Modular Arithmetic in RSA Cryptography

Abstract

Faster implementations of public-key cryptography and in particular of RSA are of utmost importance nowadays. Performing fast modular multiplication for large integers is of special interest because it provides the basis for performing fast modular exponentiation, which is the key operation of the RSA cryptosystem. Currently, it seems that in a radix representation, all major performance improvements have been achieved. Nevertheless, the use of Residue Number System proves to be a promising alternative for achieving a breakthrough. All these aspects are detailed throughout this research paper. Also presents an overview of the RSA cryptosystem, followed by a short proof of why the encryption-decryption mechanism works. With considerations regarding the employed key-sizes and with an example of a small RSA cryptosystem.