Analysis of lattice reduction attack against the somewhat homomorphic encryption based on ideal lattices

Masaya Yasuda, Jun Yajima, Takeshi Shimoyama, Jun Kogure

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

3 Citations (Scopus)

Abstract

In 2009, Gentry first proposed a concrete method for constructing a fully homomorphic encryption (FHE) scheme, which supports arbitrary operations on encrypted data. The construction of the FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, which only supports limited operations but can be much faster than the FHE scheme. The Gentry's scheme is based on ideal lattices, and Chen and Nguyen estimated that it needs at least 10,000 lattice dimension to make the FHE scheme secure. In contrast, the security of the SHE scheme can be guaranteed for lower lattice dimensions, depending on the possible operations which are determined by key parameters. The aim of this paper is to classify which key parameters are feasible to be solved. We attack the lattice problem of lower dimensions by practical lattice reduction algorithms, and estimate the key parameters which can be solved in practice.

Original languageEnglish
Title of host publicationPublic Key Infrastructures, Services and Applications - 9th European Workshop, EuroPKI 2012, Revised Selected Papers
Pages1-16
Number of pages16
DOIs
Publication statusPublished - Dec 1 2013
Externally publishedYes
Event9th European Workshop on Public Key Infrastructures, Services and Applications, EuroPKI 2012 - Pisa, Italy
Duration: Sep 13 2012Sep 14 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7868 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th European Workshop on Public Key Infrastructures, Services and Applications, EuroPKI 2012
CountryItaly
CityPisa
Period9/13/129/14/12

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, M., Yajima, J., Shimoyama, T., & Kogure, J. (2013). Analysis of lattice reduction attack against the somewhat homomorphic encryption based on ideal lattices. In Public Key Infrastructures, Services and Applications - 9th European Workshop, EuroPKI 2012, Revised Selected Papers (pp. 1-16). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7868 LNCS). https://doi.org/10.1007/978-3-642-40012-4_1