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The Role of Number Theory in Cryptography and Cybersecurity

Author(s) Dr. Suman Jain
Country India
Abstract This review paper explores the critical role of number theory in shaping the foundations and advancements of modern cryptography and cybersecurity. As digital communication and data security become increasingly vital, the mathematical intricacies of number theory—such as prime number generation, modular arithmetic, and elliptic curves—form the backbone of secure encryption protocols like RSA, Diffie-Hellman, and Elliptic Curve Cryptography (ECC). The study employs a structured review methodology, drawing upon a wide range of scholarly publications and verified data up to 2014, including both global and Indian contexts. Key mathematical equations, comparative algorithmic performance, and numerical analyses have been integrated to assess the computational hardness and practical effectiveness of number theory-based cryptosystems. Results indicate that while traditional cryptographic schemes remain effective under classical computation, they face significant vulnerabilities in the face of emerging quantum technologies. The Indian mathematical tradition and its contribution to algorithmic logic further enrich the narrative, underscoring the need for indigenous innovation. This paper identifies major research gaps, particularly in the areas of post-quantum cryptography, algorithmic efficiency for low-resource environments, and provable security models. Future directions suggest hybrid mathematical frameworks and deeper exploration of algebraic structures to build resilient and scalable cryptographic systems. Overall, the paper establishes that number theory is not only a theoretical pursuit but a practical necessity in safeguarding digital infrastructure in an increasingly interconnected world.
Published In Volume 6, Issue 1, January-March 2015
Published On 2015-01-08
Cite This The Role of Number Theory in Cryptography and Cybersecurity - Dr. Suman Jain - IJSAT Volume 6, Issue 1, January-March 2015. DOI 10.71097/IJSAT.v6.i1.3616
DOI https://doi.org/10.71097/IJSAT.v6.i1.3616
Short DOI https://doi.org/g9d686
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