Abstract

Abstract- Nowadays, public-key cryptography, especially RSA, is becoming more and more crucial for e-commerce transactions. Several digital consumer appliances, such as set-top boxes and smart cards, may now send and receive many RSA-encoded messages. However, due to the exponentiation and multiplications of very large numbers, the RSA algorithm is inappropriate for encrypting large messages. Hence to fill this gap, this paper proposes an efficient modular exponentiation technique for the RSA cryptosystem which can enhance the execution speed of the standard RSA cryptosystem by applying the square-multiply technique of exponentiation. The MATLABR2019a programming platform is employed for the actual implementation. The proposed work discusses the Standard RSA (SRSA) and Modified RSA (MRSA) cryptographic algorithms by considering different performance evaluation metrics such as encryption time, decryption time, memory usage, throughput, and avalanche effect through a practical implementation using MATLAB. Concerning the encryption and decryption time performance, the MRSA algorithm outperforms the SRSA algorithm by 17.46442% and 18.70409%, respectively. Moreover, the MRSA has a 14.53511% higher avalanche value than the SRSA, showing its greater security. Also, it outperforms the SRSA algorithm in terms of encryption and decryption throughput by 15.80883% and 15.12928% respectively. However, because the MRSA algorithm uses an array list, which uses more memory than the SRSA, it consumes slightly more memory (1.05849%) overall.Keywords: Modular Exponentiation, RSA, Encryption and Decryption, Cryptography, Private Key, Public Key, Security