Comment on “An enhanced and secured RSA public cryptosystem algorithm using Chinese remainder theorem (ESRPKC)”

Abstract

In [1], Kumar et al. proposed an enhanced and secured RSA public key cryptosystem (ESRPKC) algorithm using Chinese remainder theorem. In their scheme, the public key is defined as (N,e,μ) where N is the product of four distinct large prime numbers, e is a public exponent, and μ is a parameter called encryption key to encrypt the message. Compared to the traditional RSA cryptosystem, the authors used the extra parameter μ, and claimed that security increased due to this extra parameter. They claimed that it is required to use a brute force attack to break the system even if the number N is factorized by an adversary to obtain the private parameters k1 and k2 which are components of μ. The authors claimed that ESRPKC is a highly secure and not easily breakable scheme compared to the traditional RSA scheme.In this paper, we do a cryptanalysis on Kumar et al.'s scheme given in [1] and demonstrate some major security weaknesses. We prove that if N is factorized, there is no need to use brute force to break the system. Additionally, choosing four prime numbers instead of two prime numbers decreases the security significantly and only increases the computation time. Therefore, the proposed system (ESRPKC) is not as efficient as the traditional RSA algorithm.