So What’s A Finite Field and Why Is It So Important to your Privacy?

The demonstration of the methods defined in this article are here.

Sometimes when you read research papers your head can spin a little, but you should try and stick with it, as the learning of new knowledge often involves breaking down the barriers to that knowledge.

For one you may not have the background that prepares you for the subject, but, with the Internet, there are very few barriers to learning new subjects. All you need is an enquiring mind, and to not take “No” for an answer. At one time knowledge was passed through privileged sources … through physical libraries and seats of learning … but now it is freely available.

The second thing is the terminology that is used, and which can be an even create a barrier. So let’s break down a few barriers by talking about finite fields.

A finite field and a Galois field

A finite field is just a set with a finite number of elements. In cryptography, we often time a finite field of integers modulo p (where modulo is the remainder of an integer division), and where p is a prime number. This is defined as GF(p) — Galois field of p — or with 𝔽p.

The following are some examples:

• 𝔽2 or GF(2) is [0,1]