Security analysis of cryptosystems using short generators over ideal lattices

Shinya Okumura, Shingo Sugiyama, Masaya Yasuda, Tsuyoshi Takagi

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

In this paper, we analyze the security of cryptosystems using short generators over ideal lattices. Our approach is based on a recent work by Cramer et al. on analysis of the recovering short generators problem on q-th cyclotomic fields with prime powers q. In their analysis, implicit lower bounds of the special values of Dirichlet L-functions at 1 are essentially used for estimating some sizes of the dual bases of the log-unit lattices of the q-th cyclotomic fields. Our contribution is to improve Cramer et al.’s analysis by giving explicit lower and upper bounds of the special values of Dirichlet L-functions at 1. Our improvement allows one to analyze the RSG attack not only asymptotically but also explicitly for fixed practical parameters. Moreover, we give experimental evidence that recovering short generators over 2 k-th cyclotomic fields for k≥ 10 is succeeded with high probability.

本文言語英語
ページ(範囲)739-771
ページ数33
ジャーナルJapan Journal of Industrial and Applied Mathematics
35
2
DOI
出版ステータス出版済み - 7 1 2018

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

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