I’m going to talk about the security behind Bitcoin addresses and keys, called Public Key Cryptography. This includes SHA256, Random Number Generators(RNGs), Hash Functions, and Elliptic Curve Digital Signatures (ECDSA.) If you have questions beyond this, please feel free to DM me. I am a mathematician by training, and I have a deep love for it. If you find that you have a new interest in cryptography as a hobby, there are many people who create cryptographic algorithms for fun, and their community can be helpful for your journey.
I promise that you only need some basic algebra for this, as well as a simple understanding of exponential functions. If you are familiar with modular arithmetic, that’s wonderful. If not,no biggie.
Cryptography has been around for thousands of years, and currently has a very robust community of professionals and hobbyists alike. The technology has come an extremely long way, and its current iterations allow for the online security which we hardly have to think about.
Let’s start with the concept of Public Key Cryptography, specifically within the context of Bitcoin. On the most basic level, PKC involves your private keys, and the public keys generated from them. PKC utilizes what are called “trapdoor functions” which are easy to solve (easy to generate a public key from a private key), but almost impossible to reverse engineer (find a private key given a public key.) This is due to the usage of modular arithmetic, exponential functions, and very large prime numbers.
Your bitcoin private keys are probably words, but they can also be a very large number. To be specific, when we begin