arXiv 2602.026892026-02cs.CRcs.AIcs.LG

Eidolon: 图神经网络时代基于k-可着色性的后量子签名方案

Eidolon: A Post-Quantum Signature Scheme Based on k-Colorability in the Age of Graph Neural Networks

Laboratory of Mathematical Analysis, Algebra and Applications (LAM2A), Faculty of Sciences Ain Chock (FSAC), University Hassan II, Casablanca, Morocco（哈桑二世大学阿因-奇克学院数学分析与代数实验室）；Department of Geometry and Topology, Faculty of Mathematics, University of Seville, Seville, Spain（塞维利亚大学数学系几何与拓扑系）；Departments of Computer Science and Mathematics, Queens College, City University of New York, USA（纽约市立大学皇后学院计算机科学与数学系；数学博士项目，理论科学倡议，研究生中心，纽约市立大学；计算机科学与工程系，纽约大学塔朗分校；计算机科学系，英国约克大学）；PhD Program in Mathematics, and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, USA（英国约克大学计算机科学系）；Department of Computer Science and Engineering, Tandon School of Engineering, New York University, USA；Department of Computer Science, University of York, United Kingdom；Department of Computer Science, University of York, United Kingdom

Asmaa Cherkaoui, Ramon Flores, Delaram Kahrobaei, Richard Wilson

备注：: 20 pages, 4 figures
发表信息：: Proceedings of WAIFI 2026, Lecture Notes in Computer Science (LNCS), Vol. 16611, Springer, 2026
DOI：: 10.1007/978-3-032-27574-5_3

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AI总结：

提出一种基于NP完全问题k-可着色性的后量子签名方案Eidolon，通过推广Goldreich-Micali-Wigderson零知识协议、应用Fiat-Shamir变换和Merkle树压缩，并利用植入着色法生成困难实例，实验表明对经典求解器和图神经网络攻击具有抵抗性。

摘要：

我们提出Eidolon，一种基于NP完全问题k-可着色性的后量子签名方案。我们的构造将Goldreich-Micali-Wigderson零知识协议推广到任意k >= 3，应用Fiat-Shamir变换，并使用Merkle树承诺将签名从O(tn)压缩到O(t log n)。我们通过植入着色法生成困难实例，同时旨在保留随机图的统计特征。我们对此类方案进行了针对经典求解器（ILP、DSatur）和定制图神经网络（GNN）攻击者的实证安全分析。实验表明，对于n >= 60，两种方法均无法恢复与植入解匹配的有效着色，表明精心设计的k-着色实例能够抵抗所考虑的传统和基于学习的密码分析方法。这些实验表明，构造的实例能够抵抗我们评估中考虑的攻击。

英文摘要：

We propose Eidolon, a post-quantum signature scheme grounded on the NP-complete k-colorability problem. Our construction generalizes the Goldreich-Micali-Wigderson zero-knowledge protocol to arbitrary k >= 3, applies the Fiat-Shamir transform, and uses Merkle-tree commitments to compress signatures from O(tn) to O(t log n). We generate hard instances by planting a coloring while aiming to preserve the statistical profile of random graphs. We present an empirical security analysis of such a scheme against both classical solvers (ILP, DSatur) and a custom graph neural network (GNN) attacker. Experiments show that for n >= 60, neither approach is able to recover a valid coloring matching the planted solution, suggesting that well-engineered k-coloring instances can resist the considered classical and learning-based cryptanalytic approaches. These experiments indicate that the constructed instances resist the attacks considered in our evaluation.

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