Oriented Steiner quasigroups
arXiv:1402.4644 · doi:10.1142/S0219498814500728
Abstract
We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type -extensions for quasigroups (cf. earlier works \cite{S, NSt, NSt2}) achieved through oriented Steiner triple systems. This is done in a fashion similar to in \cite{SS} where an analogous construction was established for loops. As a justification of this concept briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.