Welcome to the resource topic for 2020/1326
Title:
Towards Fine-Grained One-Way Functions from Strong Average-Case Hardness
Authors: Chris Brzuska, Geoffroy Couteau
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 NP 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 nontrivial speedups can be obtained for all NP 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 NP 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 (\exists 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 black-box proof for the implication (\exists exponentially average-case hard language whose hardness amplifies optimally through parallel repetitions => FGOWF). This separation forms the core technical contribution of our work.
ePrint: https://eprint.iacr.org/2020/1326
Talk: https://www.youtube.com/watch?v=Ijyq0p-_Tmo
Slides: https://iacr.org/submit/files/slides/2022/eurocrypt/eurocrypt2022/45/slides.pdf
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .