Why Galois field
The Galois fields are mainly used in cryptography and error correction algorithm.
If you never deal with Galois field, at the beginning the topic could seem very hard to understand. In this post we want to address the galois field theory from the practical application point of view.
We will review:
- the Galois arithmetic notation, just to understand how to interpret the equation
- add/sum operation in Galois field
- multiplier in Galois field
the third point maybe is the most difficult to understand.
It might put noses out of joint after reading this post because I will not be very rigorous in the representation of the theory of the Galois fields. This post wishes to give you a practical implementation starting point for your VHDL design using Galois arithmetic.
I put a lot of references at the bottom of this post that will help you to go deeper in the Galois field theory if you are really interested in it.