Displaying similar documents to “Infinitary Quasigroups”

On the structure of finite paramedial quasigroups

V. A. Shcherbacov, D. I. Pushkashu (2010)

Commentationes Mathematicae Universitatis Carolinae

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Information on the structure of finite paramedial quasigroups, including a classification of finite simple paramedial quasigroups, is given. The problem ``Classify the finite simple paramedial quasigroups'' was posed by J. Ježek and T. Kepka at the conference LOOPS'03, Prague 2003.

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...

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...