Cryptology ePrint Archive: Report 2016/737

Zero Knowledge Authentication Protocols With Algebraic Geometry Techniques

Edgar González and Guillermo Morales-Luna and Feliú D. Sagols

Abstract: Several cryptographic methods have been developed based on the difficulty to determine the set of solutions of a polynomial system over a given field. We build a polynomial ideal whose algebraic set is related to the set of isomorphisms between two graphs. The problem {\sc isomorphism}, posed in the context of Graph Theory, has been extensively used in zero knowledge authentication protocols. Thus, any cryptographic method based on {\sc isomorphism} can be translated into an equivalent method based on the problem of finding rational points in algebraic sets associated to polynomial ideals.

Category / Keywords: cryptographic protocols / zero knowledge procedures, graph isomorphism problem, multivariate polynomial system

Date: received 26 Jul 2016

Contact author: egonzalez at computacion cs cinvestav mx

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Version: 20160728:194333 (All versions of this report)

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