Results 71 to 80 of about 166 (137)

A Note on the Quasigroup of Lai–Massey Structures

Cryptography
In our paper, we explore the consequences of replacing the commutative group operation used in Lai–Massey structures with a quasigroup operation. We introduce four quasigroup versions of the Lai–Massey structure and prove that for quasigroups isotopic ...
George Teşeleanu
doaj   +1 more source

Securing Retinal Template Using Quasigroups

Journal of Advances in Information Technology, 2011
Biometric plays important role in person recognition and identification. It is more secure than the traditional systems like password and token based systems. The traditional systems can be stolen, misplaced or destroyed.
N. Radha, T. Rubya, S. Karthikeyan
doaj   +1 more source

A message recovery attack on multivariate polynomial trapdoor function. [PDF]

PeerJ Comput Sci, 2023
Ali R, Hussain MM, Kanwal S, Hajjej F, Inam S.   +4 more
europepmc   +1 more source

Quantum Quasigroups and the Quantum Yang–Baxter Equation

Axioms, 2016
Quantum quasigroups are algebraic structures providing a general self-dual framework for the nonassociative extension of Hopf algebra techniques. They also have one-sided analogues, which are not self-dual.
Jonathan Smith
doaj   +1 more source

On Multiplication Groups of Quasigroups

European Journal of Combinatorics, 1984
The author shows that all finite dihedral, symmetric, alternating, general linear and projective general linear groups and the Mathieu- groups \(M_{11}\) and \(M_{23}\) have the following property: they are isomorphic to multiplication groups of quasigroups.
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On Birkhoff's quasigroup axioms

Journal of Algebra, 2016
Quasigroups form a variety only if two additional operations, namely \(/\) and \(\backslash\) are considered. Birkhoff formulated six identities that define equationally the variety of quasigroups. Evans proved that only the most natural four identities are needed.
Phillips, J. D., Pushkashu, D. I., Shcherbacov, A. V., Shcherbacov, V. A.   +3 more
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T-quasigroups with Stein 2-nd and 3-rd identity

Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
In this paper we prolong research of T-quasigroups with Stein 2-rd (xy ⋅ x = y ⋅ xy) and Stein 3-rd (xy ⋅ yx = y) identities [9].
Victor Shcherbacov, Irina Radilova, Petr Radilov   +2 more
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Pentagonal quasigroups [PDF]

Quasigroups and related systems, 2011
In this paper the concept of pentagonal quasigroup is introduced as {; ; ; IM}; ; ; -quasigroup satisfying the additional property of pentagonality. Some basic identities which are valid in a general pentagonal quasigroup are proved. Four different models for pentagonal quasigroups and their mutual relations are studied.
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Parastrophes of quasigroups

, 2015
Parastrophes (conjugates) of a quasigroup can be divided into separate classes containing isotopic parastrophes. We prove that the number of such classes is always 1, 2, 3 or 6. Next we characterize quasigroups having a fixed number of such classes.
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The Universality of the variety of quasigroups [PDF]

Journal of the Australian Mathematical Society, 1976
AbstractThe variety of quasigroups is universal for varieties of algebras of the most general kind in the sense that each such variety can be interpreted in a natural way in a suitably chosen subvariety of quasigroups. More precisely, for any algebra〈A, f0, f1, f2, …〉wheref0, f1, f2, …is an arbitrary finite or infinite sequence of operations of finite ...
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