I'm quite new to the intricacies of bitcoin cryptography and ECDSA and elliptic curve cryptography has me quite stymied. I am faced with a curve with the equation:
y^2 = x^3 + 7 of order
N=39 with subgroups of the order
n = 13 and generator point
G = (8,1). We also sign the message J with the private key 8. I'm supposed to figure out the public key, point P using a random number i=5 and also create the signature (r,s).
For the public key, I believe I understand the bare basics. Using elliptic curve multiplication, one can gain the public key using
Kpub = k_priv * G. Using the doubling method, with my example, this would be
2 x G = 2G, 2 x 2G = 4G, 2 x 4G = 8G. But I'm very confused as to how to exactly compute this. I could not find any calculators online that could help me understand the steps either.
As for the Point P generation with random number i=5, I'm completely lost and the same goes for the signature.
Any help in calculation, or better yet, an explanation as to how this works would be highly appreciated!