Having perused the stackexchange, I discovered some related questions, however am having problem understanding methods to arrive on the resolution to (n-1)*x=1 mod np, the place:
n: Finite group order of the Bitcoin secp256k1 curve
n=115792089237316195423570985008687907852837564279074904382605163141518161494337
p: Prime order of the curve
p=115792089237316195423570985008687907853269984665640564039457584007908834671663
np: (n-1)+(p-1)
np=231584178474632390847141970017375815706107548944715468422062747149426996165998
and (n-1) is just not coprime to modulo np.
Having carried out the next step of np/2 and including .5 to outcome one, in order to attain:
F1=115792089237316195423570985008687907853053774472357734211031373574713498083000
Then subtracting the preliminary outcome with .5 to attain:
F2=115792089237316195423570985008687907853053774472357734211031373574713498082999
And following directions from solutions to associated posts, (n-1) is to be multiplicativeley inversed over mod F1 and F2. Nonetheless, neither F1 or F2 are coprime to (n-1). With a purpose to overcome this, it’s defined that GCD and CRT are for use as a way to precisely calculate the modular inverse.
What steps are required and the way are the operations carried out to perform this?
Thanks.