On the performance of Elliptic Curve public cryptosystem

Elliptic curve cryptosystem has been heavily studied by computer scientists for many decades. This form of cryptosystem is based on elliptic curves over some Galois fields. Elliptic Curve Cryptography or Cryptosystem (ECC) is a public-key cryptosystem that makes use of public and private key pairs as a means of encrypting and decrypting information in the internet. The critical security of ECC relies on the ability to compute multiplication of a point by an integer easily and the unfeasibility or failure to find out the multiplier and multiplicand given product point within a time window. The size of the elliptic curve determines the security of the system. The main advantage and benefit of using ECC compared to other cryptosystems is that we can use smaller keys without compromising the security of the system. The performances of elliptic curve cryptosystem are critically evaluated in this paper.