Paper 2021/890 Original: eprint.iacr.org/2021/890 ↗
On One-way Functions and Sparse Languages
Abstract
We show equivalence between the existence of one-way functions and the existence of a \emph{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 $S(\cdot)$-sparse language $L$ that is hard-on-average with respect to some samplable distribution with Shannon entropy $h(\cdot)$ such that $h(n)-\log(S(n)) \geq 4\log n$; - The existence of a $S(\cdot)$-sparse language $L \in \NP$, that is hard-on-average with respect to some samplable distribution with Shannon entropy $h(\cdot)$ such that $h(n)-\log(S(n)) \geq n/3$; - The existence of one-way functions. Our results are inspired by, and generalize, the recent elegant paper by Ilango, Ren and Santhanam (ECCC'21), which presents similar characterizations for concrete sparse languages.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2023-02-10: last updated
- 2021-06-29: published
- Short URL
- https://ia.cr/2021/890
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/890,
author = {Yanyi Liu and Rafael Pass},
title = {On One-way Functions and Sparse Languages},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/890},
year = {2021},
url = {https://eprint.iacr.org/2021/890}
}