The previous posts covered mathematical curiosities. Now we can leave that realm, find an application and turn them into tools to work with elliptic curve cryptography. That means finding and choosing which particular values of the parameters bring us into a curve we can use for cryptography.
When merging the last two posts, I immediately run into serious difficulties. Haskell’s type system just made my work harder(well my ignorance did). Until I could come up with a solution, I could not appreciate how the strictness of the type system actually gives flexibility.
In this series of posts I’m solving the exercises of Programming Bitcoin in Haskell, I’m learning Bitcoin and Haskell in one go. To describe a point in the elliptic curve, we need four data points. \((x, y)\) are the coordinates themselves, additionally we need the constants \((a, b)\) that define the elliptic curve given by the equation \(y^2 = x^3 + ax +b\). Finally, there is the special case of the point at infinity, which does not really fit in the previous constrain. In other languages I would just describe with an invalid or null value, in Python for example I would use the None value in both \((x, y)\) coordinates, yet in Haskell it can be beautifully defined as an element of the type. That is certainly a killer feature of the language, and I expect to be using it more often.
Bitcoin’s price has gone crazy up, and now I’m really responsible for learning it. I found the book Programming Bitcoin by Jimmy Song, it looks good enough to give it a try. It uses Python to teach, which is uninteresting and I end up only skimming over it, which leads to low retention. Learning necessitates inefficiencies, trial and error, solving problems and sharing. Thus to learn I need to throw an extra challenge. I’m going to learn another programming language(Haskell) to solve the book’s problems.
There are plenty of reasons: Get out of your comfort zone, build character, discover your limits. There are plenty of justifications: Simply crazy, settling a bet, religious penitence/purification. All those might apply, however for me it is a CELEBRATION. A celebration of how well I’m doing nowadays. I was born in a big city, I grew up surrounded by the grayness of concrete. The river in my city was so polluted that its smell alone would keep you away. Going into nature implied a family trip, implied planning, implied getting everyone to agree and then traveling far away until we could reach a clean river, a waterfall or a lake. Only then could I jump into those clean, refreshing and relaxing waters. In those day it didn’t matter how cold they were.