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Research & Reviews: Discrete Mathematical Structures Review Article

Key Generation Algorithms Using Difference Equations with Multi-Precision Arithmetic: A Review

  1. Nalini S Department of Mathematics, Arulmigu Arthanareeswarar Arts and Science College, Tiruchengode

Abstract

Modern cryptographic systems rely on robust key generation to secure data and communication. This review explores the integration of difference equations and multi-precision arithmetic for cryptographic key generation, addressing limitations in traditional methods like pseudorandom number generators and chaotic systems. Difference equations produce deterministic yet chaotic sequences ideal for cryptography due to their sensitivity to initial conditions and nonlinearity. However, finite precision arithmetic can lead to periodicity and loss of randomness, compromising security. Multi-precision arithmetic overcomes these challenges by enabling computations with arbitrary precision, supporting the generation of extended, nonperiodic sequences, and expanding the cryptographic key space. This paper reviews the theoretical foundations of difference equations and their cryptographic relevance, examines multi-precision arithmetic's role in enhancing sequence quality and highlights research progress in combining these approaches. Key advancements include generating longer, high entropy keys suitable for modern cryptographic needs, especially in resource-constrained environments like Internet of Things (IoT) and blockchain applications. The review identifies gaps, such as computational efficiency, scalability, and resistance to emerging threats, including quantum computing. It also proposes directions for future research, including adaptive parameter selection, hybrid systems, and enhanced randomness testing. This synthesis underscores the potential of difference equations and multi-precision arithmetic as a transformative approach to secure key generation, ensuring robust and scalable cryptographic solutions

Keywords

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