Multi-Factor Analysis of RSA Based on Variations in Primes Used for Modulus Generation

The RSA cryptosystem encompasses some of the most common and popular encryption-decryption algorithms. In conjunction with other encryption schemes, RSA encryption is often used as a method to prove the authenticity and integrity of messages. Due to its less efficient and resource-intensive nature, it is generally, not used to encrypt entire multi-line messages or files. In order to crack an RSA encrypted asset, it is important for attackers to be able to factorize humongous primes; which, with the advent of quantum computing is slowly turning into a possibility thereby causing the factoring problem to lose its relevance. The purpose of this paper is to examine the cryptosystem for potential correlations that might exist between factors such as “the number of primes used” and the algorithm's “level of security”. Classical RSA involves the use of a pair of prime numbers for the process of key generation. In this paper, we aim to propose a generalized algorithm for generating RSA keys using
$N$
distinct prime numbers. Previously, papers have been published on the RSA algorithm subject to changing “the number of primes” used to generate the RSA modulus. However, the aim of this paper is to generalize this approach while simultaneously illustrating the changes in the classical algorithm's properties over a spectrum of different values of the factors involved.