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

INFORMATION PROCESSING LETTERS, vol.177, 2022 (SCI-Expanded)

• Publication Type: Article / Editorial Material
• Volume: 177
• Publication Date: 2022
• Doi Number: 10.1016/j.ipl.2022.106263
• Journal Name:
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
• Keywords: ESRPKC algorithm, Cryptanalysis, RSA algorithm, Public key, Private key, Encryption
• Erciyes University Affiliated: Yes

#### 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, mu) where N is the product of four distinct large prime numbers, e is a public exponent, and mu is a parameter called encryption key to encrypt the message. Compared to the traditional RSA cryptosystem, the authors used the extra parameter mu, 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 k(1) and k(2) which are components of mu. 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.& nbsp;(c) 2022 Elsevier B.V. All rights reserved.