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1. What is a polynomial? A polynomial is an expression built from a variable $x$, using only addition, multiplication, and non-negative integer exponents: $$P(x) = 3x^2 + 2x + 1$$The degree is the highest power of $x$. The example above is degree 2 (...

This post assumes you've read the Schnorr signatures post. You should be comfortable with s = k + ex, the verification equation sG = R + eP, and why nonce reuse is catastrophic. We're picking up exactly where that left off. 1. Schnorr as a conversa...

In the previous post, we built up to the key equation: Public Key = x * G. A private key x, a generator point G, and a public key P that anyone can see but nobody can reverse. This post picks up exactly where that left off. What is a digital signat...

If you ever wondered how elliptic curves and private keys actually work, and you never liked math like me - let's try to get the idea without too much of it. First: why does any of this exist? Blockchain needs to solve one problem: how do you prove...
