On One-Way Functions and Sparse Languages

Yanyi Liu; Rafael Pass

doi:10.1007/978-3-031-48615-9_8

On One-Way Functions and Sparse Languages

Yanyi Liu^*, Rafael Pass

^*Corresponding author for this work

School of Computer Science

Cornell University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We show equivalence between the existence of one-way functions and the existence of a sparse language that is hard-on-average w.r.t. some efficiently samplable “high-entropy” distribution. In more detail, the following are equivalent: The existence of a S(· ) -sparse language L that is hard-on-average with respect to some samplable distribution with Shannon entropy h(· ) such that h(n) - log (S(n) ) ≥ 4 log n ;The existence of a S(· ) -sparse language L∈ NP, that is hard-on-average with respect to some samplable distribution with Shannon entropy h(· ) such that h(n) - log (S(n) ) ≥ n/ 3 ;The existence of one-way functions. where a language L is said to be S(· ) -sparse if | L∩ { 0, 1 }ⁿ| ≤ S(n) for all n∈ N. Our results are inspired by, and generalize, results from the elegant recent paper by Ilango, Ren and Santhanam (IRS, STOC’22), which presents similar connections for specific sparse languages.

Original language	English
Title of host publication	Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings
Editors	Guy Rothblum, Hoeteck Wee
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	219-237
Number of pages	19
ISBN (Print)	9783031486142
DOIs	https://doi.org/10.1007/978-3-031-48615-9_8
State	Published - 2023
Event	21st International conference on Theory of Cryptography Conference, TCC 2023 - Taipei, Taiwan, Province of China Duration: 29 Nov 2023 → 2 Dec 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14369 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st International conference on Theory of Cryptography Conference, TCC 2023
Country/Territory	Taiwan, Province of China
City	Taipei
Period	29/11/23 → 2/12/23

Funding

Funders	Funder number
Algorand Centres of Excellence
Algorand Foundation
National Science Foundation	CNS 2149305, CNS-2128519, RI-1703846
Air Force Office of Scientific Research	FA9550-18-1-0267, FA9550-23-1-0312
Defense Advanced Research Projects Agency	HR00110C0086

Access to Document

10.1007/978-3-031-48615-9_8

Cite this

Liu, Y., & Pass, R. (2023). On One-Way Functions and Sparse Languages. In G. Rothblum, & H. Wee (Eds.), Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings (pp. 219-237). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14369 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-48615-9_8

Liu, Yanyi ; Pass, Rafael. / On One-Way Functions and Sparse Languages. Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings. editor / Guy Rothblum ; Hoeteck Wee. Springer Science and Business Media Deutschland GmbH, 2023. pp. 219-237 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Liu, Y & Pass, R 2023, On One-Way Functions and Sparse Languages. in G Rothblum & H Wee (eds), Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14369 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 219-237, 21st International conference on Theory of Cryptography Conference, TCC 2023, Taipei, Taiwan, Province of China, 29/11/23. https://doi.org/10.1007/978-3-031-48615-9_8

On One-Way Functions and Sparse Languages. / Liu, Yanyi; Pass, Rafael.
Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings. ed. / Guy Rothblum; Hoeteck Wee. Springer Science and Business Media Deutschland GmbH, 2023. p. 219-237 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14369 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Liu Y, Pass R. On One-Way Functions and Sparse Languages. In Rothblum G, Wee H, editors, Theory of Cryptography - 21st International Conference, TCC 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 219-237. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-48615-9_8