scholarly journals Division algebras that generalize Dickson semifields

2020 ◽  
Vol 28 (2) ◽  
pp. 89-102
Author(s):  
Daniel Thompson
Keyword(s):  
Division Algebras ◽  
Central Simple Algebras ◽  
Central Division ◽  
Simple Algebras ◽  
Dimension 2 ◽  
Central Simple

AbstractWe generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension 2s2 by doubling central division algebras of degree s. Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

scholarly journals An identification system based on the explicit isomorphism problem

2021 ◽  
Author(s):  
Sándor Z. Kiss ◽  
Péter Kutas
Keyword(s):  
Quadratic Forms ◽  
Isomorphism Problem ◽  
Identification System ◽  
Division Algebras ◽  
Central Simple Algebras ◽  
Zero Knowledge ◽  
Algorithmic Problems ◽  
Simple Algebras ◽  
Central Simple ◽  
Integral Equivalence

AbstractWe propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras. We design a statistical zero knowledge protocol which relies on the hardness of computing isomorphisms between orders in division algebras which generalizes a protocol by Hartung and Schnorr, which relies on the hardness of integral equivalence of quadratic forms.

Locally Finite Central Simple Algebras

2021 ◽  
Author(s):  
Tamar Bar-On ◽  
Shira Gilat ◽  
Eliyahu Matzri ◽  
Uzi Vishne
Keyword(s):  
Central Simple Algebras ◽  
Locally Finite ◽  
Simple Algebras ◽  
Central Simple
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