Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings from the Point of DDT and LAT Distributions

Authors:
Bora Aslan;M. Tolga Sakalli;Ercan Bulus
Affiliations:
Computer Tech. and Programming Dept., Kirklareli University, Luleburgaz-Kirklareli, Turkey and Computer Engineering Dept., Trakya University, Edirne, Turkey and Computer Engineering Dept., Namik K ...;Computer Tech. and Programming Dept., Kirklareli University, Luleburgaz-Kirklareli, Turkey and Computer Engineering Dept., Trakya University, Edirne, Turkey and Computer Engineering Dept., Namik K ...;Computer Tech. and Programming Dept., Kirklareli University, Luleburgaz-Kirklareli, Turkey and Computer Engineering Dept., Trakya University, Edirne, Turkey and Computer Engineering Dept., Namik K ...
Venue:
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Year:
2008

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Abstract

S-boxes are vital elements in the design of symmetric ciphers. To date, the techniques for the construction of S-boxes have included pseudo-random generation, finite field inversion, power mappings and heuristic techniques. From these techniques, the use of finite field inversion in the construction of an S-box is so popular because it presents good cryptographic properties. On the other hand, while S-boxes such as AES, Shark, Square and Hierocrypt that are based on inversion mapping over GF(2n) use an affine transformation after the output of the S-box, in some ciphers like Camellia, an additional affine transformation is used before the input. In this paper, we classify 8-bit to 8-bit S-boxes based on power mappings into classes according to DDT and LAT distributions. Moreover, a formula is given for the calculation of the number of terms in the algebraic expression for a power mapping based S-box according to the given three probable cases.