We propose Eidolon, a post-quantum signature scheme grounded in the NP-complete k-colorability problem. Our construction generalizes the Goldreich–Micali–Wigderson zero-knowledge protocol to arbitrary \(k \ge 3\) , applies the Fiat-Shamir transform, and uses Merkle-tree commitments to compress signatures from O(tn) to \(O(t \log n)\) . We generate 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 \(n \ge 60\) , 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.