Foundations of Number Theory in the Design and Security of the RSA Cryptosystem

Abstract

In today’s digital communication world, protecting data from unauthorized access and cyber threats is crucial, for cryptographic techniques are to protect information security. Cryptography supplies substorage system security and secrecy, including digital signature authentication.In the field of mathematical cryptography, the Rivest, Shamir, and Adleman (RSA) Algorithm endures as one of the most secure and extensively used public-key cryptography algorithms.RSA cryptography is used to secure the encryption key between sender and receivers. The role of number n in RSA is important and depends on primes, Euler’s totient function, modular inverses, and applications of Fermat’s Little Theorem and Euler’s Theorem. This abstract has introduced the foundations of mathematics for cryptography and the RSA public-key cryptosystem for secure communication in mathematical aspects.