Abstract
We define a new notion of relatively-sound non-interactive zero-knowledge (NIZK) proofs, where a private verifier with access to a trapdoor continues to be sound even when the Adversary has access to simulated proofs and common reference strings. It is likely that this weaker notion of relative-soundness suffices in most applications that need simulation-soundness. We show that for certain languages which are diverse groups, and hence allow smooth projective hash functions, one can obtain more efficient single-theorem relatively-sound NIZKs as opposed to simulation-sound NIZKs. We also show that such relatively-sound NIZKs can be used to build rather efficient publicly-verifiable CCA2-encryption schemes.
By employing this new publicly-verifiable encryption scheme along with an associated smooth projective-hash, we show that a recent PAK-model single-round password-based key exchange protocol of Katz and Vaikuntanathan, Proc. TCC 2011, can be made much more efficient. We also show a new single round UC-secure password-based key exchange protocol with only a constant number of group elements as communication cost, whereas the previous single round UC-protocol required Ω(k) group elements, where k is the security parameter.
Authors were supported in part by the Department of Homeland Security under grant FA8750-08-2-0091.
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Jutla, C., Roy, A. (2012). Relatively-Sound NIZKs and Password-Based Key-Exchange. In: Fischlin, M., Buchmann, J., Manulis, M. (eds) Public Key Cryptography – PKC 2012. PKC 2012. Lecture Notes in Computer Science, vol 7293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30057-8_29
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