RO EN
Periodic quasigroup string transformations
Authors: V. Dimitrova, S. Markovski and A. Mileva
– 0.24 Mb
Abstract
Given a finite quasigroup (Q,*), a quasigroup string transformations el and dl over the strings of elements from Q are defined as follows. el(a1a2...an)=b1b2...bn if and only if bi=bi-1*ai and dl(a1a2...an) =b1b2...bn if and only if bi = ai-1*ai, for each i=1,2,...,n, where l=a0=b0 is a fixed element of Q. A quasigroup string e- or d-transformation t is periodical if for some periodic string we have t(a1a2...aka1a2...ak...a1a2...ak)= a1a2...aka1a2...ak...a1a2...ak. The quasigroup string transformations are used in many fields, like: cryptography for designing different cryptographic tools, coding theory for designing error-detecting and error-correcting codes, etc. The properties of the quasigroup string transformations depend on the used quasigroups, and some quasigroups are suitable for cryptographic designs, while some others are suitable for code designs. We give a characterization of the quasigroups producing periodic string transformations, and for that aim quasigroups with period k are defined. One can use this characterization for choosing suitable quasigroups in some applications.Fulltext
– 0.24 Mb
Contents
- New fuzzy subquasigroups
- Vague Lie subalgebras over a vague field
- A probabilistic model of error-detecting codes based on quasigroups
- Pure ideals in ternary semigroups
- Secret-sharing schemes and orthogonal systems of k-ary operations
- Prolongations of quasigroups by middle translations
- Periodic quasigroup string transformations
- Skew endomorphisms on some n-ary groups
- Construction for subdirectly irreducible sloops of cardinality n2^m
- N-fuzzy quasi-ideals in ordered semigroups
- Generalized quadratic quasigroup equations with tree variables
- New primitives for digital signature algorithms
- Congruencies on an inverse AG**-groupoid via the natural partial order
