International Journal of Scientific Research and Engineering Development

The foundation of modern cryptography is number theory. It provides the mathematics required for safe message delivery and data protection. Common building blocks cryptography techniques, including RSA and Diffie If you ask Hellman include modular arithmetic and prime numbers. Progress in modern cryptographic algorithm development that guarantee safe communication and data privacy in many real-world applications depends heavily on the foundations of number theory. RSA and elliptic curve are two examples of number-theory-based cryptographic algorithms that are now in use and are used to secure digital signatures, restricted access systems, and monetary dealings conducted over the Internet. It is the fundamental goal of this study to investigate uses for number theory in Modern Cryptographic Systems. An explanation of the number theoretic techniques and the importance of these approaches in cryptography is provided in this paper.

Tripti Gautam, Dr. Narendra Bahadur Singh, "Role of Elementary Number Theory in Modern Cryptographic Systems" International Journal of Scientific Research and Engineering Development, V9(5): Page(215-221) September - October 2026. ISSN: 2581-7175. www.ijsred.com. Published by Scientific and Academic Research Publishing.