Work

Classical Hardness of Learning with Errors

Year: 2013

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1306.0281

Authors: Brakerski, Zvika, Langlois, Adeline, Peikert, Chris, Regev, Oded, Stehlé, Damien

Institutions: Stanford University, Lyon 1 Université, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de l'Informatique du Parallélisme, Georgia Institute of Technology, York University, Courant Institute of Mathematical Sciences, New York University

Language: English

Topic: Cryptography and Data Security

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, York University, Centre National de la Recherche Scientifique, Defense Advanced Research Projects Agency, Australian Research Council

Awards: G3000816038, G4713059963, Lattices as a constructive and destructive cryptographic tool, G6671297155, CAREER: Lattices in Cryptography

OpenAlex ID: W2953258282

Cites: 8

Cited by: 36

Related to: 20