Random self-reducibility of Optimal Polynomial Interpolation (OPI)

Determine whether the Optimal Polynomial Interpolation (OPI) problem possesses random self-reducibility analogous to the discrete logarithm problem, that is, whether solving average-case instances of OPI reduces to solving worst-case instances of OPI.

Background

Within the discussion of typicality and average-case hardness, the authors contrast problems like the discrete logarithm problem (DLP), which is randomly self-reducible, with newer candidates for typical quantum advantage. They highlight Optimal Polynomial Interpolation (OPI) as a promising candidate where decoded quantum interferometry (DQI) achieves efficient performance in certain parameter regimes while no known classical algorithm solves those cases in polynomial time on average.

However, the key structural property that often underwrites average-case hardness—the random self-reducibility known for DLP—has not been established for OPI. Clarifying whether OPI enjoys random self-reducibility would significantly strengthen average-case hardness evidence and the typicality of any associated quantum advantage.