DESIGN AND ANALYSIS OF LIGHTWEIGHT S-BOXES USING SPARSE PERMUTATION POLYNOMIALS OVER F_(2^8 ) FOR IOT NETWORK SECURITY

Abstract

The rapid proliferation of Internet of Things (IoT) networks and ubiquitous computing has fundamentally altered the landscape of digital communication, introducing billions of interconnected, resource-constrained devices. Securing data transmitted across these vulnerable networks requires cryptographic protocols that balance robust mathematical security with ultra-low power and memory footprints. Substitution boxes (S-boxes) serve as the critical, non-linear core in symmetric-key block ciphers, dictating the algorithm's resilience against differential and linear cryptanalysis. Traditional paradigms, such as the Advanced Encryption Standard (AES), employ mathematically rigorous S-boxes predicated on finite field inversion. While highly secure, these structures demand substantial hardware resources (Gate Equivalents), rendering them suboptimal for lightweight micro-sensors, RFID tags, and embedded IoT controllers. This comprehensive research proposes a novel, highly optimized framework for constructing lightweight, cryptographically resilient S-boxes utilizing sparse permutation polynomials (PPs) over the finite field . By leveraging specific trinomial and quadrinomial permutations derived from low-degree rational functions, the proposed methodology significantly curtails the hardware footprint. Concurrently, it maintains stringent cryptographic bounds, achieving high non-linearity, low differential uniformity, and robust algebraic immunity. Extensive theoretical analysis and hardware synthesis demonstrate that the proposed PP-based S-boxes achieve an optimal equilibrium between cryptographic strength and execution efficiency. This paper details the mathematical construction, cryptanalytic evaluation, and hardware simulation of the proposed primitives, establishing their viability for secure, real-time data transmission in constrained IoT network protocols.