Of the major problems Bitcoin set out to solve, one was the risk of centralization — and that’s part of what has made it one of the quickest growing currency today. Another was the issue of security. Both of these are deeply tied to cryptography — the science of securing information using mathematical algorithms. At the heart of the cryptography that powers Bitcoin are modular arithmetic and finite field. Modular Arithmetic Simpler than it sounds, it’s something you already use every day whenever you read a clock. Modular arithmetic deals with the remainder left after division. An analog clock never shows 13, 14, or 30. It counts from 1 to 12, then wraps back around. A digital clock goes up to 24, but if your clock reads 23:00 and you want to convert it to a 12-hour format, you apply modulo 12. Here’s the idea: numbers wrap around once they hit a limit. In this case: 23 mod 12 = 11 So, 23:00 becomes 11 PM. No matter how large the number gets, modulo arithmetic always brings it back within a fixed range.…