Making NTRU as secure as worst-case problems over ideal lattices

Damien Stehlé*, Ron Steinfeld

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

197 Citations (Scopus)

Abstract

NTRUEncrypt, proposed in 1996 by Hoffstein, Pipher and Silverman, is the fastest known lattice-based encryption scheme. Its moderate key-sizes, excellent asymptotic performance and conjectured resistance to quantum computers could make it a desirable alternative to factorisation and discrete-log based encryption schemes. However, since its introduction, doubts have regularly arisen on its security. In the present work, we show how to modify NTRUEncrypt to make it provably secure in the standard model, under the assumed quantum hardness of standard worst-case lattice problems, restricted to a family of lattices related to some cyclotomic fields. Our main contribution is to show that if the secret key polynomials are selected by rejection from discrete Gaussians, then the public key, which is their ratio, is statistically indistinguishable from uniform over its domain. The security then follows from the already proven hardness of the the R-LWE problem.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2011, 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsKenneth G. Paterson
Place of PublicationHeidelberg, Germany
PublisherSpringer, Springer Nature
Pages27-47
Number of pages21
Volume6632 LNCS
ISBN (Print)9783642204647
DOIs
Publication statusPublished - 2011
Event30th Annual International Conference on the Theory and Applications of Cryptographic Techniques Advances in Cryptology, EUROCRYPT 2011 - Tallinn, Estonia
Duration: 15 May 201119 May 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6632 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other30th Annual International Conference on the Theory and Applications of Cryptographic Techniques Advances in Cryptology, EUROCRYPT 2011
CountryEstonia
CityTallinn
Period15/05/1119/05/11

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