{"paper":{"title":"Eidolon: A Post-Quantum Signature Scheme Based on k-Colorability in the Age of Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Eidolon turns the NP-complete k-colorability problem into a post-quantum signature scheme whose planted instances resist tested classical solvers and graph neural networks for graphs of size 60 and larger.","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.CR","authors_text":"Asmaa Cherkaoui, Delaram Kahrobaei, Ramon Flores, Richard Wilson","submitted_at":"2026-02-02T19:05:50Z","abstract_excerpt":"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. Exp"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the planted-coloring instances preserve the statistical profile of random graphs sufficiently to inherit their hardness, and that the tested attackers (ILP, DSatur, and one custom GNN) adequately represent the best possible classical and learning-based attacks.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Eidolon is a post-quantum signature scheme based on planted k-colorable graphs whose empirical tests show resistance to classical solvers and a custom GNN attacker for n >= 60.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Eidolon turns the NP-complete k-colorability problem into a post-quantum signature scheme whose planted instances resist tested classical solvers and graph neural networks for graphs of size 60 and larger.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fffdd48728bddbb2f74c2c11c4722dea576f5aa10ea3a8cd478efc999a3eb1a8"},"source":{"id":"2602.02689","kind":"arxiv","version":2},"verdict":{"id":"b4a17ac9-2d1e-4bb9-86a3-b9951a315eb4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T07:59:28.739080Z","strongest_claim":"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.","one_line_summary":"Eidolon is a post-quantum signature scheme based on planted k-colorable graphs whose empirical tests show resistance to classical solvers and a custom GNN attacker for n >= 60.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the planted-coloring instances preserve the statistical profile of random graphs sufficiently to inherit their hardness, and that the tested attackers (ILP, DSatur, and one custom GNN) adequately represent the best possible classical and learning-based attacks.","pith_extraction_headline":"Eidolon turns the NP-complete k-colorability problem into a post-quantum signature scheme whose planted instances resist tested classical solvers and graph neural networks for graphs of size 60 and larger."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.02689/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}