Elliptic curve cryptography

Elliptic curve (EC) public key cryptosystems were proposed independently in 1985 by Victor Miller and Neal Koblitz and are gaining favor as an efficient and attractive alternative to the more conventional public key cryptosystems (e.g., RSA) in some applications. The author surveys the mathematical and practical challenges one faces when designing and implementing an EC cryptosystem, with special attention given to the point counting problem.