S-boxes – parameters, characteristics and classifications

Dusan Bikov; Stefka Bouyuklieva; Aleksandra Stojanova

Dusan Bikov University “Goce Delcev” – Shtip
Stefka Bouyuklieva St.Cyril and St.Methoduis University of Veliko Tarnovo
Aleksandra Stojanova University “Goce Delcev” – Shtip

Abstract

S-Boxes are the key building blocks in the design of the block ciphers. They are basically used to hide the relationship between the plaintext and the ciphertext.
In this paper we study the parameters of Boolean functions and S-boxes, which are important in the design of good cryptosystems. We give a brief overview of the selection criteria on S-boxes to be resistant to different type of cryptanalytic attacks. For this goal optimality of S-box is defined. We present different variants for classification of S-boxes and give some examples. Also we list the results of our computer calculations for the parameters of Boolean functions and S-boxes that are essential in the cryptographic research. Finally, we give general framework of the direction in which our study is focused.

References

C. E. Shannon: “Communication Theory of Secrecy Systems.” Bell System Technical Journal, Vol 28, pp. 656–717, October 1949.

G. Leander and A. Poschmann: “On the Classification of 4 Bit S-Boxes.” In C. Carlet and B. Sunar (Eds.): WAIFI 2007, LNCS 4547, pp. 159–176. Springer (2007).

M. Matsui. Linear cryptanalysis method for DES cipher. In Advances in Cryptology – EUROCRYPT’93, vol. 765 of LNCS, pp.386-397, Springer Verlag, 1994.

Biham, E., Shamir, A.: Diﬀerential cryptanalysis of des-like cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1990).

M. Ullrich, C. De Cannière, S. Indesteege, Ö. Küçük, N. Mouha, and B. Preneel: “Finding Optimal Bitsliced Implementations of 4x4-bit S-Boxes.” SKEW 2011 Symmetric Key Encryption Workshop, Copenhagen, Denmark, 16-17 February 2011.

J. Daemen and V. Rijmen. The Design of Rijndael. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2002.

An Braeken (March 2006): Cryptographic Properties of Boolean Functions and S-Boxes, PhD Thesis, Katholieke Universiteit Leuven.

Claude Carlet, “Vectorial Boolean Functions for Cryptography”, Chapter of the monography “Boolean Models and Methods in Mathematics, Computer Science, and Engineering”, Cambridge University Press, 2010.

M.J. O. Saarinen: "Cryptographic Analysis of All 4x4 Bit SBoxes." In A. Miri, S. Vaudenay (Eds.): Selected Areas in Cryptography 18th International Workshop, SAC 2011. Toronto, ON, Canada, August 1112, 2011, Revised Selected Papers. LNCS 7118, pp. 118133. Springer (2012)