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Abstract: We present a useful primitive, the hidden number problem, which can be exploited to prove that every bit is a hard core of specific cryptographic functions. Applications are RSA, ElGamal, Rabin and others. We give an efficient construction of a hard core predicate of any one-way function providing an alternative to the famous GoldreichLevin Bit [3]. Furthermore, a conjectured connection between universal hash functions and hard core predicates is disproven. (Update)
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BibTeX entry: (Update)
E. Kiltz, `A primitive for proving the security of every bit and about universal hash functions & hard core bits', Preprint , (2001), 1--19. http://citeseer.ist.psu.edu/kiltz01primitive.html More
@inproceedings{ kiltz01primitive,
author = "Eike Kiltz",
title = "A Primitive for Proving the Security of Every Bit and About Universal Hash Functions \& Hard Core Bits",
booktitle = "Proceedings of the 13th International Symposium on Fundamentals of Computation Theory, {FCT 2001}",
year = "2001",
url = "citeseer.ist.psu.edu/kiltz01primitive.html" }
Citations (may not include all citations):149 A hard-core predicate for all one-way functions (context) - Goldreich, Levin - 1989
55 Hardness of computing the most significant bits of secret ke.. (context) - Boneh, Venkatesan
10 A survey of hard core functions (context) - Vasco, Naslund - 2000
6 All bits in ax + b mod p are hard (context) - Naslund - 1996
5 Universal hash functions & hard core bits - Naslund - 1995
4 The security of all RSA and discrete log bits - Hastad, Naslund - 1999
3 Spectral bounds on general hard core predicates (context) - Russell - 2000
2 A useful primitive to prove security of every bit and about .. (context) - Kiltz - 2001
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