Spinel: 一种基于SL_n(F_p)哈希的后量子签名方案
Spinel: A Post-Quantum Signature Scheme Based on $\mathrm{SL}_n(\mathbb{F}_p)$ Hashing
AI总结：
Spinel是一种基于SL_n(F_p)哈希的后量子签名方案，结合了SPHINCS+的安全性与新的代数哈希函数，提供了一种安全且可行的数字签名解决方案。
摘要：
量子计算的出现迫使密码学界设计出安全性和经典难题假设之外的数字签名方案。在本工作中，我们介绍了Spinel，一种结合已证明安全的SPHINCS+（CCS 2019）与新家族的代数哈希函数（Adv. Math. Commun. 2025）的后量子数字签名方案。这些哈希函数基于Tillich-Zemor范式（Eurocrypt 2008），其安全性根植于在SL_n(F_p)上导航扩张图的难度，这一问题被认为即使对量子对手也难以解决。我们首先提供了该哈希函数安全性的实证证据，补充了原始理论分析。然后展示如何将该哈希函数整合到SPHINCS+框架中，以提供安全的签名方案。接着，我们建模并分析了所提方案的安全性退化，这指导了我们接下来讨论的参数选择。最后，我们提供了该哈希函数和所提签名方案Spinel的实现，以及Spinel性能的详细实证结果，展示了其在实践中的可行性。我们的方法为设计基于代数哈希的签名方案奠定了基础，扩展了后量子密码学的工具箱。
英文摘要：
The advent of quantum computation compels the cryptographic community to design digital signature schemes whose security extends beyond the classical hardness assumptions. In this work, we introduce Spinel, a post-quantum digital signature scheme that combines the proven security of SPHINCS+ (CCS 2019) with a new family of algebraic hash functions (Adv. Math. Commun. 2025) derived from the Tillich-Zemor paradigm (Eurocrypt 2008) with security rooted in the hardness of navigating expander graphs over $\mathrm{SL}_n(\mathbb{F}_p)$, a problem believed to be hard even for quantum adversaries. We first provide empirical evidence of the security of this hash function, complementing the original theoretical analysis. We then show how the hash function can be integrated within the SPHINCS+ framework to give a secure signature scheme. We then model and analyze the security degradation of the proposed scheme, which informs the parameter selection we discuss next. Finally, we provide an implementation of the hash function and the proposed signature scheme Spinel as well as detailed empirical results for the performance of Spinel showing its feasibility in practice. Our approach lays the foundations for the design of algebraic hash-based signature schemes, expanding the toolkit of post-quantum cryptography.
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