Key Generation Algorithm Using Difference  Equation With  Multi -Precision – Arithmetic : A Review


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Year : 2024 | Volume : 11 | 03 | Page : –
    By

    S. Nalini,

  1. Head & Assistant Professor, Department of Mathematics Arulmigu Arthanareeswarar Arts and Science College, Tamil Nadu, India

Abstract

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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, non-periodic 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 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: Cryptographic key generation, Difference equations, Multi-precision arithmetic, Pseudorandom sequences, Chaotic systems, Nonlinear dynamics, Quantum-resistant cryptography

How to cite this article:
S. Nalini. Key Generation Algorithm Using Difference  Equation With  Multi -Precision – Arithmetic : A Review. Research & Reviews: Discrete Mathematical Structures. 2025; 11(03):-.
How to cite this URL:
S. Nalini. Key Generation Algorithm Using Difference  Equation With  Multi -Precision – Arithmetic : A Review. Research & Reviews: Discrete Mathematical Structures. 2025; 11(03):-. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=0


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Ahead of Print Subscription Review Article
Volume 11
03
Received 24/12/2024
Accepted 31/01/2024
Published 03/01/2025
47