I am trying to learn how ECDSA works. I do not have a background in maths, but have been following a guide which has built me up from finite fields, elliptic curves. I am unable to figure out how a signature is generated , a description of it is here.
To state what i understand.
- e = private key
- G = generator point
- P = Public key
- k = Ephemeral key
The public key is a point on the curve computed as
e.G = P
The signing algorithm starts by taking a random target R
kG = R
The guide straight up represents R as follows (where u/v are chosen by user):
uG + vP = kG
I sort of fail to understand how or why this relation holds true. It seems to be starting with a random point on the curve uG and it adds a scalar multiple of the public key (which could be further expressed v.e.G)