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

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 , applies the Fiat-Shamir transform, and uses Merkle-tree commitments to compress signatures from O(tn) to . 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 , 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.