Randomized Cunningham Numbers in Cryptography

Randomized Cunningham Numbers in Cryptography

Randomization theory, Cryptanalysis, RSA cryptosystem, Primality testing, Cunningham numbers, Optimization theory

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In this research, we study primality testing of arbitrary integers via number theory, randomized algorithms and optimization theories. Concerning fundamentals of modern cryptography, we focus on the cryptanalysis, cryptosystems and RSA keys, which are widely used in secure communications, e.g., banking systems and other platforms with an online security. For a given n-bit integer N, our consideration is realized as a decision problem, viz. an optimized algorithm rendering the output YES, if N is a prime, and NO otherwise. In order to design such an algorithm, we begin by examining essential in...