A Review of Probabilistic Analysis of Elliptic Curve Cryptography in IoT: Intelligent Modeling, Electronics Integration, and Real-World Applications

Abstract

Elliptic Curve Cryptography (ECC) has become a fundamental security mechanism for Internet of Things (IoT) environments due to its ability to deliver strong cryptographic protection with relatively low computational overhead. As IoT systems expand across domains such as smart cities, healthcare, industrial automation, and autonomous systems, ensuring secure, efficient, and scalable communication is increasingly important. A major challenge in ECC-based IoT systems is managing uncertainty, noise, and variability in real-world conditions, which has led to the adoption of probabilistic analysis techniques. These approaches enable the modeling of uncertainties in cryptographic processes, hardware reliability, communication channels, and potential attack scenarios, providing insights into system performance, fault tolerance, and security robustness. This review examines probabilistic methods applied to ECC in IoT, including probabilistic security modeling, stochastic performance evaluation, machine learning-based analysis, hardware-aware designs, and real-world applications. It highlights how probabilistic techniques enhance ECC by enabling adaptive security, improving resilience, and optimizing performance under dynamic conditions. However, challenges such as computational complexity, scalability, and accuracy trade-offs persist, emphasizing the need for more efficient and intelligent cryptographic frameworks.