Re: How to calculate public key manually?

[archyone]

Here's some working python code that generates the point of the public key for private key = 2

Code:

# Inversion using Extended Euclidean algorithm.
def EEA_invert(a, b):
    r = {}; s = {}; r[0] = a; r[1] = b; s[0] = 1; s[1] = 0
    i = 1;
    while True:
        if r[i]==0: break
        q = r[i-1]//r[i]; r[i+1] = r[i-1] - q*r[i]; s[i+1] = s[i-1] - q*s[i]
        i += 1
    return s[i-1] % b

# Bitcoin's EC parameters: see https://en.bitcoin.it/wiki/Secp256k1
G = '79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8'.replace(' ', '')
gx, gy = int(G[:64], 16), int(G[64:], 16)
p = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1

# Calculate differential at the generator point.      
slope = (3*gx**2)*EEA_invert(2*gy, p) % p

# Calculate x, y.
x = (slope**2 - 2*gx) % p
y = (slope*(gx - x) - gy) % p

print(hex(x), hex(y))

which yields:

Code:

('0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5',
 '0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a')

Hello everyone !

I know it is a very old thread but is it possible for someone to explain what is the differential at the generator point (slope ?) and why it is use in calculation ?
I see this function give the result for the private key 2 (doubling Gx) but is it possible with this formula to obtain the result for 200 (for example) or is it and another formula.

Thanks in advance

[1715113993]

1715113993

[c_atlas]

Hello everyone !

I know it is a very old thread but is it possible for someone to explain what is the differential at the generator point (slope ?) and why it is use in calculation ?
I see this function give the result for the private key 2 (doubling Gx) but is it possible with this formula to obtain the result for 200 (for example) or is it and another formula.

Thanks in advance

I think this graph should clear things up. The differential is the slope of the tangent line. The tangent line to G will intersect the curve at some other point, that point is -2G. On reflection over the x axis, you obtain 2G. You can keep playing this game and jumping around to get (+/-)(2^k)G for any natural number k.

[nniicckk]

You can find information how to calculate Public key from Private here https://bitcoin-math.000webhostapp.com Also, you can find Doubling, Addition and Scalar multiply functions on C# without NBitcoin class Key, BigInteger is used only.