Theories of homomorphic encryption, unification, and the finite variant property

Fan Yang, Santiago Escobar, Catherine Meadows, José Meseguer, Paliath Narendran

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recent advances in the automated analysis of cryptographic protocols have aroused new interest in the practical application of unification modulo theories, especially theories that describe the algebraic properties of cryptosystems. However, this application requires unification algorithms that can be easily implemented and easily extended to combinations of different theories of interest. In practice this has meant that most tools use a version of a technique known as variant unification. This requires, among other things, that the theory be decomposable into a set of axioms B and a set of rewrite rules R such that R has the finite variant property with respect to B. Most theories that arise in cryptographic protocols have decompositions suitable for variant unification, but there is one major exception: the theory that describes encryption that is homomorphic over an Abelian group. In this paper we address this problem by studying various approximations of homomorphic encryption over an Abelian group. We construct a hierarchy of increasingly richer theories, taking advantage of new results that allow us to automatically verify that their decompositions have the finite variant property. This new verification procedure also allows us to construct a rough metric of the complexity of a theory with respect to variant unification, or variant complexity. We specify different versions of protocols using the different theories, and analyze them in the Maude-NPA cryptographic protocol analysis tool to assess their behavior. This gives us greater understanding of how the theories behave in actual application, and suggests possible techniques for improving performance.

Original languageEnglish (US)
Title of host publicationPPDP 2014 - Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming
PublisherAssociation for Computing Machinery, Inc
Pages123-134
Number of pages12
ISBN (Electronic)9781450329477
DOIs
StatePublished - Sep 8 2014
Event16th International Symposium on Principles and Practice of Declarative Programming, PPDP 2014 - Canterburry, United Kingdom
Duration: Sep 8 2014Sep 10 2014

Publication series

NamePPDP 2014 - Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming

Other

Other16th International Symposium on Principles and Practice of Declarative Programming, PPDP 2014
CountryUnited Kingdom
CityCanterburry
Period9/8/149/10/14

Keywords

  • Cryptographic protocol analysis
  • Finite variant property
  • Homomorphic encryption
  • Unification

ASJC Scopus subject areas

  • Software

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  • Cite this

    Yang, F., Escobar, S., Meadows, C., Meseguer, J., & Narendran, P. (2014). Theories of homomorphic encryption, unification, and the finite variant property. In PPDP 2014 - Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming (pp. 123-134). (PPDP 2014 - Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming). Association for Computing Machinery, Inc. https://doi.org/10.1145/2643135.2643154