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 SL_n(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.

翻译：量子计算的出现迫使密码学界设计其安全性超越经典困难性假设的数字签名方案。本文提出尖晶石（Spinel），这是一种后量子数字签名方案，它将SPHINCS+（CCS 2019）的已证实安全性与源自Tillich-Zemor范式（Eurocrypt 2008）的新代数哈希函数族（Adv. Math. Commun. 2025）相结合，其安全性根植于在SL_n(F_p)上导航扩展图的困难性——该问题被认为即使对于量子对手也是困难的。我们首先为该哈希函数的安全性提供了实验证据，以补充原有的理论分析。接着，我们展示了如何将该哈希函数集成到SPHINCS+框架中以构建安全的签名方案。随后，我们对所提出方案的安全性衰减进行了建模与分析，这为我们接下来讨论的参数选择提供了依据。最后，我们提供了该哈希函数及所提出的签名方案尖晶石的实现，并给出了详细的性能实验结果，证明了其实际可行性。我们的方法为基于代数哈希的签名方案设计奠定了基础，从而扩展了后量子密码学的工具箱。