Paper 2012/284

Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages

Fabrice Ben Hamouda, Olivier Blazy, Céline Chevalier, David Pointcheval, and Damien Vergnaud


\emph{Authenticated Key Exchange} (AKE) protocols enable two parties to establish a shared, cryptographically strong key over an insecure network using various authentication means, such as cryptographic keys, short (\emph{i.e.}, low-entropy) secret keys or \emph{credentials}. In this paper, we provide a general framework, that encompasses several previous AKE primitives such as \emph{(Verifier-based) Password-Authenticated Key Exchange} or \emph{Secret Handshakes}, we call \emph{LAKE} for \emph{Language-Authenticated Key Exchange}. We first model this general primitive in the \emph{Universal Composability} (UC) setting. Thereafter, we show that the Gennaro-Lindell approach can efficiently address this goal. But we need \emph{smooth projective hash functions} on new languages, whose efficient implementations are of independent interest. We indeed provide such hash functions for languages defined by combinations of linear pairing product equations. Combined with an efficient commitment scheme, that is derived from the highly-efficient UC-secure Lindell's commitment, we obtain a very practical realization of Secret Handshakes, but also \emph{Credential-Authenticated Key Exchange protocols}. All the protocols are UC-secure, in the standard model with a common reference string, under the classical Decisional Linear assumption.

Note: Clarification of the functionality and the corresponding proofs.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Full version of the PKC 2013 paper
Authenticated Key ExchangeUniversal ComposabilitySecret Handshakes
Contact author(s)
David Pointcheval @ ens fr
2012-12-14: last of 2 revisions
2012-05-29: received
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Creative Commons Attribution


      author = {Fabrice Ben Hamouda and Olivier Blazy and Céline Chevalier and David Pointcheval and Damien Vergnaud},
      title = {Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages},
      howpublished = {Cryptology ePrint Archive, Paper 2012/284},
      year = {2012},
      note = {\url{}},
      url = {}
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