Back around 2000, I found a copy of Neal Koblitz’s text *A Course in Number Theory and Cryptography *at the Borders bookstore in Bangor, Maine. I only worked my way through the first chapter, but was fascinated with these ideas. I found Professor Koblitz’s website which, at the time, had a tutorial section on finite fields and elliptic curve cryptography (this may have been on the Certicom website, I can’t remember now). I moved on to other forms of digital cryptography, like the Diffie-Hellman Key Exchange and RSA Cryptosystem, but always appreciated Prof. Koblitz’s work. Recently, we dressed up for Halloween as a number and I chose to be the number 4. As part of my costume, I drew the addition table for the Galois Field of order 4, , and did a lot of thinking that week about the element *a*, which was defined as the root of the equation in

This past week, I decided to look at the mathematics behind Bitcoin and blockchain, and lo and behold, it is Finite Fields and Elliptic Curve Cryptography – I don’t know why it took me so long to find this out, but now I’m excited about these topics. I am a little skeptical about the current “Bitcoin bubble.” I’m not sure that these valuations are sustainable, but from everything I’ve read, the blockchain algorithm behind Bitcoin is revolutionary and the mathematics is “supercool.”

Here’s a graph of the equation in .