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On Basing One-Way Functions on NP-Hardness

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We prove that if the hardness of inverting a size-verifiable one-way function can be based on NP-hardness via a general (adaptive) reduction, then NP is contained in coAM. This claim was made by Akavia, Goldreich, Goldwasser, and Moshkovitz (STOC 2006), but was later retracted (STOC 2010). This is joint work with Andrej Bogdanov.

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