A Trace Map Attack Against Special Ring-LWE Samples

Yasuhiko Ikematsu, Satoshi Nakamura, Masaya Yasuda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationAdvances in Information and Computer Security - 16th International Workshop on Security, IWSEC 2021, Proceedings
EditorsToru Nakanishi, Ryo Nojima
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages20
ISBN (Print)9783030859862
Publication statusPublished - 2021
Event16th International Workshop on Security, IWSEC 2021 - Virtual, Online
Duration: Sept 8 2021Sept 10 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12835 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Workshop on Security, IWSEC 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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