PUBLIC ECDSA KEY

Question

I want to know how I can build a Python script that can Calculate Public Key ECDSA from a Private Key (HEX) and the result is similar to the imagen

Answer 1

This has been answered already in:
(How do you get a Bitcoin Public Key from a Private Key)

Look at the answer of @user1658887 for example.

EDIT: Given the fact that you're asking for the public key output in uncompressed hex format explicitly, here are some wrapping code lines around the the stuff that user1658887 posted in the answer referenced above:

import binascii
import struct
import sys

# code taken from user1658887's answer at: https://bitcoin.stackexchange.com/questions/25024/how-do-you-get-a-bitcoin-public-key-from-a-private-key

def sk_to_pk(sk):
    """
    Derive the public key of a secret key on the secp256k1 curve.

    Args:
        sk: An integer representing the secret key (also known as secret
      exponent).

    Returns:
        A coordinate (x, y) on the curve repesenting the public key
      for the given secret key.

    Raises:
        ValueError: The secret key is not in the valid range [1,N-1].
    """
    # base point (generator)
    G = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
     0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8)

    # field prime
    P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F

    # order
    N = (1 << 256) - 0x14551231950B75FC4402DA1732FC9BEBF

    # check if the key is valid
    if not(0 < sk < N):
        msg = "{} is not a valid key (not in range [1, {}])"
        raise ValueError(msg.format(hex(sk), hex(N-1)))

    # addition operation on the elliptic curve
    # see: https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_addition
    # note that the coordinates need to be given modulo P and that division is
    # done by computing the multiplicative inverse, which can be done with
    # x^-1 = x^(P-2) mod P using fermat's little theorem (the pow function of
    # python can do this efficiently even for very large P)
    def add(p, q):
        px, py = p
        qx, qy = q
        if p == q:
            lam = (3 * px * px) * pow(2 * py, P - 2, P)
        else:
            lam = (qy - py) * pow(qx - px, P - 2, P)
        rx = lam**2 - px - qx
        ry = lam * (px - rx) - py
        return rx % P, ry % P

    # compute G * sk with repeated addition
    # by using the binary representation of sk this can be done in 256
    # iterations (double-and-add)
    ret = None
    for i in xrange(256):
        if sk & (1 << i):
            if ret is None:
                ret = G
        else:
            ret = add(ret, G)
        G = add(G, G)

    return ret

if len(sys.argv) >= 2:
    sk = long(sys.argv[1], 16)
else:
    raise ValueError('Please provide the private key in hex format as a 1st parameter')

pk = sk_to_pk(sk)
pkx, pky = pk
ybyte=0x02 if pky % 2 == 0 else 0x03       # can be used when a compressed pubkey is desired
hexpk = "%s%s%s" % ("04",hex(pkx),hex(pky))    # 04 indicates that an uncompressed pubkey is desired
print (hexpk.replace("0x","",2).replace("L","",2));

Which gives you your desired result:

~/$ python priv2pub.py B54FD9915A8B6870647705E91D4D953BA34B2B53F4681FDEFD50ECC13507BEFC
0413775e7a37881a284dac76217f12d610fc8fc67f82e73cd56a4d98f149cbc8e3ef8b012e9670ab1ba1cf40125921a59cc736cc7cfe8c6a6bacdd1327440343cf