Polynomials Will Secure The Internet …
The security of the Internet will radically change over the next decade or so, and the methods we use to prove identity, to digitally sign, and to create our secure tunnels for information will radically change. Why? Because quantum computers threaten our existing public-key methods. We will thus need to find other ways to do our public key trap door functions, and many of the routes lead to lattice cryptography.
With lattice methods, we have multi-dimensional spaces, and where to plot our points within there. Most of the time we think in one dimension (x), or it two dimensions (x, y) or three dimensions (x,y and z), but, in a lattice, we may have thousands of dimensions. Each point we have then fitted into a lattice of these points. To make a hard problem to solve, we add a small amount of error to the point. It is then extremely difficult to find the nearest point to the point with the error.
So, why have I said polynomials in the title, when we are dealing with lattice methods? Well, it’s quite simple … they are an excellent way of representing multi-dimension spaces. For example, if I have a point of (9, 5, 16), I would represent it with a quadratic equation of:
16x²+5x+9
This could be represented by a polynomial of [16, 9, 5]. If I have another polynomial of 2x²+x+7, and I multiplied them…
