaotic S-box transformation. Optics and Laser Technology, 61, 50–56.CrossRef
29.
30.
31.
32.
Miller, V. (1986). Uses of elliptic curves in cryptography. Advances in Cryptology, 85, 417–426.MathSciNet
33.
34.
Jung, H. C., Seongtaek, C., & Choonsik, P. (1999). S-boxes with controllable nonlinearity, EUROCRYPT’99. LNCS, 1592, 286–294.MATH
35.
Neal, K., Alfred, M., & Scott, V. (2000). The state of elliptic curve cryptography. Designs, Codes and Cryptography, 19, 173–193.MathSciNetCrossRefMATH
36.
Amara, M., & Siad, A.(2011). Elliptic curve cryptography and its applications. In 7th international workshop on systems, signal processing and their applications (pp. 247–250).
37.
Vansfone, S. A. (1997). Elliptic curve cryptography. The answer to strong, fast public-key cryptography for securing constrained environments. Information Security Technical Report, 2(2), 78–87.CrossRef
38.
Williams, S. (2000). Cryptography and network security (4th ed.). New York: Prentice Hall.
39.
Gong, G., Berson, T. A., & Stinson, D. R. (2000). Elliptic curve pseudorandom sequence generators. In Selected areas in cryptography (Kingston, ON, 1999), (pp. 34–48). Berlin: Springer.
40.
Caragiu, M., Johns, R. A., & Gieseler, J. (2006). Quasi-random structures from elliptic curves. Journal of Algebra, Number Theory and Applications, 6, 561–571.MathSciNetMATH
41.
Farashahi, R. R., & Sidorenko, S. B. A. (2007). Efficient pseudorandom generators based on the DDH assumption. In Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS (Vol. 4450, pp. 426–441). Heidelberg: Springer.
42.
Omar, R., & Zbigniew, K. (2015). On pseudo-random number generators using elliptic curves and chaotic systems. Applied Mathematics and Information Sciences, 9(1), 31–38.MathSciNetCrossRef
43.
Brown, D. R. L. (2009). SEC 1: Elliptic curve cryptography. Mossossaiga: Certicom Corp.
44.
Webster, A. F., & Tavares, S. E. (1986). On the design of S-boxes. Advances in Cryptology–CRYPT0 ‘85 LNCS, 218, 523–534.
45.
Lidl, R., & Niederreiter, H. (1994). Introduction to finite fields and their applications (2nd ed.). Cambridge: Cambridge University Press.CrossRefMATH
46.
Bustamante, M. D., & Hayat, U. (2013). Complete classification of discrete resonant Rossby/drift wave triads on periodic domains. Communications in Nonlinear Science and Numerical Simulation, 18, 2402–2419.MathSciNetCrossRefMATH
Metadata
Title
A Method of Generating 8 × 8 Substitution Boxes Based on Elliptic Curves
Authors
Umar Hayat
Naveed Ahmed Azam
Muhammad Asif
Publication date
09-04-2018
Publisher
Springer US
Published in
Wireless Personal Communications / Issue 1/2018
Print ISSN: 0929-6212
Electronic ISSN: 1572-834X
DOI
https://doi.org/10.1007/s11277-018-5698-1

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