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• W4285155293 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 $$mathsf {NP}$$ 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 $$mathsf {NP} $$ 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 $$mathsf {NP} $$ 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 $$implies $$ $$exists $$ 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 $$implies $$ $$exists $$ FGOWF). This separation forms the core technical contribution of our work." @default.
• W4285155293 created "2022-07-14" @default.
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• W4285155293 date "2022-01-01" @default.
• W4285155293 modified "2023-10-18" @default.
• W4285155293 title "On Building Fine-Grained One-Way Functions from Strong Average-Case Hardness" @default.
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• W4285155293 doi "https://doi.org/10.1007/978-3-031-07085-3_20" @default.
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