Advances in Networks 2018; 6(1): 40-47 http://www.sciencepublishinggroup.com/j/net doi: 10.11648/j.net.20180601.14 ISSN: 2326-9766 (Print); ISSN: 2326-9782 (Online) Rivest Shamir Adleman Encryption Scheme Based on the Chinese Remainder Theorem Salifu Abdul-Mumin 1, * , Kazeem Alabge Gbolagade 2 1 Department of Computer Science, University for Development Studies, Navrongo, Ghana 2 Computer Science Department, Kwara State University, Malete, Nigeria Email address: * Corresponding author To cite this article: Salifu Abdul-Mumin, Kazeem Alabge Gbolagade. Rivest Shamir Adleman Encryption Scheme Based on the Chinese Remainder Theorem. Advances in Networks. Vol. 6, No. 1, 2018, pp. 40-47. doi: 10.11648/j.net.20180601.14 Received: February 19, 2018; Accepted: March 13, 2018; Published: April 4, 2018 Abstract: Sensitive information is transmitted across the internet every day and keeping such information as sacred is an important adventure. This is because malicious activities are on the increase as hackers are doing everything possible to steal such information. In this paper, we have implemented a new Rivest Shamir Adleman (RSA) encryption scheme based on the Chinese Remainder Theorem (CRT). The scheme consists of two level of encryption and two level of decryption. The first level of encryption is the classical RSA encryption and in the second level of encryption, we used forward conversion technique in Residue Number System. In the first level of decryption, we employed the CRT and the classical RSA decryption process is used for the second level of decryption. This new scheme will ensure that smaller messages, m for which c=m e <n can be encrypted which would otherwise not be able to be encrypted with the classical RSA encryption scheme. The proposed scheme is evaluated with the state of the art and the classical RSA cryptosystem. The proposed scheme performs better than the classical RSA cryptosystem for smaller messages in terms of security and performs better than the state of the art in terms of delay and cost. The private key length in the new scheme is also enhanced by 1-bit as against the state of the art. Keywords: Security, Encryption, Decryption, Rivest Shamir Adleman, Residue Number System, Chinese Remainder Theorem 1. Introduction Confidentiality and security requirements are becoming more rigorous as malicious activities are on the increase every day. The use of internet applications to ease and to maximize returns are gradually gaining more attention in the areas of e-business, military surveillance, medicine and education. During the last decade, fast hardware implementations of public key cryptosystems have been widely studied [1-4]. Different approaches have been proposed to accelerate the implementation of RSA. For the deciphering, a well-known solution performs the computations over ℤ ℤ p = and ℤ ℤ q = independently and reconstructs the final result via the Chinese Remainder Theorem (CRT) [1, 5]. More recently, other CRT-based solutions have been proposed [6-9]. They all use a quite similar version of the Montgomery multiplication based on the Residue Number System (RNS) which is well-adapted to fast parallel arithmetic [10]. Most public-key cryptosystems currently in use, including RSA, depend on the intractability of factoring and computing discrete logarithms. However, in 1994, Shor proposed efficient quantum algorithms to solve these problems [11]. This implies when the quantum computer is finally built, current public key cryptosystems will be broken. Hence the need for research on efficient post-quantum public-key cryptosystems is most valuable. In some instances in the classical RSA cryptosystem, it is easy to compute modular roots without knowledge of the prime factors. For example, if m is known to be very small, such that c = m e < n, then m can be recovered from c by taking e th roots over the integers, which is easy. In this paper, we proposed and implement a CRT based RSA encryption system which will have a two level