Interrelation Among RSA Security, Strong Primes, and Factoring

The security of RSA depends critically on the inability of an adversary to compute private key from the public key. The problem of computing private key from public key is equivalent to the problem of factoring n into its prime factors. Therefore it is important for the RSA user to select prime numbers in such a way that the problem of factoring n is computationally infeasible for an adversary. Choosing the factors as “strong primes” has been recommended as a way of maximizing the difficulty of factoring n. There are such arguments that say that strong primes are needed to protect against factoring attacks. The purpose of this paper is to extend this scrutiny by carefully examining the common recommendation that one should use strong primes when constructing keys for an RSA. We review the RSA security and describe that this problem can be solved using more key size, more factors or choosing strong primes numbers.