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Robustness of average-case meta-complexity via pseudorandomness

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Rahul SanthanamAuthors Info & Claims

STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing

Pages 1575 - 1583

https://doi.org/10.1145/3519935.3520051

Published: 10 June 2022 Publication History

Abstract

We show broad equivalences in the average-case complexity of many different meta-complexity problems, including Kolmogorov complexity, time-bounded Kolmogorov complexity, and the Minimum Circuit Size Problem. These results hold for a wide range of parameters (various thresholds, approximation gaps, weak or strong average-case hardness, etc.) and complexity notions, showing the theory of meta-complexity is very *robust* in the average-case setting.

Our results are shown by establishing new and generic connections between meta-complexity and the theory of pseudorandomness and one-way functions. Using these connections, we give the first unconditional characterization of one-way functions based on the average-case hardness of the Minimum Circuit Size Problem. We also give a surprising and clean characterization of one-way functions based on the average-case hardness of (the worst-case uncomputable) Kolmogorov complexity. Moreover, the latter is the first characterization of one-way functions based on the average-case hardness of a fixed problem on *any* samplable distribution.

We give various applications of these results to the foundations of cryptography and the theory of meta-complexity. For example, we show that the average-case hardness of deciding k-SAT or Clique on any samplable distribution of high enough entropy implies the existence of one-way functions. We also use our results to unconditionally solve various meta-complexity problems in CZK (computational zero-knowledge) on average, and give implications of our results for the classic question of proving NP-hardness for the Minimum Circuit Size Problem.

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Cited By

Huang YIlango RRen HSaha BServedio R(2023)NP-Hardness of Approximating Meta-Complexity: A Cryptographic ApproachProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585154(1067-1075)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585154
Ilango R(2023)SAT Reduces to the Minimum Circuit Size Problem with a Random Oracle2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00048(733-742)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00048
Ball MLiu YMazor NPass R(2023)Kolmogorov Comes to Cryptomania: On Interactive Kolmogorov Complexity and Key-Agreement2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00034(458-483)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00034
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Index Terms

Robustness of average-case meta-complexity via pseudorandomness
1. Theory of computation
  1. Computational complexity and cryptography
  2. Randomness, geometry and discrete structures
    1. Pseudorandomness and derandomization

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cover image ACM Conferences

STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing

June 2022

1698 pages

ISBN:9781450392648

DOI:10.1145/3519935

General Chair:
Stefano Leonardi
Sapienza University of Rome, Italy
,
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Anupam Gupta
Carnegie Mellon University, USA

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Cited By

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https://dl.acm.org/doi/10.1145/3564246.3585154
Ilango R(2023)SAT Reduces to the Minimum Circuit Size Problem with a Random Oracle2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00048(733-742)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00048
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https://doi.org/10.1109/FOCS57990.2023.00034
Hirahara SNanashima M(2023)Learning in Pessiland via Inductive Inference2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00033(447-457)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00033

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