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Gap MCSP Is Not (Levin) NP-Complete in Obfustopia

Authors Noam Mazor, Rafael Pass

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Author Details

Noam Mazor
  • Tel Aviv University, Israel
Rafael Pass
  • Tel Aviv University, Israel
  • Cornell Tech, New York, NY, USA

Funding

  • Mazor, Noam: Research partly supported by NSF CNS-2149305 and DARPA under Agreement No. HR00110C0086.
  • Pass, Rafael: Supported in part by AFOSR Award FA9550-23-1-0387, AFOSR Award FA9550-23-1-0312, and an Algorand Foundation grant. This material is based upon work supported by DARPA under Agreement No. HR00110C0086. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, DARPA, AFOSR or the Algorand Foundation.

Cite AsGet BibTex

Noam Mazor and Rafael Pass. Gap MCSP Is Not (Levin) NP-Complete in Obfustopia. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CCC.2024.36

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Kolmogorov complexity
  • MCSP
  • Levin Reduction

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