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GB Belyavskaya (1994)
Abelian quasigroups are T-quasigroupsQuasigroups Relat. Syst., 1
S. Markovski, D. Gligoroski, S. Andova (2002)
Using quasigroups for one one secure encoding
J. Daemen, V. Rijmen (2002)
The Design of Rijndael
J. Daemen, V. Rijmen (2002)
The Design of Rijndael: AES - The Advanced Encryption Standard
(1992)
Characteristic of linear and alinear quasigroups
V. Artamonov, S. Chakrabarti, S. Pal (2017)
Characterizations of highly non-associative quasigroups and associative triples,, 25
V. Shcherbacov (2017)
Elements of Quasigroup Theory and Applications
VA Artamonov (2012)
Polynomially complete algebrasUch. Zap. Orlov Gos. Univ., 6
V. Artamonov, Sucheta Chakrabarti, S. Pal (2016)
Characterization of polynomially complete quasigroups based on Latin squares for cryptographic transformationsDiscret. Appl. Math., 200
Drury Wall (1957)
Sub-quasigroups of finite quasigroupsPacific Journal of Mathematics, 7
V. Dimitrova, J. Markovski (2003)
On Quasigroup Pseudo Random Sequence Generators
G. Horváth, Chrystopher Nehaniv, Csaba Szabó (2008)
An assertion concerning functionally complete algebras and NP-completenessTheor. Comput. Sci., 407
(2013)
On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts,
(1999)
Part 1,” Proc
V. Artamonov (2020)
Automorphisms of finite quasigroups with no subquasigroups
O. Grošek, P. Horák (2012)
On quasigroups with few associative triplesDesigns, Codes and Cryptography, 64
Jonathan Smith (2006)
An Introduction to Quasigroups and Their Representations
(1972)
T -quasigroups. I
(1982)
Arithmetical locally equational classes and representation of partial functions,
J. Phillips, Jonathan Smith (1999)
Quasiprimitivity and quasigroupsBulletin of the Australian Mathematical Society, 59
S. Markovski, V. Bakeva (2017)
QUASIGROUP STRING PROCESSING: PART 4
A. Galatentko, A. Pankrat’ev, Sergei Rodin (2018)
Polynomially Complete Quasigroups of Prime OrderAlgebra and Logic, 57
(2019)
Singular 4-1-2-A Computer Algebra System for Polynomial Computations
Many important properties are identified and criteria are developed for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of proper subquasigroups in a given finite quasigroup, or finds all its proper subquasigroups. This has an important application in checking the cryptographic suitability of a quasigroup. Using arithmetic of finite fields, we introduce a binary operation to construct quasigroups of order pr. Criteria are developed under which the quasigroups mentioned have desirable cryptographic properties, such as polynomial completeness and absence of proper subquasigroups. Effective methods are given for constructing cryptographically suitable quasigroups. The efficiency of the methods is illustrated by some academic examples and implementation of all proposed algorithms in the computer algebra system Singular.
Algebra and Logic – Springer Journals
Published: Sep 1, 2022
Keywords: quasigroup; subquasigroup; polynomial completeness
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