Classical Hardness of Learning with Errors
Computational Complexity
2013-06-04 v1 Cryptography and Security
Abstract
We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems, even with polynomial modulus. Previously this was only known under quantum reductions. Our techniques capture the tradeoff between the dimension and the modulus of LWE instances, leading to a much better understanding of the landscape of the problem. The proof is inspired by techniques from several recent cryptographic constructions, most notably fully homomorphic encryption schemes.
Cite
@article{arxiv.1306.0281,
title = {Classical Hardness of Learning with Errors},
author = {Zvika Brakerski and Adeline Langlois and Chris Peikert and Oded Regev and Damien Stehlé},
journal= {arXiv preprint arXiv:1306.0281},
year = {2013}
}
Comments
Preliminary version in STOC'13