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Title: Gap MCSP Is Not (Levin) NP-Complete in Obfustopia
We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: - Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. - Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.  more » « less
Award ID(s):
2149305
PAR ID:
10643225
Author(s) / Creator(s):
;
Editor(s):
Santhanam, Rahul
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
300
ISSN:
1868-8969
Page Range / eLocation ID:
36:1-36:21
Subject(s) / Keyword(s):
Kolmogorov complexity MCSP Levin Reduction Theory of computation → Computational complexity and cryptography
Format(s):
Medium: X Size: 21 pages; 848831 bytes Other: application/pdf
Size(s):
21 pages 848831 bytes
Sponsoring Org:
National Science Foundation
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