Improved security proofs in lattice-based cryptography: using the rényi divergence rather than the statistical distance

Shi Bai*, Adeline Langlois, Tancrède Lepoint, Damien Stehlé, Ron Steinfeld

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

39 Citations (Scopus)

Abstract

The Rényi divergence is a measure of closeness of two probability distributions. We show that it can often be used as an alternative to the statistical distance in security proofs for lattice-based cryptography. Using the Rényi divergence is particularly suited for security proofs of primitives in which the attacker is required to solve a search problem (e.g., forging a signature).We show that it may also be used in the case of distinguishing problems (e.g., semantic security of encryption schemes), when they enjoy a public sampleability property. The techniques lead to security proofs for schemes with smaller parameters, and sometimes to simpler security proofs than the existing ones.

Original languageEnglish
Title of host publicationAdvances in Cryptology - ASIACRYPT 2015
Subtitle of host publication21st International Conference on the Theory and Application of Cryptology and Information Security,Auckland, New Zealand, November 29 - December 3, 2015, Proceedings
EditorsTetsu Iwata, Jung Hee Cheon
Place of PublicationHeidelberg
PublisherSpringer, Springer Nature
Pages3-24
Number of pages22
VolumePart 1
ISBN (Electronic)9783662487976
ISBN (Print)9783662487969
DOIs
Publication statusPublished - 2015
Event21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015 - Auckland, New Zealand
Duration: 29 Nov 20153 Dec 2015

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume9452
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015
CountryNew Zealand
CityAuckland
Period29/11/153/12/15

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