Randomness and hiding information

The level of randomness is crucial for hiding information. The higher the level of randomness, the better. The design of cryptosystem is aiming at constructing crypto codes with “perfect avalanche” and good randomness.

Using optimal normal basis (or polynomial basis) math that looks like scrambled bits over an elliptic curve produce a fundamentally nonlinear output. A single bit change in the input will cause a nonlinear and very drastic change in the output.

Well, while symmetric crypto designers are working very hard on this, elliptic curves do it automatically 😉