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Designs, Codes and Cryptography

Erschienen in:

14.09.2017

A method to calculate differential uniformity for permutations

verfasst von: Li Shuai, Miao Li

Erschienen in: Designs, Codes and Cryptography | Ausgabe 7/2018

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Abstract

We introduce a search algorithm to find permutation S-boxes with low differential uniformity, high nonlinearity and high algebraic degree, which play important roles in block ciphers. Inspired by the results of our search algorithm, we propose a method to calculate differential uniformity for permutations. We establish a sufficient condition for differentially 4-uniform permutations based on our method and construct some example classes of differentially 4-uniform permutations.

Vorheriger Artikel Upper bound of the length of truncated impossible differentials for AES

Nächster Artikel On MDS linear complementary dual codes and entanglement-assisted quantum codes

Shannon C.E.: Communication theory of secrecy systems*. Bell Syst. Tech. J. 28(4), 656–715 (1949).MathSciNetCrossRefMATH

Biham E., Shamir A.: Differential cryptanalysis of DES-like cryptosystems. In: Advances in Cryptology-CRYPTO, vol. 90, pp. 2–21. Springer, New York (1991).

Nyberg, K.: Perfect nonlinear S-boxes. In: Advances in Cryptology EUROCRYPT’91, pp. 378–386. Springer, New York(1991).

Knudsen L.R.: Truncated and higher order differentials. In: Fast Software Encryption, pp. 196–211. Springer, Berlin (1994).

Carlet C.: On known and new differentially uniform functions. In: Information Security and Privacy, pp. 1–15. Springer, New York (2011).

Nyberg K.: Differentially uniform mappings for cryptography. In: Workshop on the Theory and Application of of Cryptographic Techniques, pp. 55–64. Springer, Berlin (1993).

Tang D., Carlet C., Tang X.: Differentially 4-uniform bijections by permuting the inverse function. Des. Codes Cryptogr. 77(1), 117–141 (2015).MathSciNetCrossRefMATH

Dillon J.F.: APN polynomials: an update. In: International Conference on Finite Fields and Applications-Fq9 (2009).

Perrin L., Udovenko A., Biryukov A.: Cryptanalysis of a theorem: decomposing the only known solution to the big APN problem. In: Annual Cryptology Conference, pp. 93–122. Springer, Berlin (2016).

10.

Bracken C., Leander G: New families of functions with differential uniformity of 4. In: Proceedings of the Conference BFCA (2008).

11.

Bracken C., Leander G.: A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree. Finite Fields Appl. 16(4), 231–242 (2010).MathSciNetCrossRefMATH

12.

Bracken C., Tan C.H., Tan Y.: Binomial differentially 4 uniform permutations with high nonlinearity. Finite Fields Appl. 18(3), 537–546 (2012).MathSciNetCrossRefMATH

13.

Li Y., Wang M., Yuyin Y.: Constructing differentially 4-uniform permutations over \({GF}(2^{2k})\) from the inverse function revisited. IACR Cryptol. ePrint Arch. 2013, 731 (2013).

14.

Li Y., Wang M.: Constructing differentially 4-uniform permutations over \(\text{ GF }(2^{2m})\) from quadratic APN permutations over \(\text{ GF }(2^{2m+1})\). Des. Codes Cryptogr. 72(2), 249–264 (2014).MathSciNetCrossRefMATH

15.

Longjiang Qu, Tan Yin, Tan Chik How, Li Chao: Constructing differentially 4-uniform permutations over \({\mathbb{F}}_{2^{2k}}\) via the switching method. IEEE Trans. Inf. Theory 59(7), 4675–4686 (2013).MathSciNetCrossRefMATH

16.

Zha Z., Hu L., Sun S.: Constructing new differentially 4-uniform permutations from the inverse function. Finite Fields Appl. 25, 64–78 (2014).MathSciNetCrossRefMATH

17.

Jacobson N.: Basic Algebra I. Courier Corporation, New York (2012).MATH

18.

Carlet C., Charpin P., Zinoviev V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Des Codes Cryptogr. 15(2), 125–156 (1998).MathSciNetCrossRefMATH

19.

Budaghyan L., Carlet C., Pott A.: New classes of almost bent and almost perfect nonlinear polynomials. IEEE Trans. Inf. Theory 52(3), 1141–1152 (2006).MathSciNetCrossRefMATH

20.

Leander G., Poschmann A.: On the classification of 4 bit S-boxes. In: Arithmetic of Finite Fields, pp. 159–176. Springer, New York (2007).

21.

Pommerening K.: Quadratic Equations in Finite Fields of Characteristic 2 (2000).

22.

Yu Y., Wang M., Li Y.: Constructing differentially 4 uniform permutations from known ones. Chin. J. Electron. 22(3), 0018–9448 (2013).

Titel: A method to calculate differential uniformity for permutations
verfasst von: Li Shuai
Miao Li
Publikationsdatum: 14.09.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 7/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0412-y

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