aalto1 untyped-item.component.html
On Building Fine-Grained One-Way Functions from Strong Average-Case Hardness
Loading...
Access rights
openAccess
CC BY
CC BY
Creative Commons license
Except where otherwised noted, this item's license is described as openAccess
publishedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Authors
Date
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
Journal of Cryptology, Volume 38, issue 1
Abstract
Constructing one-way functions from average-case hardness is a long-standing open problem. A positive result would exclude Pessiland (Impagliazzo ’95) and establish a highly desirable win–win situation: either (symmetric) cryptography exists unconditionally, or all problems can be solved efficiently on the average. Motivated by the lack of progress on this seemingly very hard question, we initiate the investigation of weaker yet meaningful candidate win–win results of the following type: either there are fine-grained one-way functions (FGOWF), or non-trivial speedups can be obtained for all problems on the average. FGOWFs only require a fixed polynomial gap (as opposed to superpolynomial) between the running time of the function and the running time of an inverter. We obtain three main results: Construction. We show that if there is an language having a very strong form of average-case hardness, which we call block finding hardness, then FGOWF exist. We provide heuristic support for this very strong average-case hardness notion by showing that it holds for a random language. Then, we study whether weaker (and more natural) forms of average-case hardness could already suffice to obtain FGOWF and obtain two negative results: Separation I. We provide a strong oracle separation for the implication ( exponentially average-case hard language FGOWF). Separation II. We provide a second strong negative result for an even weaker candidate win–win result. Namely, we rule out a relativizing proof for the implication ( exponentially average-case hard language whose hardness amplifies optimally through parallel repetitions FGOWF). This separation forms the core technical contribution of our work.
Description
Other note
Citation
Brzuska, C & Couteau, G 2025, 'On Building Fine-Grained One-Way Functions from Strong Average-Case Hardness', Journal of Cryptology, vol. 38, no. 1, 8. https://doi.org/10.1007/s00145-024-09518-1