QRELHE-X: Extended Quantum-Resistant Edge Learning with Homomorphic Encryption for Next-Generation Distributed Intelligence Systems

Recent proliferation of edge intelligence systems, including Internet of Things (IoT) sensor networks, self-driving vehicles, wearable medical devices and industrial control platforms—requires privacy-preserving computation subject to availability constraints on resources. At the same time, the recent arrival of large-scale quantum computers can break all classical cryptographic protocols with Shor's algorithm in a short time. State-of-the-art post-quantum homomorphic encryption systems incur computational overhead orders of magnitude larger than the energy and memory budgets of resource-constrained microcontrollers, giving rise to a disparity between security and deployability that remains unaddressed. We introduce QRELHE-X in this paper, a comprehensive framework building on post-quantum edge learning with four novel contributions: (1) a tri-family hybrid cryptography architecture leveraging Algebraic Geometry (AG) codes, Hidden Field Equations minus (HFE-) and eXtended Merkle Signature Scheme (XMSS), which guards against cryptanalytic attacks targeting any single family using defend-in-depth approach; (2) our Deep Reinforcement Learning Parameter Orchestration (DRL-PO) engine that dynamically tunes cryptographic parameters based on real-time device telemetry via PPO-trained policy network yielding 23.4% efficiency optimization compared against static configurations; (3) our Structured Noise Calculus framework providing Lyapunov-stable guarantees of the noise growth within deep level homomorphic neural circuits enabling T*=47 operations between bootstrapping — 3.9x fewer than prior art implementations of state-of-the-art systems; and finally, we present BREFL, the first Byzantine Resilient Encrypted Federated Learning protocol capable of detecting malicious gradient submissions completely within encrypted domain at detection rate 98.7%. Over six hardware platforms, we establish a 5.1x latency improvement over CRYSTALS-KyberHE, while reducing energy by 4.7x, and successfully deploy on,256 KB RAM microcontrollers—the lowest memory footprint ever reported of any post-quantum homomorphic inference solution.