Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages
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 (i.e., low-entropy) secret keys or credentials. In this paper, we provide a general framework, that encompasses several previous AKE primitives such as (Verifier-based) Password-Authenticated Key Exchange or Secret Handshakes, we call LAKE for Language-Authenticated Key Exchange.
We first model this general primitive in the Universal Composability (UC) setting. Thereafter, we show that the Gennaro-Lindell approach can efficiently address this goal. But we need 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 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.
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- 2.Ateniese, G., Kirsch, J., Blanton, M.: Secret handshakes with dynamic and fuzzy matching. In: NDSS 2007. The Internet Society (February/March 2007)Google Scholar
- 3.Balfanz, D., Durfee, G., Shankar, N., Smetters, D.K., Staddon, J., Wong, H.-C.: Secret handshakes from pairing-based key agreements. In: IEEE Symposium on Security and Privacy, pp. 180–196. IEEE Computer Society (2003)Google Scholar
- 5.Bellovin, S.M., Merritt, M.: Encrypted key exchange: Password-based protocols secure against dictionary attacks. In: 1992 IEEE Symposium on Security and Privacy, pp. 72–84. IEEE Computer Society Press (May 1992)Google Scholar
- 6.Ben Hamouda, F., Blazy, O., Chevalier, C., Pointcheval, D., Vergnaud, D.: Efficient UC-Secure Authenticated Key-Exchange for Algebraic Languages. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 272–291. Springer, Heidelberg (2013), Full version available from the web page of the authors or from http://eprint.iacr.org/2012/284Google Scholar
- 10.Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press (October 2001)Google Scholar
- 21.Shacham, H.: A cramer-shoup encryption scheme from the linear assumption and from progressively weaker linear variants. Cryptology ePrint Archive, Report 2007/074 (2007)Google Scholar