Abstract
Summary - Public-key encryption, particularly RSA, is becoming increasingly important for e-commerce transactions these days. Many RSA-encoded messages can now be sent and received by a variety of digital consumer appliances, including smart cards and set-top boxes. However, the RSA algorithm is not suited to encrypt long communications since it involves exponentiation and multiplication of very large numbers. To close this gap, this study suggests an effective modular exponentiation method for the RSA cryptosystem that uses the square-multiply exponentiation methodology to increase the standard RSA cryptosystem's execution performance. The actual implementation is carried out using the MATLAB R2019a programming environment. Through a real-world MATLAB implementation, the proposed study examines the Standard RSA (SRSA) and Modified RSA (MRSA) cryptographic algorithms while considering several evaluation metrics like encryption time, decryption time, memory usage, throughput, and the avalanche effect. In terms of encryption and decryption time performance, the MRSA method performs 18.70409% and 17.46442% better than the SRSA algorithm, respectively. Additionally, the MRSA's avalanche value is 14.53511% higher than the SRSA's, showing its greater security. Furthermore, it achieves 15.80883% encryption throughput and 15.12928% decryption throughput, respectively, better than the SRSA approach. Overall, nevertheless, the MRSA algorithm requires a little more memory (1.05849%) than the SRSA since it makes use of an array list, which needs more memory.

Key words: Ciphertext, plaintext, RSA, Encryption, Decryption, Cryptography, Private Key, Public Key