Methods Of Prime Number Generation In Cryptographic Systems And Their Analysis

This article analyzes the methods of prime number generation used in modern cryptographic systems and their mathematical foundations. The processes of generating large prime numbers, random number generators, and the operating principles of primality testing algorithms are examined. The efficiency and practical advantages of the Fermat and Miller–Rabin tests in prime number generation are evaluated. In addition, safe primes and their role in public-key cryptosystems such as RSA and Diffie–Hellman are analyzed. The research results demonstrate the significant importance of prime number generation algorithms in ensuring the security of cryptographic systems.

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