代数学与密码学的交汇:通过数学基础增强信息安全

Q4 Mathematics
Shashi Raj, Dr. M. Manicka Raja, Dr Vijay More, Dr Ch Madhava Rao, Dr. M Kavitha, Dr. Gurwinder Singh
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引用次数: 0

摘要

随着数字技术的飞速发展,有必要开发强大的信息安全措施。本文探讨了代数学与密码学的交叉点,重点是代数原理如何增强密码技术,从而提供更强大的安全基础。通过利用群、环和场等数学结构,我们可以解决加密、安全通信和数据隐私方面的关键挑战。本研究回顾了当代密码协议中使用的关键代数方法,包括椭圆曲线密码学、同态加密和基于网格的密码学,并通过详细的案例研究展示了它们的实际应用。与传统方法相比,我们的对比分析凸显了基于代数的加密解决方案的卓越性能和安全性。最后,我们讨论了代数密码学的新兴趋势和未来方向,强调了这些数学基础在应对不断变化的信息安全威胁方面的潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Intersection of Algebra and Cryptography: Enhancing Information Security through Mathematical Foundations
The rapid advancements in digital technologies have necessitated the development of robust information security measures. This paper explores the intersection of algebra and cryptography, focusing on how algebraic principles can enhance cryptographic techniques to provide stronger security foundations. By leveraging mathematical structures such as groups, rings, and fields, we can address critical challenges in encryption, secure communications, and data privacy. This study reviews key algebraic methods used in contemporary cryptographic protocols, including elliptic curve cryptography, homomorphic encryption, and lattice-based cryptography, and demonstrates their practical applications through detailed case studies. Our comparative analysis highlights the superior performance and security of algebra-based cryptographic solutions compared to traditional methods. Finally, we discuss the emerging trends and future directions in algebraic cryptography, emphasizing the potential of these mathematical foundations to address the evolving threats in information security.
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0.30
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