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Unification Modulo Homomorphic Encryption

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Abstract

Encryption ‘distributing over pairs’ is a technique employed in several cryptographic protocols. We show that unification is decidable for an equational theory HE specifying such an encryption. The method consists in transforming any given problem in such a way, that the resulting problem can be solved by combining a graph-based reasoning on its equations involving the homomorphisms, with a syntactic reasoning on its pairings. We show HE-unification to be NP-hard and in EXPTIME. We also indicate, briefly, how to extend HE-unification to Cap unification modulo HE, that can be used as a tool for modeling and analyzing cryptographic protocols where encryption follows the ECB mode, i.e., is done block-wise on messages.

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Author information

Authors and Affiliations

  1. LIFO, University of Orléans, Orléans, France

    Siva Anantharaman

  2. Clarkson University, Potsdam, NY, USA

    Hai Lin & Christopher Lynch

  3. University at Albany-SUNY, Albany, NY, USA

    Paliath Narendran

  4. Loria-INRIA Lorraine, Nancy, France

    Michael Rusinowitch

Authors
  1. Siva Anantharaman
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  2. Hai Lin
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  3. Christopher Lynch
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  4. Paliath Narendran
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  5. Michael Rusinowitch
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Corresponding author

Correspondence to Siva Anantharaman.

Additional information

Work supported by NSF Grants CNS-0831305 and CNS-0831209, and partially supported by the FP7-ICT-2007-1 Project no. 216471, AVANTSSAR.

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Anantharaman, S., Lin, H., Lynch, C. et al. Unification Modulo Homomorphic Encryption. J Autom Reasoning 48, 135–158 (2012). https://doi.org/10.1007/s10817-010-9205-y

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  • DOI: https://doi.org/10.1007/s10817-010-9205-y

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