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Generating quasigroups for cryptographic applications

Czesław Kościelny (2002)

International Journal of Applied Mathematics and Computer Science

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 are of...

Invertibility criterion of composition of two multiary quasigroups

Fedir M. Sokhatsky, Iryna V. Fryz (2012)

Commentationes Mathematicae Universitatis Carolinae

We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and n -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We establish...

Le semi-groupe libre des carrés magiques

Lionel Cozar (1996)

Journal de théorie des nombres de Bordeaux

Nous étudions une loi de composition sur les carrés magiques, qui a déjà été introduite dans la littérature, qui munit l'ensemble de tous les carrés magiques d'une structure de semi-groupe (monoïde). Nous prouvons ensuite une conjecture de Adler et Li, ce semi-groupe est libre.

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