Mind the Gap: Modular Machine-Checked Proofs of One-Round Key Exchange Protocols

  • Gilles Barthe
  • Juan Manuel Crespo
  • Yassine Lakhnech
  • Benedikt Schmidt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9057)

Abstract

Using EasyCrypt, we formalize a new modular security proof for one-round authenticated key exchange protocols in the random oracle model. Our proof improves earlier work by Kudla and Paterson (ASIACRYPT 2005) in three significant ways: we consider a stronger adversary model, we provide support tailored to protocols that utilize the \(\mathsf {Naxos}\) trick, and we support proofs under the Computational DH assumption not relying on Gap oracles. Furthermore, our modular proof can be used to obtain concrete security proofs for protocols with or without adversarial key registration. We use this support to investigate, still using EasyCrypt, the connection between proofs without Gap assumptions and adversarial key registration. For the case of honestly generated keys, we obtain the first proofs of the \(\mathsf {Naxos}\) and \(\mathsf {Nets}\) protocols under the Computational DH assumption. For the case of adversarial key registration, we obtain machine-checked and modular variants of the well-known proofs for \(\mathsf {Naxos}\), \(\mathsf {Nets}\), and \(\mathsf Naxos \text {}\)+.

Keywords

Provable security Security protocols EasyCrypt Key exchange Interactive theorem proving 

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Gilles Barthe
    • 1
  • Juan Manuel Crespo
    • 1
    • 2
  • Yassine Lakhnech
    • 3
  • Benedikt Schmidt
    • 1
  1. 1.IMDEA Software InstituteMadridSpain
  2. 2.FireEye GermanyDresdenGermany
  3. 3.University of Grenoble and VERIMAGGrenobleFrance

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