Elliptic Curve Cryptography over Gaussian Integers

A new approach is used to implement elliptic curve cryptography (ECC) over prime finite fields. The new approach uses Gaussian integers instead of rational integers. It generates a much larger number of points under the same curve equation and the same prime p. The elliptic curve arithmetic is basically the same but works on complex numbers. The security of the proposed method is far higher. When compared to the original prime field, the new method requires double the space to store cryptographic keys represented by points but the security level, in terms of the group order, is roughly squared. Key words