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Fuzzy Extractors (FEs) and Fuzzy Signatures (FSs) are promising primitives for template-protected biometric authentication, and lattice-based constructions of them are known. In this paper, to reveal lattices more suitable for FEs/FSs in terms of application to biometric authentication, we evaluate the accuracy of FEs/FSs for various lattices, along with the computation time of finding the closest lattice vector \(\textrm{CV}_L(\cdot )\) required in the authentication process when FEs/FSs are applied to biometric authentication. Specifically, we treat the integer lattice \(\mathbb {Z}^n\) , a triangular lattice \(L_n^{(\textrm{tri})}\) , and the direct product \(E_8^{n/8}\) of the Gosset lattice, which have been treated in conventional studies on FEs/FSs, and additionally the dual lattice \(L_n^{(\mathrm {d-tri})}\) of a triangular lattice and the checkerboard lattice \(D_n\) . To evaluate the accuracy of FEs/FSs with these lattices, we give algorithms for computing the lattice norm for \(L_n^{(\mathrm {d-tri})}\) , \(D_n\) , and \(E_8^{n/8}\) , where the lattice norm can be utilized for efficient accuracy evaluation and algorithms for \(\mathbb {Z}^n\) and \(L_n^{(\textrm{tri})}\) are known. Then, we evaluate the accuracy of FEs/FSs based on these lattices utilizing the lattice norm. Although \(L_n^{(\textrm{tri})}\) is often used for FEs and FSs conventionally, the evaluation results show that \(E_8^{n/8}\) achieves the highest accuracy of the evaluated lattices, and \(D_n\) achieves accuracy close to \(L_n^{(\textrm{tri})}\) with shorter computation time of \(\textrm{CV}_L(\cdot )\) . Also, to obtain the lattice norm for \(L_n^{(\mathrm {d-tri})}\) , we give a similarity transformation from a non-full-rank lattice to a full-rank one, which transforms the zero-sum root lattice \(A_n\) and its dual \(A_n^*\) to \(L_n^{(\textrm{tri})}\) and \(L_n^{(\mathrm {d-tri})}\) , respectively. Using this transformation, we discuss a relation between \(L_n^{(\textrm{tri})}\) , often used for FEs/FSs, and \(A_n\) , a well-studied lattice in lattice theory.

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Comparative Evaluation of Lattices for Fuzzy Extractors and Fuzzy Signatures

  • 会议论文

  • 发表日期：

    2026年

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  • Wataru Nakamura,
  • Yusei Suzuki,
  • Masakazu Fujio,
  • Kenta Takahashi

摘要

Fuzzy Extractors (FEs) and Fuzzy Signatures (FSs) are promising primitives for template-protected biometric authentication, and lattice-based constructions of them are known. In this paper, to reveal lattices more suitable for FEs/FSs in terms of application to biometric authentication, we evaluate the accuracy of FEs/FSs for various lattices, along with the computation time of finding the closest lattice vector \(\textrm{CV}_L(\cdot )\) required in the authentication process when FEs/FSs are applied to biometric authentication. Specifically, we treat the integer lattice \(\mathbb {Z}^n\) , a triangular lattice \(L_n^{(\textrm{tri})}\) , and the direct product \(E_8^{n/8}\) of the Gosset lattice, which have been treated in conventional studies on FEs/FSs, and additionally the dual lattice \(L_n^{(\mathrm {d-tri})}\) of a triangular lattice and the checkerboard lattice \(D_n\) . To evaluate the accuracy of FEs/FSs with these lattices, we give algorithms for computing the lattice norm for \(L_n^{(\mathrm {d-tri})}\) , \(D_n\) , and \(E_8^{n/8}\) , where the lattice norm can be utilized for efficient accuracy evaluation and algorithms for \(\mathbb {Z}^n\) and \(L_n^{(\textrm{tri})}\) are known. Then, we evaluate the accuracy of FEs/FSs based on these lattices utilizing the lattice norm. Although \(L_n^{(\textrm{tri})}\) is often used for FEs and FSs conventionally, the evaluation results show that \(E_8^{n/8}\) achieves the highest accuracy of the evaluated lattices, and \(D_n\) achieves accuracy close to \(L_n^{(\textrm{tri})}\) with shorter computation time of \(\textrm{CV}_L(\cdot )\) . Also, to obtain the lattice norm for \(L_n^{(\mathrm {d-tri})}\) , we give a similarity transformation from a non-full-rank lattice to a full-rank one, which transforms the zero-sum root lattice \(A_n\) and its dual \(A_n^*\) to \(L_n^{(\textrm{tri})}\) and \(L_n^{(\mathrm {d-tri})}\) , respectively. Using this transformation, we discuss a relation between \(L_n^{(\textrm{tri})}\) , often used for FEs/FSs, and \(A_n\) , a well-studied lattice in lattice theory.