Linear-Complexity Unified Defense Against Deception Attacks in Distributed Economic Dispatch Using Cryptography and Machine Learning

Deception attacks, including false data injection, replay, and Byzantine manipulation, can corrupt broadcast price signals in distributed economic dispatch (DED), breaking fairness and increasing generation costs while remaining stealthy. Existing defenses are often attack-specific and rely on inter-supplier cross-verification, incurring O(n2) communication overhead, and many provide probabilistic detection that can cause false alarms or missed attacks. To deterministically detect multiple deception attacks with O(n) complexity, this paper proposes a unified security layer for DED based on threshold Schnorr signatures, ensuring data integrity, freshness, and global consistency of price broadcasts. Upon detection, the framework triggers a machine-learning-based robust post-attack recovery mechanism that estimates the true marginal price from historical demand-price correlations, enabling suppliers to continue near-optimal updates. Supplier privacy is preserved via lightweight pairwise masking that reveals only aggregate supply without sacrificing accuracy. The proposed scheme tolerates up to ⌊(n-1)/3⌋ malicious suppliers among n. Experiments on the IEEE 14-bus system quantify efficiency loss under representative attacks. Large-scale studies on the IEEE 118-bus system demonstrate that Byzantine manipulation can increase the system cost by up to 47%. In contrast, the proposed scheme limits the resulting efficiency loss to 0.3% by leveraging an offline-trained LightGBM predictor that achieves an R2 score of 0.985 on the test set.