Abstract
Dwork and Stockmeyer showed 2-round zero-knowledge proof systems secure against provers which are resource-bounded during the interaction [6]. The resources considered are running time and advice (the amount of precomputed information). We re-cast this construction in the language of list-decoding. This perspective leads to the following improvements:
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1
We give a new, simpler analysis of the protocol’s unconditional security in the advice-bounded case. Like the original, the new analysis is asymptotically tight.
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2
When the prover is bounded in both time and advice, we substantially improve the analysis of [6]: we prove security under a worst-case (instead of average-case) hardness assumption. Specifically, we assume that there exists g ∈ DTIME(2s) such that g is hard in the worst case for MAM circuits of size \(O(2^{s(\frac{1}{2}+\gamma)})\) for some γ> 0. Here s is the input length and MAM corresponds the class of circuits which are verifiers in a 3-message interactive proof (with constant soundness error) in which the prover sends the first message. In contrast, Dwork and Stockmeyer require a function that is average-case hard for “proof auditors,” a model of computation which generalizes randomized, non-deterministic circuits.
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3
Our analyses rely on new results on list-decodability of codes whose codewords are linear functions from {0,1}ℓ to {0,1}ℓ. For (1), we show that the set of all linear transformations is a good list-decodable code. For (2), we give a new, non-deterministic list-decoding procedure which runs in time quasi-linear in ℓ.
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Dwork, C., Shaltiel, R., Smith, A., Trevisan, L. (2004). List-Decoding of Linear Functions and Analysis of a Two-Round Zero-Knowledge Argument. In: Naor, M. (eds) Theory of Cryptography. TCC 2004. Lecture Notes in Computer Science, vol 2951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24638-1_6
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DOI: https://doi.org/10.1007/978-3-540-24638-1_6
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