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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...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

On the unit sphere 𝕊 in a real Hilbert space 𝐇 , we derive a binary operation such that ( 𝕊 , ) is a power-associative Kikkawa left loop with two-sided identity 𝐞 0 , i.e., it has the left inverse, automorphic inverse, and A l properties. The operation is compatible with the symmetric space structure of 𝕊 . ( 𝕊 , ) is not a loop, and the right translations which fail to be injective are easily characterized. ( 𝕊 , ) satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....

Group conjugation has non-trivial LD-identities

Aleš Drápal, Tomáš Kepka, Michal Musílek (1994)

Commentationes Mathematicae Universitatis Carolinae

We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.

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