Główne pojęcia
Quantum-average-hardness of the GapK problem implies the existence of one-way puzzles, a fundamental primitive in quantum cryptography.
Streszczenie
The paper presents a construction of one-way puzzles (OWPuzzs) from the assumption of quantum-average-hardness of the GapK problem.
The key insights are:
Quantum-average-hardness of the GapK problem implies quantum-average-hardness of the probability estimation problem.
Quantum-average-hardness of the probability estimation problem implies the existence of OWPuzzs.
The GapK problem is a promise problem to decide whether a given bit string has a small Kolmogorov complexity or not. Its quantum-average-hardness means that an instance is sampled from a quantum-polynomial-time-samplable distribution, and no quantum-polynomial-time algorithm can solve the problem with high probability.
The authors show that this assumption, which is studied in the field of meta-complexity, can be used to construct OWPuzzs, a fundamental primitive in quantum cryptography. This is the first time a "Microcrypt" primitive is constructed based on concrete hardness assumptions that do not seem to imply one-way functions.
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