Nearly One-Sided Tests and the Goldreich–Levin Predicate

AbstractWe 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.

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