Tighter security for efficient lattice cryptography via the rényi divergence of optimized orders

Katsuyuki Takashima, Atsushi Takayasu*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)

Abstract

In security proofs of lattice based cryptography, to bound the closeness of two probability distributions is an important procedure. To measure the closeness, the Rényi divergence has been used instead of the classical statistical distance. Recent results have shown that the Rényi divergence offers security reductions with better parameters, e.g. smaller deviations for discrete Gaussian distributions. However, since previous analyses used a fixed order Rényi divergence, i.e., order two, they lost tightness of reductions. To overcome the deficiency, we adaptively optimize the orders based on the advantages of the adversary for several lattice-based schemes. The optimizations enable us to prove the security with both improved efficiency and tighter reductions. Indeed, our analysis offers security reductions with smaller parameters than the statistical distance based analysis and the reductions are tighter than that of previous Rényi divergence based analysis. As applications, we show tighter security reductions for sampling discrete Gaussian distributions with smaller precomputed tables for BLISS signatures, and variants of learning with errors (LWE) problem and small integer solution (SIS) problem called k-LWE and k-SIS.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages412-431
Number of pages20
DOIs
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9451
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • BLISS
  • LWE
  • Lattice based cryptography
  • Rényi divergence
  • SIS
  • Sampling discrete Gaussian
  • Tight reduction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint

Dive into the research topics of 'Tighter security for efficient lattice cryptography via the rényi divergence of optimized orders'. Together they form a unique fingerprint.

Cite this