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.

翻译：我们提出Eidolon，一种基于NP完全k-可着色性问题的后量子签名方案。该构造将Goldreich-Micali-Wigderson零知识协议推广至任意k ≥ 3，应用Fiat-Shamir变换，并通过Merkle树承诺将签名从O(tn)压缩至O(t log n)。我们通过植入染色方案生成困难实例，同时力求保留随机图的统计特征。针对经典求解器（ILP、DSatur）和自定义图神经网络（GNN）攻击者，我们对该方案进行了实证安全性分析。实验表明，当n ≥ 60时，两种方法均无法恢复与植入解匹配的有效染色方案，这表明精心设计的k-染色实例能够抵御本文所考虑的经典及基于学习的密码分析手段。这些实验证明所构造的实例能够抵抗我们评估中考虑的各类攻击。