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Cryptographic Primitives with Quasigroup Transformations

Mileva, Aleksandra (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: Primary 20N05, Secondary 94A60The 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 quasigroup based family of...

Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

Peng Shan (2011)

Annales scientifiques de l'École Normale Supérieure

We define the i -restriction and i -induction functors on the category 𝒪 of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.

Cyclic and dihedral constructions of even order

Aleš Drápal (2003)

Commentationes Mathematicae Universitatis Carolinae

Let G ( ∘ ) and G ( * ) be two groups of finite order n , and suppose that they share a normal subgroup S such that u ∘ v = u * v if u ∈ S or v ∈ S . Cases when G / S is cyclic or dihedral and when u ∘ v ≠ u * v for exactly n 2 / 4 pairs ( u , v ) ∈ G × G have been shown to be of crucial importance when studying pairs of 2-groups with the latter property. In such cases one can describe two general constructions how to get all possible G ( * ) from a given G = G ( ∘ ) . The constructions, denoted by G [ α , h ] and G [ β , γ , h ] , respectively, depend on a coset α (or two cosets β and γ ) modulo S , and on an...

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