Abstract
This paper presents a comprehensive mathematical framework for modeling and quantitatively assessing hardware-based cryptographic systems in resource-constrained Internet of Things (IoT) devices. We propose novel lightweight cryptographic algorithms optimized for minimal power consumption, memory footprint, and computational overhead while maintaining robust security guarantees. Our mathematical models incorporate energy consumption analysis, security margin calculations, and performance-security tradeoff optimization. We implement and evaluate three cryptographic primitives: a lightweight AES variant (AES-128-L), an optimized Elliptic Curve Cryptography implementation (ECC-163), and a hardware-accelerated hash function (BLAKE2s-H¬W¬). Experimental results on ARM Cortex-M4 and RISC-V platforms demonstrate 47% reduction in energy consumption, 62% decrease in memory usage, and 35% improvement in throughput compared to standard implementations, while maintaining 128-bit security level. Quantitative security assessment using formal verification and side-channel analysis validates the resilience of the proposed schemes against various attack vectors.