# Computing with very weak random sources

Title | Computing with very weak random sources |

Publication Type | Conference Papers |

Year of Publication | 1994 |

Authors | Srinivasan A, Zuckerman D |

Conference Name | , 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings |

Date Published | 1994/11/20/22 |

Publisher | IEEE |

ISBN Number | 0-8186-6580-7 |

Keywords | Application software, BPP simulations, Chor-Goldreich sources, computational complexity, Computational modeling, Computer science, Computer simulation, cryptography, distributed algorithms, expander constructions, hardness, MATHEMATICS, min-entropy, Physics computing, Polynomials, probability, R-bit string, randomness-efficient Leftover Hash Lemma, RP algorithms simulation, Testing, time-space tradeoffs, very weak random sources |

Abstract | For any fixed ε>0, we show how to simulate RP algorithms in time nO(log n) using the output of a δ-source with min-entropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an R-bit string such that any string has probability at most 2-R(ε). If ε>1-1/(k+1), our BPP simulations take time nO(log(k n)) (log(k) is the logarithm iterated k times). We also give a polynomial-time BPP simulation using Chor-Goldreich sources of min-entropy RΩ(1), which is optimal. We present applications to time-space tradeoffs, expander constructions, and the hardness of approximation. Also of interest is our randomness-efficient Leftover Hash Lemma, found independently by Goldreich and Wigderson |

DOI | 10.1109/SFCS.1994.365688 |