### Abstract

Suppose two provers agree in a polynomial p and want to reveal a single value y = p(x) to a verifier where x is chosen arbitrarily by the verifier. Whereas honest provers should be able to agree on any polynomial p the verifier wants to be sure that with any (cheating) pair of provers the value y he receives is a polynomial function of x. We formalize this question and introduce multi-prover (quasi-)encoding schemes to solve it. Multi-prover quasi-encoding schemes are used to develop new interactive proof techniques. The main result of [BGLR] is the existence of one-round four-prover interactive proof system for any language in NP achieving any constant error probability with O(log n) random bits and poly(log log n) answer-sizes. We improve this result in two respects. First we decrease the number of provers to three, and then we decrease the answer-size to a constant. Reduction of each parameter is critical for applications. Using unrelated (parallel repetition) techniques, the same was independently and simultaneously achieved by [FK] with only two provers. When the error-probability is required to approach zero, our technique is more efficient in the number of random bits and in the answer size.

Original language | English |
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Title of host publication | Proceedings of the IEEE Annual Structure in Complexity Theory Conference |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 308-317 |

Number of pages | 10 |

ISBN (Print) | 0818656727 |

Publication status | Published - Dec 1 1994 |

Event | Proceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth Duration: Jun 28 1994 → Jul 1 1994 |

### Publication series

Name | Proceedings of the IEEE Annual Structure in Complexity Theory Conference |
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ISSN (Print) | 1063-6870 |

### Other

Other | Proceedings of the 9th Annual Structure in Complexity Theory Conference |
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City | Amsterdam, Neth |

Period | 6/28/94 → 7/1/94 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE Annual Structure in Complexity Theory Conference*(pp. 308-317). (Proceedings of the IEEE Annual Structure in Complexity Theory Conference). Publ by IEEE.