When you sign a transaction you provide two bits of evidence. The signature of the hash of the transaction you are signing that is mixed with a random number, and a random point on the elliptical curve that was computed with the random number. With the random point plus the public key the verifier can validate you must have the private key to the public key and that signature was made with the same private key because they can produce the same random point with those two data points ?

In school when you did algebra you were given various values for a or b or x and y and if you were given enough real life values for those things you could figure out all the values of the other letters in the equation. When you sign a Bitcoin transaction you need to use a random number to prevent people eventually having enough values for the a/b/x/y and figure out your private key if you do multiple transactions with it. Deterministic nonces (nonce = random number) are based off the hash of the transaction you’re signing so will only ever be used once. This prevents signers messing up the random number that protects your private key. This is what I think I learned this weekend. Now I think I know why NVK keeps mentioning them in Bitcoin Review.

Let’s have some way of having vaults before states stack too much and get short term regulation ideas.