Adi Akavia
Oded Goldreich
Shafi Goldwasser
ABSTRACT
We consider the possibility of basing one-way functions on NP-Hardness; that is, we study possible reductions from a worst-case decision problem to the task of average-case inverting a polynomial-time computable function f. Our main findings are the following two negative results:
If given y one can efficiently compute |f-1(y)| then the existence of a (randomized) reduction of NP to the task of inverting f implies that coNP ⊆ AM. Thus, it follows that such reductions cannot exist unless coNP ⊆ AM.
For any function f, the existence of a (randomized) non-adaptive reduction of NP to the task of average-case inverting f implies that coNP ⊆ AM.
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Index Terms
- On basing one-way functions on NP-hardness
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