Lattice Problems beyond Polynomial Time
Divesh Aggarwal, Huck Bennett, Zvika Brakerski, Alexander Golovnev, Rajendra Kumar, Zeyong Li, Spencer Peters, Noah Stephens-Davidowitz, Vinod Vaikuntanathan · 2023
We study the complexity of lattice problems in a world where algorithms, reductions, and protocols can run in superpolynomial time. Specifically, we revisit four foundational results in this context—two protocols and two worst-case to average-case reductions. We show how to improve the approximation factor in each result by a factor of roughly √n/logn when running the protocol or reduction in 2є n time instead of polynomial time, and we show a novel protocol with no polynomial-time analog. Our results are as follows.