We develop a unified mathematical formulation for post-quantum authenticated telemetry and actuation in FADEC-coupled dual-spool turbofan cyber-physical systems. The formulation integrates lattice-based key establishment under LWE/SIS-style assumptions, PUF-derived attestation entropy, authenticated encryption, radar-altimeter integrity, avionics-bus timing, and Kalman residual monitoring in a stochastic hybrid model. Within this model, plant evolution, communication latency, leakage, adversarial channel quality, and cryptographic state evolve under a common filtration. We show that channel uncertainty tightens admissible key-renewal periods, that ciphertext expansion enters bus-level schedulability constraints, and that sensing and actuator limits shape integrity thresholds and allowable control delay. We further relate PUF smooth min-entropy to distinguishing advantage and connect innovation statistics to conservative alarm design. Overall, the results characterize how post-quantum security, real-time schedulability, and closed-loop stability interact in safety-critical aerospace control architectures within a defensive analytical treatment that does not provide operational guidance for interference with real platforms.

翻译：我们为FADEC耦合双轴涡扇信息物理系统中的后量子认证遥测与驱动建立了统一的数学框架。该框架在随机混合模型中整合了基于LWE/SIS型假设的格基密钥建立、PUF衍生的认证熵、认证加密、雷达高度计完整性、航空电子总线时序以及卡尔曼残差监测。在此模型下，被控对象演化、通信延迟、信息泄露、对抗信道质量及密码状态均在同一过滤下演进。研究表明：信道不确定性会收紧可接受的密钥更新周期；密文扩展将进入总线级可调度性约束；感知与驱动限制塑造了完整性阈值与允许的控制延迟。我们进一步将PUF平滑最小熵与区分优势关联，并将新息统计量连接至保守报警设计。总体而言，这些结果表征了后量子安全、实时可调度性与闭环稳定性在安全关键航空控制架构中的相互作用——该防御性分析处理不提供针对真实平台干扰的操作指导。