Cryptographic properties of parastrophic quasigroup transformation

Abstract

We consider cryptographic properties of parastrophic quasigroup transformation defined elsewhere. Using this transformation we classify the quasigroups of order 4 into three classes: 1) parastrophic fractal; 2) fractal and parastrophic non-fractal; and 3) non-fractal. We investigate the algebraic properties of above classes and present a relationship between fractal and algebraic properties of quasigroups of order 4. We also find a number of different parastrophes of each quasigroup of order 4 and use it to divide the set of all quasigroups of order 4 into four classes. Using these classifications the number of quasigroups of order 4 which are suitable for designing of cryptographic primitives is increased compared to the case where parastrophes are not used.