## Abstract

This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W - that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant "perfectly oneway" hash functions in the sense of Canetti et al. [7], which in turn leads to obfuscation of proximity queries for high entropy secrets W; (b) private fuzzy extractors [11], which allow one to extract uniformly random bits from noisy and nonuniform data W, while also insuring that no sensitive information about W is leaked; and (c) noise tolerance and stateless key re-use in the Bounded Storage Model, resolving the main open problem of Ding [10]. The heart of our constructions is the design of strong randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W′ which is close to W.

Original language | English (US) |
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Pages (from-to) | 654-663 |

Number of pages | 10 |

Journal | Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - Dec 1 2005 |

Event | 13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States Duration: Nov 7 2005 → Nov 11 2005 |

## All Science Journal Classification (ASJC) codes

- Software