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COCO
2005
Springer

If NP Languages are Hard on the Worst-Case Then It is Easy to Find Their Hard Instances

13 years 9 months ago
If NP Languages are Hard on the Worst-Case Then It is Easy to Find Their Hard Instances
We prove that if NP ⊆ BPP, i.e., if SAT is worst-case hard, then for every probabilistic polynomial-time algorithm trying to decide SAT, there exists some polynomially samplable distribution that is hard for it. That is, the algorithm often errs on inputs from this distribution. This is the first worst-case to average-case reduction for NP of any kind. We stress however, that this does not mean that there exists one fixed samplable distribution that is hard for all probabilistic polynomial-time algorithms, which is a pre-requisite assumption needed for one-way functions and cryptography (even if not a sufficient assumption). Nevertheless, we do show that there is a fixed distribution on instances of NPcomplete languages, that is samplable in quasi-polynomial time and is hard for all probabilistic polynomial-time algorithms (unless NP is easy in the worst case). Our results are based on the following lemma that may be of independent interest: Given the description of an efficient (...
Dan Gutfreund, Ronen Shaltiel, Amnon Ta-Shma
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where COCO
Authors Dan Gutfreund, Ronen Shaltiel, Amnon Ta-Shma
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