Automatically Verified Mechanized Proof of One-Encryption Key Exchange

Abstract

We present a mechanized proof of the password-based protocol One-Encryption Key Exchange (OEKE) using the computationally-sound protocol prover CryptoVerif. OEKE is a non-trivial protocol, and thus mechanizing its proof provides additional confidence that it is correct. This case study was also an opportunity to implement several important extensions of CryptoVerif, useful for proving many other protocols. We have indeed extended CryptoVerif to support the computational Diffie-Hellman assumption. We have also added support for proofs that rely on Shoup\u27s lemma and additional game transformations. In particular, it is now possible to insert case distinctions manually and to merge cases that no longer need to be distinguished. Eventually, some improvements have been added on the computation of the probability bounds for attacks, providing better reductions. In particular, we improve over the standard computation of probabilities when Shoup\u27s lemma is used, which allows us to improve the bound given in a previous manual proof of OEKE, and to show that the adversary can test at most one password per session of the protocol. In this paper, we present these extensions, with their application to the proof of OEKE. All steps of the proof are verified by CryptoVerif. This document is an updated version of a report from 2012. In the 10 years between 2012 and 2022, CryptoVerif has made a lot of progress. In particular, the probability bound obtained by CryptoVerif for OEKE has been improved, reaching an almost optimal probability: only statistical terms corresponding to collisions between group elements or between hashes are overestimated by a small constant factor