%0 Journal Article %T Oriented Steiner quasigroups %A Izabella Stuhl %J Mathematics %D 2014 %I arXiv %R 10.1142/S0219498814500728 %X 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 $f$-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. %U http://arxiv.org/abs/1402.4644v2