Implications of the Arithmetic Ratio of Prime Numbers for RSA Security

Abstract

Abstract The most commonly used public key cryptographic algorithms are based on the difficulty in solving mathematical problems such as the integer factorization problem (IFP), the discrete logarithm problem (DLP) and the elliptic curve discrete logarithm problem (ECDLP). In practice, one of the most often used cryptographic algorithms continues to be the RSA. The security of RSA is based on IFP and DLP. To achieve good data security for RSA-protected encryption, it is important to follow strict rules related to key generation domains. It is essential to use sufficiently large lengths of the key, reliable generation of prime numbers and others. In this paper the importance of the arithmetic ratio of the prime numbers which create the modular number of the RSA key is presented as a new point of view. The question whether all requirements for key generation rules applied up to now are enough in order to have good levels of cybersecurity for RSA based cryptographic systems is clarified.