Close but Bitcoin uses ECDSA and Schnorr Sigs, which don’t rely on hardness factoring primes like in RSA. They rely on the hardness of the Discrete Log Problem.
Otherwise yes, by double hashing the pub key, we make it much harder to find the actually used pubkey to try to attack the DLP with.
ECDSA using Secp256k1 can still be brute forced (albeit inefficiently) using a discrete log solving method like rho:
from sympy import isprime, nextprime def pollards_rho(G, Q, curve_order): x = G y = G factor = 1 while factor == 1: x = curve_add(x, G, curve_order) y = curve_add(y, G, curve_order) y = curve_add(y, G, curve_order) factor = gcd(abs(x[0]-y[0]), curve_order) return factor def curve_add(p1, p2, curve_order): # Simplified elliptic curve addition return (p1[0] + p2[0], p1[1] + p2[1]) % curve_order def gcd(a, b): while b: a, b = b, a % b return a # Example parameters (not for secp256k1) G = (3, 7) # Generator point Q = (13, 17) # Public key curve_order = 19 # Elliptic curve order d = pollards_rho(G, Q, curve_order) print(f"Private key (d): {d}")
This would take a gazillion lifetimes of the universe to compute. It could be ported to Shor's on a quantum cluster if the cluster gets stupid large and actually corrects for errors.
Schnorr signatures are also reliant on the difficulty of solving the discrete log problem.
Yes correct, Nothing to do with prime factoring as your previous message indicated. Did ChatGPT write that code block?
hah, my brain is still wired in GPG/PGP thinking. Correct, I have a tendency to blurt "large primes! It's all primes!" in my sleep. And yes, that's some unoptimized quick hackery from chatgpt in python. Not usable but readable enough to make the point.
AI gen code sucks, you will notice it’s importing but not using the isprime, nextprime. We generally called that “Pollards Rho”, not “Rho”.
It’s hallucinating fragments contextually related from a cryptography library.
I would recommend not using chatgpt for code.
it is absolute garbage at writing code. I didn't even notice that excess import. It did at least correctly name the function pollards_rho :)
Yes :-) all good! Just wanted to mention ECC/DLP va RSA in terminology;
I see people confuse factoring primes (RSA) with ECDLP (ECC). Bitcoin doesn’t specifically have to worry about prime factoring! (It may however indicate further advances in number theory…)