Abstract
In this paper, we continue the study of the round complexity of black-box zero knowledge in the bare public-key (BPK, for short) model previously started by Micali and Reyzin in [11]. Specifically we show the impossibility of 3-round concurrent (and thus resettable) black-box zero-knowledge argument systems with sequential soundness for non-trivial languages. In light of the previous state-of-the-art, our result completes the analysis of the round complexity of black-box zero knowledge in the BPK model with respect to the notions of soundness and black-box zero knowledge.
Further we give sufficient conditions for the existence of a 3-round resettable zero-knowledge proof (in contrast to argument) system with concurrent soundness for \(\mathcal{NP}\) in the upperbounded public-key model introduced in [14].
The work presented in this paper has been supported in part by the European Commission through the IST Programme under contract IST-2002-507932 ECRYPT.
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Alwen, J., Persiano, G., Visconti, I. (2005). Impossibility and Feasibility Results for Zero Knowledge with Public Keys. In: Shoup, V. (eds) Advances in Cryptology – CRYPTO 2005. CRYPTO 2005. Lecture Notes in Computer Science, vol 3621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11535218_9
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