A Trace Map Attack Against Special Ring-LWE Samples

Yasuhiko Ikematsu, Satoshi Nakamura, Masaya Yasuda

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

The learning with errors (LWE) problem is one of the hard problems supporting the security of modern lattice-based cryptography. Ring-LWE is the analog of LWE over the ring of integers of a cyclotomic field, and it has provided efficient cryptosystems. In this paper, we give cryptanalysis against ring-LWE using the trace map over the ring of integers of a cyclotomic field, without using any reduction to other structured lattice problems. Since it maps to a ring of a smaller degree, a trace map attack is expected to be able to decrease the hardness of ring-LWE. However, the trace map does not necessarily transform ring-LWE samples to samples over the smaller ring with a common secret. We give a sufficient and necessary condition on a pair of ring-LWE samples for which the trace map attack is applicable. We call such a pair of samples special. We demonstrate how efficiently the trace map attack can solve ring-LWE when a special pair of samples is given. Specifically, we compare blocksizes of the Blockwise Korkine-Zolotarev (BKZ) algorithm required for solving ring-LWE in the trace map attack and a standard attack. Moreover, we discuss the (in)feasibility of the trace map attack for random ring-LWE samples to evaluate how the trace map attack can give a threat against ring-LWE-based cryptosystems on a practical side.

本文言語英語
ホスト出版物のタイトルAdvances in Information and Computer Security - 16th International Workshop on Security, IWSEC 2021, Proceedings
編集者Toru Nakanishi, Ryo Nojima
出版社Springer Science and Business Media Deutschland GmbH
ページ3-22
ページ数20
ISBN(印刷版)9783030859862
DOI
出版ステータス出版済み - 2021
イベント16th International Workshop on Security, IWSEC 2021 - Virtual, Online
継続期間: 9 8 20219 10 2021

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)
12835 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議16th International Workshop on Security, IWSEC 2021
CityVirtual, Online
Period9/8/219/10/21

All Science Journal Classification (ASJC) codes

  • 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)

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