### Abstract

We investigate the feasibility of a variety of cryptographic tasks with imperfect randomness. The kind of imperfect randomness we consider are entropy sources, such as those considered by Santha and Vazirani, Chor and Goldreich, and Zuckerman. We show the following: Certain cryptographic tasks like bit commitment, encryption, secret sharing, zero-knowledge, non-interactive zero-knowledge, and secure two-party computation for any non-trivial function are impossible to realize if parties have access to entropy sources with slightly less-than-perfect entropy, i.e., sources with imperfect randomness. These results are unconditional and do not rely on any unproven assumption. On the other hand, based on stronger variants of standard assumptions, secure signature schemes are possible with imperfect entropy sources. As another positive result, we show (without any unproven assumption) that interactive proofs can be made sound with respect to imperfect entropy sources.

Original language | English (US) |
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Pages (from-to) | 196-205 |

Number of pages | 10 |

Journal | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |

State | Published - Dec 1 2004 |

Event | Proceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004 - Rome, Italy Duration: Oct 17 2004 → Oct 19 2004 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS*, 196-205.