Spinel: A Post-Quantum Signature Scheme Based on $\mathrm{SL}_n(\mathbb{F}_p)$ Hashing

2026-02-10

AI Summary

This work proposes a quantum-resistant digital signature scheme that does not rely on classical computational hardness assumptions. By integrating the SPHINCS+ framework with a novel algebraic hash function based on the navigational problem over expander graphs of SLₙ(𝔽ₚ), the scheme introduces such algebraic hash functions into hash-based signatures for the first time, thereby expanding the toolkit of post-quantum cryptography. The resulting Spinel construction achieves provable security in the standard model and strikes a favorable balance between practical performance and cryptographic strength, demonstrating its feasibility and real-world applicability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

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.

Problem

• post-quantum cryptography
• digital signature
• quantum-resistant
• hash-based signature
• SLn(Fp)

Innovation

• post-quantum cryptography
• algebraic hash functions
• expander graphs
• SL_n(F_p)
• SPHINCS+