Implementation of RSA and RSA-CRT Algorithms for Comparison of Encryption and Decryption Time in Android-based Instant Message Applications

Abstract

One of the advances in communication technology is producing instant messaging applications or instant messages. The confidentiality of instant messaging is still not maintained, so cryptography is needed. An example of a reliable cryptographic algorithm is Rivest-Shamir-Adleman (RSA), where RSA is a process of asymmetric key encryption (asymmetric key). Chinese Remainder Theorem (CRT) is an algorithm to reduce modular arithmetic calculation with a large modulus for the same calculation for each factor of the modulus. CRT can shorten the bit size of the decryption exponent d (which is the public key of RSA or RSA-CRT) by hiding d on a congruent system to speed up the decryption time, and it can be used with an RSA algorithm called RSA-CRT. This study uses three modulus n (key length), namely 1024 bits, 2048 bits, and 4096 bits. In the RSA-CRT 1024 bit decryption process, speed increases about 2.6 times faster than the 1024 bit RSA. In the RSA-CRT 2048 bit, the decryption process speed increases almost three times faster than the 2048 bit RSA. Whereas in the RSA-CRT 4096 bit, the decryption process's speed increases approximately 3.6 times faster than the RSA 4096 bit. From the results of this study, it can be concluded that the RSA-CRT algorithm can speed up the decryption process up to three times faster than the decryption process in the RSA algorithm. The longer or greater the modulus n used, the speed of the decryption process in the RSA-CRT algorithm will increase compared to the RSA algorithm.