View : 30 Download: 0

An efficient lattice reduction using reuse technique blockwisely on NTRU

Title
An efficient lattice reduction using reuse technique blockwisely on NTRU
Authors
Chung, KyungmiLee, Hyang-SookLim, Seongan
Ewha Authors
이향숙임선간
SCOPUS Author ID
이향숙scopus; 임선간scopusscopus
Issue Date
2016
Journal Title
DISCRETE APPLIED MATHEMATICS
ISSN
0166-218XJCR Link1872-6771JCR Link
Citation
vol. 214, pp. 88 - 98
Keywords
NTRU latticeLLL algorithmiLLL algorithmReuse technique
Publisher
ELSEVIER SCIENCE BV
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we propose a lattice reduction algorithm for use with NTRU lattices. Given an NTRU lattice as its input, the algorithm computes an LLL-reduced basis. The proposed lattice reduction algorithm is more efficient than the classical LLL algorithm. Recently, a lattice reduction algorithm for ideal lattices, named iLLL, was proposed by Plantard, Susilo, and Zhang. This algorithm is identical to that of the LLL except for the fact that it contains an additional subroutine, named Reuse. The subroutine serves to further reduce a set of short vectors that has already been computed by the algorithm prior to its initiation. As a result, the iLLL is able to output an LLL-reduced basis more efficiently than the LLL is able to do so. However, the iLLL cannot be directly applied to an NTRU lattice, because it is not an ideal lattice. Yet, from the fact that an NTRU lattice is also a module lattice (a generalization of an ideal lattice), we can adapt the main idea behind the iLLL blockwisely in our approach to NTRU lattices. We demonstrate that the proposed algorithm (containing a modified version of the aforementioned subroutine Reuse) is asymptotically 5 times faster at outputting an LLL-reduced basis than the LLL when applied to NTRU lattices of dimension n. In the case of small n, our experiments show that the proposed algorithm is slightly faster at outputting an LLL-reduced basis than the LLL. In addition, we present an example of how to recover a private key of an NTRU encryption scheme by using the proposed algorithm in the case of n = 22. (C) 2016 Elsevier B.V. All rights reserved.
DOI
10.1016/j.dam.2016.05.029
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE