A Study of RSA Algorithm in Cryptography

The RSA algorithm has solved an intimidating challenge in network security, enabling the secure but transparent exchange of encrypted communications between users and other parties (rsa.com, 2011). The following paper explores the history of RSA and the method. Keywords— RSA algorithm, security, key size. I. LITERATURE REVIEW The idea of the RSA public key cryptosystem was from Diffie and Hellman, who introduced the method of the exponential key exchange. The Diffie-Hellman key exchange is the second most popular public key algorithms, after the RSA. However, the first ever known description of a similar system was made in 1973 by Cifford Cocks, a mathematician working at the GCHQ, a UK intelligence agency. The system was never set up considering the relatively expensive computers required to implement it at the time. Because of its top secret classification, it was not until, 1998 that his discovery was revealed. During the fall of 1976, Ronald Rivest, Adi Shamir and Leonard Adleman, all young faculty members at the Masschusettes Institute of Technology began working on a novel type of cryptographic design. Rivest and Shamir were computer scientists at the MIT while Adleman was a number theorist at the Institution. In their project, Ronald and Adi would develop ideas while Leonard would attempt to bring the ideas down, by cracking them. Leonard was time and again successful at cracking them until one night when Ronald developed an algorithm that Leonard could not crack. The Algorithm was named RSA from their names Rivest, Shamir, and Adleman. To this day, the algorithm has never been broken (Ohya & Volovich 2011). The core of RSA has withstood every attack from the best cryptographic minds. The robustness of the algorithm, the absence of rigorous proof notwithstanding, provides a sense of security. According to Dan Boney, a computer science professor at the Stanford University, “we kind to chip at the sides, but no one have figured out how to get at the heart of it.” (Robinson, 2003, pp.6) RSA has come to play a vital role in electronic communications. Being the first example in history of the public key cryptosystem and, worth nothing, the only type that has withstood more than three decades of attacks, the RSA has become the choice algorithm for functions such as authenticating phonecalls, encrypting credit-card transactions over the Internet, Security e-mail and providing numerous other Internet security functions. The functions of the RSA continue to increase, and to award their efforts, Rivest, Shamir, and Adleman received one of the highest awards in the field of mathematics, the Association for Computing Machinery’s 2002 Alan Turing Award. It is without surprise that the security of RSA remains a major focus of cryptographic research, in theoretical as well as practical functions (Abhijit, 2009).