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Paper 2019/1009

LLL and stochastic sandpile models

Jintai Ding and Seungki Kim and Tsuyoshi Takagi and Yuntao Wang

Abstract

We introduce stochastic sandpile models which imitate numerous aspects of the practical behavior of the LLL algorithm with compelling accuracy. In addition, we argue that the physics and mathematics of sandpile models provide satisfactory heuristic explanations to much of the mysteries of LLL, and pleasant implications for lattice-based cryptography as a whole. Based on these successes, we suggest a paradigm in which one regards blockwise reduction algorithms as 1-d stochastic self-organized criticality(SOC) models and study them as such.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
LLL algorithmsandpile modelslattice reduction
Contact author(s)
seungki math @ gmail com
History
2019-09-09: received
Short URL
https://ia.cr/2019/1009
License
Creative Commons Attribution
CC BY
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