An identification system based on the explicit isomorphism problem

2018/12/21 by Kiss, Sándor Z., Kutas, Péter
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1812.09130

Abstract

We 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.

Related

• Computing explicit isomorphisms with full matrix algebras over \mathbbF_q(x)
• Isomorphisms of Algebraic Number Fields
• Testing isomorphism of complex and real Lie algebras
• The Isomorphism Problem On Classes of Automatic Structures
• Computation of lattice isomorphisms and the integral matrix similarity problem