Oriented Steiner quasigroups
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 f-extensions for quasigroups (cf. earlier works S, NSt, NSt2) achieved through oriented Steiner triple systems. This is done in a fashion similar to in 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.
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