Inner Product Ring LWE Problem, Reduction, New Trapdoor Algorithm for Inner Product Ring LWE Problem and Ring SIS Problem

Zhuang Shan; Leyou Zhang; Qing Wu; Qiqi Lai

Paper 2024/1179

Inner Product Ring LWE Problem, Reduction, New Trapdoor Algorithm for Inner Product Ring LWE Problem and Ring SIS Problem

Zhuang Shan

, School of Mathematics and Statistics, Xidian University, Xi’an 710126, China

Leyou Zhang

, School of Mathematics and Statistics, Xidian University, Xi’an 710126, China

Qing Wu

, School of Automation, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Qiqi Lai, School of Computer Science, Shaanxi Normal University, Xi’an, China

Abstract

Lattice cryptography is currently a major research focus in public-key encryption, renowned for its ability to resist quantum attacks. The introduction of ideal lattices (ring lattices) has elevated the theoretical framework of lattice cryptography. Ideal lattice cryptography, compared to classical lattice cryptography, achieves more acceptable operational efficiency through fast Fourier transforms. However, to date, issues of impracticality or insecurity persist in ideal lattice problems. In order to provide a reasonable and secure trapdoor algorithm, this paper introduces the concept of "Inner Product Ring LWE" and establishes its quantum resistance and indistinguishability using knowledge of time complexity, fixed-point theory, and statistical distances. Inner product Ring LWE is easier to construct trapdoor algorithms compared to Ring LWE. Additionally, leveraging the properties of NTRU, we propose a more secure Ring SIS trapdoor algorithm.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Ring LWE Ring SIS Trapdoor algorithm
Contact author(s): arcsec30 @ 163 com
lyzhang @ mail xidian edu cn
xiyouwuq @ 126 com
laiqq @ snnu edu cn
History: 2024-07-25: approved; 2024-07-22: received; See all versions
Short URL: https://ia.cr/2024/1179
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1179,
      author = {Zhuang Shan and Leyou Zhang and Qing Wu and Qiqi Lai},
      title = {Inner Product Ring {LWE} Problem, Reduction, New Trapdoor Algorithm for Inner Product Ring {LWE} Problem and Ring {SIS} Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2024/1179},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/1179}},
      url = {https://eprint.iacr.org/2024/1179}
}