A Linear-Time Algorithm for the Closest Vector Problem of Triangular Lattices

TL;DR

This paper introduces a novel linear-time algorithm for solving the closest vector problem in triangular lattices, significantly improving efficiency for high-dimensional cryptographic applications.

Contribution

The paper presents the first linear-time algorithm for CVP in triangular lattices, reducing computational complexity from quadratic to linear time.

Findings

The new algorithm operates in O(n) time for CVP in triangular lattices.

It outperforms previous methods with O(n^2) complexity.

Applicable to cryptographic schemes using high-dimensional lattices.

Abstract

Fuzzy Extractor (FE) and Fuzzy Signature (FS) are useful schemes for generating cryptographic keys from fuzzy data such as biometric features. Several techniques have been proposed to implement FE and FS for fuzzy data in an Euclidean space, such as facial feature vectors, that use triangular lattice-based error correction. In these techniques, solving the closest vector problem (CVP) in a high dimensional (e.g., 128--512 dim.) lattice is required at the time of key reproduction or signing. However, solving CVP becomes computationally hard as the dimension $n$ increases. In this paper, we first propose a CVP algorithm in triangular lattices with $O(n \log n)$-time whereas the conventional one requires $O(n^2)$-time. Then we further improve it and construct an $O(n)$-time algorithm.