Paper 2024/1179 Original: eprint.iacr.org/2024/1179 ↗

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

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.