Displaying similar documents to “Latin squars, p -Quasigroups and graph decompositions”

Generating quasigroups for cryptographic applications

Czesław Kościelny (2002)

International Journal of Applied Mathematics and Computer Science

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A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups...

On multiplication groups of relatively free quasigroups isotopic to Abelian groups

Aleš Drápal (2005)

Czechoslovak Mathematical Journal

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If Q is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group M l t Q is a Frobenius group. Conversely, if M l t Q is a Frobenius group, Q a quasigroup, then Q has to be isotopic to an Abelian group. If Q is, in addition, finite, then it must be a central quasigroup (a T -quasigroup).

A class of latin squares derived from finite abelian groups

Anthony B. Evans (2014)

Commentationes Mathematicae Universitatis Carolinae

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We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.