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.

翻译：模糊提取器（FE）与模糊签名（FS）是从生物特征等模糊数据生成密码密钥的有效方案。针对欧氏空间（如人脸特征向量）中的模糊数据，已有多种基于三角格的纠错技术被提出以实现FE和FS。这些技术在密钥恢复或签名阶段需要求解高维（例如128–512维）格中的最近向量问题（CVP）。然而，随着维度$n$的增加，求解CVP的计算复杂度急剧上升。本文首先提出了一种在三角格中求解CVP的$O(n \log n)$时间算法，而传统方法需要$O(n^2)$时间。随后我们进一步改进该算法，构建了一种$O(n)$时间的线性算法。