COEX-FL: Non-Colluding Backdoor Coexistence in Federated Learning via Semantic–Mode Coding

Many federated backdoor attacks assume that malicious clients can collude by sharing target labels, trigger parameters, training schedules, or model updates. Such coordination introduces communication and synchronization requirements and does not capture settings in which clients are compromised independently. Without coordination, multiple backdoors may induce conflicting update directions, causing some target behaviors to be attenuated or forgotten during aggregation. We propose COEX-FL, a coordination-free framework for multi-target backdoor coexistence in federated learning. COEX-FL factorizes each frequency-domain trigger into a target-semantic component and a mode-specific realization component. Orthogonal semantic components distinguish target behaviors within a shared carrier space, while multiple mode realizations provide alternative physical paths for the same target. Each malicious client constructs its trigger bank from public coding parameters and its own target label, and optimizes over the modes locally without exchanging private attack information with other clients. We characterize the resulting code and DCT-space geometry and derive a conditional linearized analysis of cross-attacker update interference. Across the evaluated datasets and federated learning protocols, COEX-FL improves the balance and retention of multiple backdoors, achieving high minimum attack success rates and low cross-attacker interference.