Analysis Of Primality Testing Algorithms And Their Applications In Cryptography
Mamaraimov BekzodAcademic Lyceum of Termez State University, UzbekistanBoykuziev IlkhomTashkent University of Information Technologies named after Muhammad ibn Musa al-Khwarizmi, Uzbekistan
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This article analyzes the theoretical foundations, operating principles, and practical efficiency of primality testing algorithms. The role of prime numbers in modern cryptographic systems and the necessity of testing large integers are discussed. The mathematical foundations, advantages, and limitations of the Fermat, Solovay–Strassen, Miller–Rabin, and AKS primality tests are examined. In addition, the computational complexity of probabilistic and deterministic algorithms and their impact on the security of cryptographic systems are evaluated. The research results demonstrate that primality testing algorithms play a crucial role in public-key cryptosystems such as RSA.
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