Classical hardness of learning with errors

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 crypto- graphic constructions, most notably fully homomorphic encryption schemes.

Original languageEnglish (US)
Title of host publicationSTOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing
Pages575-584
Number of pages10
DOIs
StatePublished - 2013
Event45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States
Duration: Jun 1 2013Jun 4 2013

Other

Other45th Annual ACM Symposium on Theory of Computing, STOC 2013
CountryUnited States
CityPalo Alto, CA
Period6/1/136/4/13

Fingerprint

Hardness
Cryptography
Polynomials

Keywords

  • Lattices
  • Learning with errors

ASJC Scopus subject areas

  • Software

Cite this

Brakerski, Z., Langlois, A., Peikert, C., Regev, O., & Stehlé, D. (2013). Classical hardness of learning with errors. In STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing (pp. 575-584) https://doi.org/10.1145/2488608.2488680

Classical hardness of learning with errors. / Brakerski, Zvika; Langlois, Adeline; Peikert, Chris; Regev, Oded; Stehlé, Damien.

STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing. 2013. p. 575-584.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Brakerski, Z, Langlois, A, Peikert, C, Regev, O & Stehlé, D 2013, Classical hardness of learning with errors. in STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing. pp. 575-584, 45th Annual ACM Symposium on Theory of Computing, STOC 2013, Palo Alto, CA, United States, 6/1/13. https://doi.org/10.1145/2488608.2488680
Brakerski Z, Langlois A, Peikert C, Regev O, Stehlé D. Classical hardness of learning with errors. In STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing. 2013. p. 575-584 https://doi.org/10.1145/2488608.2488680
Brakerski, Zvika ; Langlois, Adeline ; Peikert, Chris ; Regev, Oded ; Stehlé, Damien. / Classical hardness of learning with errors. STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing. 2013. pp. 575-584
@inproceedings{376e25e84b404269b736ebb8e3d50136,
title = "Classical hardness of learning with errors",
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 crypto- graphic constructions, most notably fully homomorphic encryption schemes.",
keywords = "Lattices, Learning with errors",
author = "Zvika Brakerski and Adeline Langlois and Chris Peikert and Oded Regev and Damien Stehl{\'e}",
year = "2013",
doi = "10.1145/2488608.2488680",
language = "English (US)",
isbn = "9781450320290",
pages = "575--584",
booktitle = "STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing",

}

TY - GEN

T1 - Classical hardness of learning with errors

AU - Brakerski, Zvika

AU - Langlois, Adeline

AU - Peikert, Chris

AU - Regev, Oded

AU - Stehlé, Damien

PY - 2013

Y1 - 2013

N2 - 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 crypto- graphic constructions, most notably fully homomorphic encryption schemes.

AB - 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 crypto- graphic constructions, most notably fully homomorphic encryption schemes.

KW - Lattices

KW - Learning with errors

UR - http://www.scopus.com/inward/record.url?scp=84879829096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879829096&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488680

DO - 10.1145/2488608.2488680

M3 - Conference contribution

AN - SCOPUS:84879829096

SN - 9781450320290

SP - 575

EP - 584

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

ER -