Abstract.
A Boolean function b is a hard-core predicate for a one-way function f if b is polynomial-time computable but b(x) is difficult to predict from f(x) . A general family of hard-core predicates is a family of functions containing a hard-core predicate for any one-way function. A seminal result of Goldreich and Levin asserts that the family of parity functions is a general family of hard-core predicates. We show that no general family of hard-core predicates can consist of functions with O(n 1-ε ) average sensitivity, for any ε > 0 . As a result, such families cannot consist of
• functions in AC0 ,
• monotone functions,
• functions computed by generalized threshold gates, or
• symmetric d -threshold functions, for d = O(n 1/2 - ε ) and ε > 0 .
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Received April 2000 and revised September 2000 Online publication 9 April 2001
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Goldmann, M., Näslund, M. & Russell, A. Complexity Bounds on General Hard-Core Predicates . J. Cryptology 14, 177–195 (2001). https://doi.org/10.1007/s00145-001-0007-6
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DOI: https://doi.org/10.1007/s00145-001-0007-6