LLL and stochastic sandpile models
Number Theory
2020-03-10 v5 Statistical Mechanics
Cryptography and Security
Abstract
Theaimofthepresentpaperistosuggestthatstatisticalphysicsprovides the correct language to understand the practical behavior of the LLL algorithm, most of which are left unexplained to this day. To this end, we propose sandpile models that imitate LLL with compelling accuracy, and prove for these models some of the most desired statements regarding LLL. We also formulate a few conjectures that formally capture our heuristics and would serve as milestones for further development of the theory.
Cite
@article{arxiv.1804.03285,
title = {LLL and stochastic sandpile models},
author = {Jintai Ding and Seungki Kim and Tsuyoshi Takagi and Yuntao Wang},
journal= {arXiv preprint arXiv:1804.03285},
year = {2020}
}