Polynomial completeness of a universal algebra A means that any operation on A is a composition of basic operations with a specialization of some variables. In the talk we consider algebraic properties of finite polynomially complete quasigroups, the problem of recognition of its completeness in terms of its Latin square. Basing on this approach we can construct polynomially complete quasigroups of any order greater than 32 which is a power of 2. As an application we consider cryptosystems based on quasigroups.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
