About cryptography systems and applications

The aim of this thesis is to define new metrics for the parameter selection of RSA the most used public key cryptosystem in daily life. The security of RSA depends on the factorization of multiplication of specially selected two large primes. Moreover, this composite number shouldn't be factorized in a reasonable time. Fermat factorization idea is known as one of the most efficient method to factorize a nonsecure composite number in terms of RSA. Other successfull factorization methods such as number field sieve cannot result in a reasonable time due to the exponential complexity. The number of prime pairs or sets for RSA is very large and all of them cannot be computed for relatively large sizes. There have been so many studies on the selection of primes for RSA resistant to well-known attacks. In this thesis, while the selection process of primes p and q, the distance between these primes is defined and some bounds are provided with experimental results This distance criterion helps us to generate secure RSA prime pairs in terms of Fermat factorization method.