Bijective S-boxes of different sizes obtained from quasi-cyclic codes
Keywords:
S-box, Simplex code, Quasi-cyclic codes
Abstract
The aim of this paper is to construct S-boxes of different sizes with good cryptographic properties. An algebraic construction for bijective S-boxes is described. It uses quasi-cyclic representations of the binary simplex code. Good S-boxes of sizes 4, 6, 8, 9, 10, 11, 12, 14, 15, 16 and 18 are obtained.
References
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C. Carlet, Boolean Functions for Cryptography and Error Correcting Codes, In: Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Crama, Hammer, Cambridge University Press, 2010.
C. Carlet, Vectorial Boolean Functions for Cryptography, In: Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Crama, Hammer, (Eds.), Cambridge University Press, 2010.
E. Z. Chen, New quasi-cyclic codes from simplex codes, IEEE Trans. Inform. Theory 53(3) (2007) 1193–1196.
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J.Daeman, V.Rijmen, The Design of Rijndael, AES–the advanced encryption standard, Springer-Verlag Berlin Heidelberg, 2002.
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K. Lally, P. Fitzpatrick, Algebraic structure of quasi-cyclic codes, Discrete Applied Mathematics 111(1–2) (2001) 157–175.
G. Leander, A. Poschmann, On the Classification of 4 Bit S-Boxes, In: Carlet C., Sunar B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg (2007) 159–176.
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