Displaying similar documents to “Left MQQs whose left parastrophe is also quadratic”

Cryptographic Primitives with Quasigroup Transformations

Mileva, Aleksandra (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: Primary 20N05, Secondary 94A60 The intention of this research is to justify deployment of quasigroups in cryptography, especially with new quasigroup based cryptographic hash function NaSHA as a runner in the First round of the ongoing NIST SHA-3 competition. We present new method for fast generation of huge quasigroup operations, based on the so-called extended Feistel networks and modification of the Sade’s diagonal method. We give new design of...

Solution of distributive-like quasigroup functional equations

Fedir M. Sokhatsky, Halyna V. Krainichuk (2012)

Commentationes Mathematicae Universitatis Carolinae

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We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like...

Invertibility criterion of composition of two multiary quasigroups

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

Commentationes Mathematicae Universitatis Carolinae

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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...

Loops and quasigroups: Aspects of current work and prospects for the future

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

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This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.

F-quasigroups isotopic to groups

Tomáš Kepka, Michael K. Kinyon, Jon D. Phillips (2010)

Commentationes Mathematicae Universitatis Carolinae

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In Kepka T., Kinyon M.K., Phillips J.D., , , we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally, we show an equivalence of equational...