Complexity-Aware Credit Gap Analysis for Secure IoT Routing

challenges of efficient routing and resilience against adversarial attacks. While constructive algorithms attempt to build optimal paths, verificational checks such as anomaly detection and cryptographic validation ensure correctness under uncertainty. This paper introduces a complexity-aware framework for quantifying the structural gap between constructive routing effort and verificational validation in IoT networks. We define a credit gap metric that measures the cumulative advantage of verificational processes over constructive ones under varying resource constraints, advice information, and attack models. Through simulation of dynamic IoT routing scenarios, we show that the credit gap provides a diagnostic signal: bounded growth corresponds to regimes where constructive routing suffices, while unbounded growth identifies conditions of attack amplification or routing instability. Our results demonstrate that the credit gap can serve as a practical indicator for adaptive routing policies, enabling networks to switch between constructive heuristics and verification-heavy defense modes. This provides a measurable and interpretable tool for analyzing the complexity trade-offs underlying IoT security, with applications to intrusion detection, resilient routing, and lightweight protocol design. Index Terms—IoT, secure routing, complexity analysis, verification gap, adaptive defense