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

TL;DR

Eidolon is a post-quantum digital signature scheme based on the NP-complete k-colorability problem, utilizing graph-based cryptography and neural network security analysis.

Contribution

It introduces a new signature scheme leveraging k-colorability, extending zero-knowledge protocols, and demonstrates empirical resistance to classical and neural network attacks.

Findings

Schemes resist classical solvers like ILP and DSatur for n >= 60.

Graph neural network attacker fails to recover valid colorings.

Signature compression reduces size from O(tn) to O(t log n).

Abstract

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.