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We consider average-case strengthenings of the traditional assumption that coNP is not contained in AM. Under these assumptions, we rule out generic and potentially non-black-box constructions of various cryptographic primitives (e.g., one-way permutations, collision-resistant hash-functions, constant-round statistically hiding commitments, and constant-round black-box zero-knowledge proofs for NP) from one-way functions, assuming the security reductions are black-box.

Towards Non-Black-Box Lower Bounds in Cryptography