Counting Functions to Generate The Primes in the RSA Algorithm and Diffie-Hellman Key Exchange

Abstract

The Rivest–Shamir–Adleman (RSA) and the Diffie-Hellman (DH) key exchange are famous methods for encryption. These methods depended on selecting the primes p and q in order to be secure enough . This paper shows that the named methods used the primes which are found by some arithmetical function .In the other sense, no need to think about getting primes p and q and how they are secure enough, since the arithmetical function enable to build the primes in such complicated way to be secure. Moreover, this article gives new construction of the RSA algorithm and DH key exchange using the primes p,qfrom areal number x.

Keywords

• (RSA algorithm and Diffie-Hellman exchange, Beurling Primes, Analytic number theory).