I have all of the Shamir's secret shares required to Lagrange-interpolate
f(0), which represents an ECDSA private key. The field of this object is
secp256k1, which has associated prime number
The Lagrange interpolation produces a negative
f(0), but because curves over
secp256k1 can have exactly 0 or exactly 2 y-coordinates at any x, I'm assuming I can use the absolute value of
My other understanding is that since we're working over the finite field Zp,
S = f(0) (mod p). Where I'm held up is how to turn this 77-byte number (
S) into the ECDSA private key.
I've tried reconstructing a wallet using
S in hexadecimal as the private key, as well as the sha256 of
S, but I don't believe either of those methods are correct.
Are my previous assumptions correct, and if so, how should I go from
S to the ECDSA private key?