A critical review on Elliptic Curve Cryptography

Elliptic curves in the geometric and algebraic parlances have been studied by computer scientists over the last few decades. Elliptic Curve Cryptography or Cryptosystem (ECC) is a public-key cryptosystem. The main advantage and benefit of using ECC instead of using RSA is that it gives equivalent security for a smaller key, thereby consuming less resource and ameliorating performance on the systems. The basics of elliptic curves and their arithmetic are discussed in this paper. We also present experimental results justifying the benefits of using elliptic curve cryptography over RSA in public cryptosystems.