Correcting errors without leaking partial information (2005)
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| Venue: | In 37th Annual ACM Symposium on Theory of Computing (STOC |
| Citations: | 35 - 5 self |
BibTeX
@INPROCEEDINGS{Dodis05correctingerrors,
author = {Yevgeniy Dodis and Adam Smith},
title = {Correcting errors without leaking partial information},
booktitle = {In 37th Annual ACM Symposium on Theory of Computing (STOC},
year = {2005},
pages = {654--663},
publisher = {ACM}
}
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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.







