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 [10, 11, 14]) achieved through oriented Steiner triple systems. This is done in a fashion similar to one in  where an analogous construction was established for loops. As a justification of this concept we briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics