ELLIPTIC CURVE CRYPTOGRAPHY

ELLIPTIC CURVE CRYPTOGRAPHY

ABSTRACT
Since the invention of public-key cryptography in 1976 by Whitfield Diffie and Martin Hellman , numerous public-key cryptographic systems have been proposed. All of these systems rely on the difficulty of a mathematical problem for their security. One such mathematical problem which is difficult to solve is Elliptic curve discrete logarithm problem (ECDLP). Its use in public key cryptography was first proposed in 1985 by Koblitz and Miller. Since then this has been an interesting field of study.
Elliptic curves have been extensively studied for over a hundred years, and there is a vast literature on the topic. The primary advantage that elliptic curve systems have over other mathematical systems is the absence of a subexponential-time algorithm. Consequently, one can use an elliptic curve group that is smaller in size while maintaining the same level of security. The result is smaller key sizes, bandwidth savings, and faster implementations, features which are especially attractive for security applications where computational power and integrated circuit space are limited.