Classical hardness of learning with errors

Authors:
Zvika Brakerski;Adeline Langlois;Chris Peikert;Oded Regev;Damien Stehlé
Affiliations:
Stanford University, Stanford, USA;LIP, ENS Lyon, Lyon, France;Georgia Institute of Technology, Atlanta, USA;Courant Institute, New York University, New York, USA;LIP, ENS Lyon, Lyon, France
Venue:
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Year:
2013

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Abstract

We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems. 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.