Improving Network Security Using Elliptic Curve Cryptosystem

Diffie–Hellman Key Exchange establishes a shared secret between two parties that can be used for secret communication for exchanging data over a public network. The following conceptual diagram illustrates the general idea of the key exchange by using colors instead of very large numbers.
The process begins by having the two parties, Alice and Bob, agree on an arbitrary starting color that does not need to be kept secret (but should be different every time); in this example the color is yellow. Each of them selects a secret color–red and aqua respectively–that they keep to themselves. The crucial part of the process is that Alice and Bob now mix their secret color together with their mutually shared color, resulting in orange and blue mixtures respectively, then publicly exchange the two mixed colors. Finally, each of the two mix together the color they received from the partner with their own private color. The result is a final color mixture (brown) that is identical to the partner's color mixture.
The simplest and the original implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime, andg is a primitive root modulo p. These two values are chosen in this way to ensure that the resulting shared secret can take on any value from 1 to p–1. Here is an example of the protocol, with non-secret values in blue, and secret values in red.
1.    Alice and Bob agree to use a modulus p = 23 and base g = 5 (which is a primitive root modulo 23).