Advanced Analysis of Primality Testing Algorithms for Secure Cryptographic Applications

Abstract

This thesis presents an analysis of the theoretical background, working mechanisms, and practical performance of primality testing algorithms. It discusses the significance of prime numbers in contemporary cryptographic systems and the importance of verifying large integers. The study examines the mathematical principles, strengths, and weaknesses of the Fermat, Solovay–Strassen, Miller–Rabin, and AKS primality tests. Furthermore, the computational complexity of deterministic and probabilistic approaches and their influence on cryptographic security are assessed. The findings indicate that primality testing algorithms constitute an essential component of public-key cryptographic schemes, particularly RSA.