Nearly One-Sided Tests and the Goldreich–Levin Predicate

Authors:
Gustav Hast
Affiliations:
Department of Numerical Analysis and Computer Science, Royal Institute of Technology, 100 44 Stockholm, Sweden
Venue:
Journal of Cryptology
Year:
2004

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Abstract

We study statistical tests with binary output that rarely outputs one, which we call nearly one-sided statistical tests. We provide an efficient reduction establishing improved security for the Goldreich–Levin hard-core bit against nearly one-sided tests. The analysis is extended to prove the security of the Blum–Micali pseudo-random generator combined with the Goldreich–Levin bit. Finally, some applications where nearly one-sided tests occur naturally are discussed.