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- W2169453948 abstract "Impagliazzo and Wigderson (1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP = BPP). Unlike results in the nonuniform setting, their result does not provide a continuous trade-off between worst-case hardness and pseudorandomness, nor does it explicitly establish an average-case hardness result. We obtain an optimal worst-case to average-case connection for EXP: if EXP BPTIME(( )), EXP has problems that are cannot be solved on a fraction 1/2 1/'( ) of the inputs by BPTIME('( )) algorithms, for ' = /sup 1/. We exhibit a PSPACE-complete downward self-reducible and random self-reducible problem. This slightly simplifies and strengthens the proof of Impagliazzo and Wigderson (1998), which used a a P-complete problem with these properties. We argue that the results in Impagliazzo and Wigderson (1998) and in this paper cannot be proved via black-box uniform reductions." @default.
- W2169453948 created "2016-06-24" @default.
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- W2169453948 date "2003-06-25" @default.
- W2169453948 modified "2023-10-16" @default.
- W2169453948 title "Pseudorandomness and average-case complexity via uniform reductions" @default.
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- W2169453948 doi "https://doi.org/10.1109/ccc.2002.1004348" @default.
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