### 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: 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. 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(2 ^{3}) such that g is hard in the worst case for MAM circuits of size O(2^{s(1/2+γ)}) 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. 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.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Moni Naor |

Publisher | Springer Verlag |

Pages | 101-120 |

Number of pages | 20 |

ISBN (Print) | 3540210008, 9783540210009 |

DOIs | |

State | Published - 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2951 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 101-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2951). Springer Verlag. https://doi.org/10.1007/978-3-540-24638-1_6