Rivest Shamir Adleman Encryption Scheme Based on the Chinese Remainder Theorem

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.

An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System

“…. , µ k,k (see (1)) and can be sufficiently large for most moduli-sets that are suitable for practical use.…”

New Algorithm for Reverse Conversion in Residue Number System

“…= ∏ =1 is the dynamic range. Any integer in the range [0, M) called the legitimate range can be unambiguously represented [5], [6].…”

A Novel Text Encryption and Decryption Scheme using the Genetic Algorithm and Residual Numbers

“…Encryption involves translating the Kalpa Publications in Computing Volume 12, 2019, Pages 20-31 Proceedings of 4th International Conference on the Internet, Cyber Security and Information Systems 2019 original message (usually in plaintext) into a cypher text using an encryption key. The reverse process of getting back the plaintext (message) from the cypher text (also with a decryption key) is termed decryption, (Abdul-mumin & Gbolagade, 2018;Pakshwar, Trivedi, & Richhariya, 2013).…”

“…Popular amongst the cryptographic schemes are the Data Encryption Standards (DES) and Advance Encryption Standards (AES) for single key cryptography and the Rivest, Shamir and Adlemnan (RSA) for double key cryptography. However, these schemes have been susceptible to cryptographic attacks such as brute force attacks in the case of DES and AES, and computational attacks on the RSA, (Abdul-mumin & Gbolagade, 2018;Almarimi, Kumar, Almerhag, & Elzoghbi, 2014).…”