Cryptographic properties of parastrophic quasigroup transformation

Abstract

In this paper, we consider cryptographic properties of parastrophic quasigroup transformation defined elsewhere. With that transformation we classify the quasigroups of order 4 in three classes: 1) parastrophic fractal; 2) fractal and parastrophic non-fractal; and 3) nonfractal. We investigate the algebraic properties of the previous classes and present a connection between fractal properties and algebraic properties of quasigroups of order 4. Also, we find a number of different parastrophes of each quasigroup of order 4 and divide the set of all quasigroups of order 4 in 4 classes. Using these classifications the number of quasigroups of order 4 which are suitable for designing of cryptographic primitives is increased.