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.
Category / Keywords: cryptographic protocols / Authenticated Key Exchange, Universal Composability, Secret Handshakes Publication Info: Full version of the PKC 2013 paper Date: received 21 May 2012, last revised 14 Dec 2012 Contact author: David Pointcheval at ens fr Available formats: PDF | BibTeX Citation Note: Clarification of the functionality and the corresponding proofs. Version: 20121214:170517 (All versions of this report) Discussion forum: Show discussion | Start new discussion