Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups

Abstract

We investigate several cryptographic properties in 8-bit S-boxes obtained by quasigroups of order 4 and 16 with several different algebraic constructions. Additionally, we offer a new construction of $N$-bit S-boxes by using different number of two layers -- the layer of bijectional quasigroup string transformations, and the layer of modular addition with $N$-bit constants. The best produced 8-bit S-boxes so far are regular and have algebraic degree 7, nonlinearity 98 (linearity 60), differential uniformity 8, and autocorrelation 88. Additionally we obtained 8-bit S-boxes with nonlinearity 100 (linearity 56), differential uniformity 10, autocorrelation 88, and minimal algebraic degree 6. Relatively small set of performed experiments compared with the extremly large set of possible experiments suggests that these results can be improved in the future.

Keywords

• 8-bit s-boxes
• nonlinearity
• differential uniformity
• autocorrelation