Understanding the average-case complexity of NP is a central goal in complexity theory and cryptography.

TR26-253 | The Gap Between Average-Case and Worst-Case Complexity | Halley Goldberg, Jinqiao Hu, Zhenjian Lu, Jingyi Lyu, Igor Oliveira https://eccc.weizmann.ac.il/report/2026/253 Understanding the average-case complexity of $mathrm{NP}$ is a central goal in complexity theory and cryptography. A necessary milestone is to understand the corresponding average-case versus worst-case question for the polynomial hierarchy ($mathrm{PH}$). In a celebrated result, Hirahara [Hir21]

The Gap Between Average-Case and Worst-Case Complexity https://arxiv.org/abs/2610.19162v1 Authors: Halley Goldberg, Jinqiao Hu, Zhenjian Lu, Jingyi Lyu, Igor C. OliveiraUnderstanding the average-case complexity of $mathsf{NP}$ is a central goal in complexity theory and cryptography. A necessary milestone is to understand the corresponding average-case versus worst-case question for the polynomial hierarchy ($mathsf{PH}$). In a celebrated result, Hirahara [Hir21] proved that if every