Paper 2023/424
A Duality Between One-Way Functions and Average-Case Symmetry of Information
Abstract
Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that relates the complexity of a pair of strings and their conditional complexities. Understanding if this property holds in the time-bounded setting is a longstanding open problem. In the nineties, Longpré and Mocas (1993) and Longpré and Watanabe (1995) established that if SoI holds for time-bounded Kolmogorov complexity then cryptographic one-way functions do not exist, and asked if a converse holds.
We show that one-way functions exist if and only if (probabilistic) time-bounded SoI fails on average, i.e., if there is a samplable distribution of pairs (x,y) of strings such that SoI for pK
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Symposium on Theory of Computing (STOC), 2023
- Keywords
- one-way functionssymmetry of informationKolmogorov complexityaverage-case complexity
- Contact author(s)
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s_hirahara @ nii ac jp
rilango @ mit edu
zhenjian lu @ cs ox ac uk
nanashima m aa @ is c titech ac jp
igor oliveira @ warwick ac uk - History
- 2023-03-24: approved
- 2023-03-23: received
- See all versions
- Short URL
- https://ia.cr/2023/424
- License
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CC BY
BibTeX
@misc{cryptoeprint:2023/424, author = {Shuichi Hirahara and Rahul Ilango and Zhenjian Lu and Mikito Nanashima and Igor C. Oliveira}, title = {A Duality Between One-Way Functions and Average-Case Symmetry of Information}, howpublished = {Cryptology {ePrint} Archive, Paper 2023/424}, year = {2023}, url = {https://eprint.iacr.org/2023/424} }