FWIW you don't need to know "the math behind bitcoin" to write a blockchain parser.
Yes. I just want to know a bit about the math for personal interest. If that book can help a bit, then good. Otherwise my primary interest is in writing a blockchain parser, with respect to the book.
It is called "G" for Generator not Q!
Thanks, I'm tired... haha. But I still needed that pointed out...
I read somewhere that G is the same for everyone in Bitcoin. I am guessing this means the Generator and its properties, not that it's a scalar or some type of simple constant. Like you say, G is a point on a curve, and everyone uses the same curve.
Order (or n) is the order of the generator or G.
Order of a point (G is a point on the curve) is the smallest positive integer such that nP = O.
Order of a point (G is a point on the curve) is the smallest positive integer such that nP = O.
So with G point on the curve, P, n is the smallest positive integer that satisfies nP = O where O is the order.
Base point is a point on the curve which is used in public key cryptography.
This seems to be the same, but with or without a prefix of 04. So this is a starting point to generate other points on the curve? Oh hang on. I'll get a book on crypto.
What you need to have in mind is that calculations used in Elliptic Curve Cryptography are not regular arithmetic. Instead they are Modular Arithmetic. So y2=... is in fact y2=... mod p.
Calculating it requires using special algorithms one example is TonelliShanks algorithm. There are special cases which can speed up the calculation. In case of secp256k1 elliptic curve that bitcoin is using, the prime number has a special characteristic which makes the calculation easier. And that is the fact that p%4=3 so you can use that formula above with (p+1/4 mod p)
Calculating it requires using special algorithms one example is TonelliShanks algorithm. There are special cases which can speed up the calculation. In case of secp256k1 elliptic curve that bitcoin is using, the prime number has a special characteristic which makes the calculation easier. And that is the fact that p%4=3 so you can use that formula above with (p+1/4 mod p)
Thanks! I appreciate the response. That was illuminating. I tried the Python code and it's becoming more concrete.
I'll have to go out now and dig around a little more. But if it gets too hard, I'll stick to the coding then, and concentrate on a blockchain parser instead of trying to understand everything...