Improved zero-knowledge identification with lattices

Authors:
Pierre-Louis Cayrel;Richard Lindner;Markus Rückert;Rosemberg Silva
Affiliations:
Center for Advanced Security Research Darmstadt, Darmstadt, Germany;Technische Universität Darmstadt, Fachbereich Informatik, Kryptographie und Computeralgebra, Darmstadt, Germany;Technische Universität Darmstadt, Fachbereich Informatik, Kryptographie und Computeralgebra, Darmstadt, Germany;State University of Campinas, Institute of Computing, Campinas, Brazil
Venue:
ProvSec'10 Proceedings of the 4th international conference on Provable security
Year:
2010

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Abstract

Zero-knowledge identification schemes solve the problem of authenticating one party to another via an insecure channel without disclosing any additional information that might be used by an impersonator. In this paper we propose a scheme whose security relies on the existence of a commitment scheme and on the hardness of worst-case lattice problems. We adapt a code-based identification scheme devised by Cayrel and Véron, which constitutes an improvement of Stern's construction. Our solution sports analogous improvements over the lattice adaption of Stern's scheme which Kawachi et al. presented at ASIACRYPT 2008. Specifically, due to a smaller cheating probability close to 1/2 and a similar communication cost, any desired level of security will be achieved in fewer rounds. Compared to Lyubashevsky's scheme presented at ASIACRYPT 2009, our proposal, like Kawachi's, offers a much milder security assumption: namely, the hardness of SIS for trinary solutions. The same assumption was used for the SWIFFT hash function, which is secure for much smaller parameters than those proposed by Lyubashevsky.