We propose Eidolon, a practical post-quantum signature scheme based 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). Crucially, we generate hard instances via planted "quiet" colorings that preserve the statistical profile of random graphs. We present the first 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 recovers the secret coloring, demonstrating that well-engineered k-coloring instances can resist modern cryptanalysis, including machine learning. This revives combinatorial hardness as a credible foundation for post-quantum signatures.

翻译：本文提出幻影（Eidolon），一种基于NP完全问题k-可着色性的实用后量子签名方案。本构造将Goldreich-Micali-Wigderson零知识协议推广至任意k ≥ 3，应用Fiat-Shamir变换，并采用Merkle树承诺将签名长度从O(tn)压缩至O(t log n)。关键创新在于通过植入"静默"着色方案生成困难实例，该方案能保持随机图的统计特性。我们首次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。实验表明当n ≥ 60时，两种方法均无法恢复秘密着色方案，证明精心设计的k-着色实例能够抵御包括机器学习在内的现代密码分析。这标志着组合数学难题作为后量子签名可信基础的理论复兴。