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. In this paper:

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We obtain an optimal worst-case to average-case connection for EXP: if EXP \nsubseteq\nsubseteq BPTIME(t(n)), then EXP has problems that cannot be solved on a fraction 1/2 + 1/t¢(n)1/2 + 1/t^{\prime}(n) of the inputs by BPTIME(t¢(n))(t^{\prime}(n)) algorithms, for t¢ = tW(1)t^{\prime}= t^{\Omega(1)}.

•	We exhibit a PSPACE-complete self-correctible and downward self-reducible problem. This slightly simplifies and strengthens the proof of Impagliazzo and Wigderson, which used a #P-complete problem with these properties.

•	We argue that the results of Impagliazzo and Wigderson, and the ones in this paper, cannot be proved via “black-box” uniform reductions.