In the bare public-key model (BPK in short), each verifier is assumed to have deposited a public key in a file that is accessible by all users at all times. In this model, introduced by Canetti et al. [STOC 2000], constant-round black-box concurrent and resettable zero knowledge is possible as opposed to the standard model for zero knowledge. As pointed out by Micali and Reyzin [Crypto 2001], the notion of soundness in this model is more subtle and complex than in the classical model and indeed four distinct notions have been introduced (from weakest to strongest): one-time, sequential, concurrent and resettable soundness. In this paper we present the first constant-round concurrently sound resettable zero-knowledge argument system in the bare public-key model for NP. More specifically, we present a 4-round protocol, which is optimal as far as the number of rounds is concerned. Our result solves the main open problem on resettable zero knowledge in the BPK model and improves the previous works of Micali and Reyzin [EuroCrypt 2001] and Zhao et al. [EuroCrypt 2003] since they achieved concurrent soundness in stronger models.
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