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

Katsuyuki Takashima, Atsushi Takayasu*

*この研究の対応する著者

研究成果: Chapter

8 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
出版社Springer Verlag
ページ412-431
ページ数20
DOI
出版ステータスPublished - 2015
外部発表はい

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
9451
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

フィンガープリント

「Tighter security for efficient lattice cryptography via the rényi divergence of optimized orders」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル