How convert Bitcoin Privat Key Compression to public address?

Question

This script gets the public address from the uncompressed private key.

import ecdsa
import hashlib
import base58

private_key = input("privatekey: ") # e41b45e722251672c01a28e4fada590471fea09f90d13b143033ed3a1107ef49

# Convert hex private key to bytes
private_key = bytes.fromhex(private_key)

# Derivation of the private key
signing_key = ecdsa.SigningKey.from_string(
    private_key, curve=ecdsa.SECP256k1)
verifying_key = signing_key.get_verifying_key()

public_key = bytes.fromhex("04") + verifying_key.to_string()

# Hashes of public key
sha256_1 = hashlib.sha256(public_key)
ripemd160 = hashlib.new("ripemd160")
ripemd160.update(sha256_1.digest())

# Adding prefix to identify Network
hashed_public_key = bytes.fromhex("00") + ripemd160.digest()

# Checksum calculation
checksum_full = hashlib.sha256(
    hashlib.sha256(hashed_public_key).digest()).digest()
checksum = checksum_full[:4]

# Adding checksum to hashpubkey
bin_addr = hashed_public_key + checksum

# Encoding to address
address = str(base58.b58encode(bin_addr))
final_address = address[2:-1]  # change 2

print(final_address)

Format (private keys):

        uncompressed: 0x80 + [32-byte secret] + [4 bytes of Hash() of previous 33 bytes], base58 encoded
        compressed: 0x80 + [32-byte secret] + 0x01 + [4 bytes of Hash() previous 34 bytes], base58 encoded
    
    case 1:

    secret (hex): 1111111111111111111111111111111111111111111111111111111111111111
    uncompressed:
        secret (base58): 5HwoXVkHoRM8sL2KmNRS217n1g8mPPBomrY7yehCuXC1115WWsh
        pubkey (hex): 044f355bdcb7cc0af728ef3cceb9615d90684bb5b2ca5f859ab0f0b704075871aa385b6b1b8ead809ca67454d9683fcf2ba03456d6fe2c4abe2b07f0fbdbb2f1c1
        address (base58): 1MsHWS1BnwMc3tLE8G35UXsS58fKipzB7a
    compressed:
        secret (base58): L4xkFv5sbttQcsgnTjzqJuQdNfHC5gk9zsK5HmaV822qu79zJA7L
        pubkey (hex): 034f355bdcb7cc0af728ef3cceb9615d90684bb5b2ca5f859ab0f0b704075871aa
        address (base58): 1Q1pE5vPGEEMqRcVRMbtBK842Y6Pzo6nK9

I need to get this code to work with two formats, but I don't understand what needs to be fixed. If I insert a compression private key 682cf5791be8d4526aacf63bb7ab201f5cd1d732c1f634e5839379191b02295925 , I get an error:

ecdsa.keys.MalformedPointError: Invalid length of private key, received 33, expected 32

I understand that the bottom part of this code can be used, but I am failing to lack knowledge.

def __private_to_compressed_public(private_key):
        private_hex = codecs.decode(private_key, 'hex')
        # Get ECDSA public key
        key = ecdsa.SigningKey.from_string(private_hex, curve=ecdsa.SECP256k1).verifying_key
        key_bytes = key.to_string()
        key_hex = codecs.encode(key_bytes, 'hex')
        # Get X from the key (first half)
        key_string = key_hex.decode('utf-8')
        half_len = len(key_hex) // 2
        key_half = key_hex[:half_len]
        # Add bitcoin byte: 0x02 if the last digit is even, 0x03 if the last digit is odd
        last_byte = int(key_string[-1], 16)
        bitcoin_byte = b'02' if last_byte % 2 == 0 else b'03'
        public_key = bitcoin_byte + key_half
        return public_key 

I've done a lot of tests, but I can't figure out what's wrong. Tell me how to modify the code correctly.

Thank you in advance for your help.

Answer 1

If I get your code and use "e41b45e722251672c01a28e4fada590471fea09f90d13b143033ed3a1107ef49" as secret hex value AKA secret private key... then I get result: "12sF1DbBbPaoNYrs28Qm7waiCcAVoF93Nn" which is uncompressed public address.

Check my script, it is more extended, but with a copule of imports for an educational point of view, to show all the process. You will get compressed and uncompressed public keys from a given secret in hexadecimal value.

First, the script will get uncompressed private key and compressed private key in hex:

'04417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3BAAA3251D2587D4E57ACBCE7991B72355EA33C44DBCF260D09B6C921879A61AA4'
'02417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3B'

Then it will get both public uncompressed and compressed public keys.

The code:

#!/usr/bin/python3
from hashlib import sha256, new
import binascii

PCURVE = 2 ** 256 - 2 ** 32 - 2 ** 9 - 2 ** 8 - 2 ** 7 - 2 ** 6 - 2 ** 4 - 1  # The proven prime
N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141  # Number of points in the field
ACURVE = 0
BCURVE = 7  # These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
GPOINT = (Gx, Gy)  # This is our generator point. Trillions of dif ones possible


def modinv(a: int, n: int = PCURVE):
    # MAXIMO COMUN DIVISOR: Extended Euclidean Algorithm/'division' in elliptic curves
    lm, hm = 1, 0
    resto = a % n
    high = n
    while resto > 1:
        ratio = high // resto
        nm = hm - lm * ratio
        new = high - resto * ratio
        lm, resto, hm, high = nm, new, lm, resto
    return lm % n


def ECadd(a, b):  # Not true addition, invented for EC. Could have been called anything.
    LamAdd = ((b[1] - a[1]) * modinv(b[0] - a[0], PCURVE)) % PCURVE
    x = (LamAdd * LamAdd - a[0] - b[0]) % PCURVE
    y = (LamAdd * (a[0] - x) - a[1]) % PCURVE
    return x, y


def ECdouble(a):  # This is called point doubling, also invented for EC.
    Lam = ((3 * a[0] * a[0] + ACURVE) * modinv((2 * a[1]), PCURVE)) % PCURVE
    x = (Lam * Lam - 2 * a[0]) % PCURVE
    y = (Lam * (a[0] - x) - a[1]) % PCURVE
    return x, y


def EccMultiply(gen_point: tuple, scalar_hex: int):  # Double & add. Not true multiplication
    if scalar_hex == 0 or scalar_hex >= N:
        raise Exception("Invalid Scalar/Private Key")
    ScalarBin = str(bin(scalar_hex))[2:]  # string binario sin el comienzo 0b
    Q = gen_point  # esto es una tupla de dos integer del punto de generacion de la curva
    for i in range(1, len(ScalarBin)):
        Q = ECdouble(Q)
        if ScalarBin[i] == "1":
            Q = ECadd(Q, gen_point)  #
    return Q


def private_to_hex_publics(hex_private_key: hex):
    public_key = EccMultiply(GPOINT, hex_private_key)
    public_uncompressed = f"04{hex(public_key[0])[2:].upper()}{hex(public_key[1])[2:].upper()}"

    if public_key[1] % 2 == 1:  # If the Y value for the Public Key is odd.
        public_compressed = ("03" + str(hex(public_key[0])[2:]).zfill(64).upper())
    else:  # Or else, if the Y value is even.
        public_compressed = ("02" + str(hex(public_key[0])[2:]).zfill(64).upper())
    return public_uncompressed, public_compressed


def hash_256_from_hex_string_like_bytes(hexstring: str):
    return sha256(bytes.fromhex(hexstring)).hexdigest()


def ripemd160_from_hex_string_like_bytes(hexstring: str):
    return new('ripemd160', bytes.fromhex(hexstring)).hexdigest()


def b58encode(hex_string, expected_length=None):
    v = binascii.unhexlify(hex_string)
    alphabet = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
    lev, number = 1, 0
    for char in reversed(v):
        number += lev * char
        lev = lev << 8  # 2^8
    string = ""
    while number:
        number, modulo = divmod(number, 58)
        string = alphabet[modulo] + string
    if not expected_length:
        return string
    elif len(string) != expected_length:
        raise Exception(f"b58encode: Expected length={expected_length} obtained length={len(string)}")
    else:
        return string


def sha256_get_checksum(hex_string_to_checksum):
    hasha1 = hash_256_from_hex_string_like_bytes(hex_string_to_checksum)
    # print("HashA1", hasha1)
    hasha2 = hash_256_from_hex_string_like_bytes(hasha1)
    # print("HashA2", hasha2)
    return hasha2[:8].upper()


def sha_ripe_digest(hex_string_to_checksum):
    hashc1 = hash_256_from_hex_string_like_bytes(hex_string_to_checksum)
    hashc2 = ripemd160_from_hex_string_like_bytes(hashc1)
    return hashc2.upper()


def wif_from_private(privkey: hex):
    # put 80 for bitcoin and concatenate with privkey
    prepend = "80"
    private_key_str = hex(privkey)[2:].zfill(64)
    prepended = (prepend + private_key_str).upper()
    compressed = (prepend + private_key_str + "01").upper()

    if len(prepended) != 66 or len(compressed) != 68:
        raise Exception("WIF conversion: Wrong prepended or compressed private key, length not 66")

    uncompressed_checksum = sha256_get_checksum(prepended)
    compressed_checksum = sha256_get_checksum(compressed)
    private_key_uncompressed_checksum = prepended + uncompressed_checksum
    private_key_compressed_checksum = compressed + compressed_checksum
    private_key_WIF_uncompressed_Base58 = b58encode(private_key_uncompressed_checksum, 51)
    private_key_WIF_compressed_Base58 = b58encode(private_key_compressed_checksum, 52)

    print("PREPENDED:\t\t\t\t", prepended)
    print("PRIV_UNCOMP+CHECKSUM:\t\t\t", private_key_uncompressed_checksum)
    print("Private_key_WIF_uncompressed_Base58:\t", private_key_WIF_uncompressed_Base58)
    print("PRIV_COMP+CHECKSUM:\t\t\t", private_key_compressed_checksum)
    print("Private_key_WIF_compressed_Base58:\t", private_key_WIF_compressed_Base58)
    return private_key_WIF_uncompressed_Base58, private_key_WIF_compressed_Base58


def hex_public_to_public_addresses(hex_publics):
    uncompressed = hex_publics[0]
    public_key_hashC_uncompressed = "00" + sha_ripe_digest(uncompressed)
    checksum = sha256_get_checksum(public_key_hashC_uncompressed)
    PublicKeyChecksumC = public_key_hashC_uncompressed + checksum
    public_address_uncompressed = "1" + b58encode(PublicKeyChecksumC, 33)
    print("Public address uncompressed:\t", public_address_uncompressed)

    compressed = hex_publics[1]
    PublicKeyVersionHashD = "00" + sha_ripe_digest(compressed)
    compressed_checksum = sha256_get_checksum(PublicKeyVersionHashD)
    PublicKeyChecksumC = PublicKeyVersionHashD + compressed_checksum
    public_address_compressed = "1" + b58encode(PublicKeyChecksumC, 33)
    print("Public address compressed:\t", public_address_compressed)
    return public_address_uncompressed, public_address_compressed


if __name__ == "__main__":
    privkey = 0xe41b45e722251672c01a28e4fada590471fea09f90d13b143033ed3a1107ef49
    print(f"PRIVATE KEY:\t {hex(privkey)[2:].zfill(64).upper()}")

    # Public hex test
    hex_publics = private_to_hex_publics(privkey)
    print(hex_publics)
    print()

    # WIF creation test
    wif = wif_from_private(privkey)
    print(wif)

    # Public keys
    public = hex_public_to_public_addresses(hex_publics)
    print(public)

The script is inspired by this site.

Finally you will obtain the two public keys, uncompressed and compressed:

'12sF1DbBbPaoNYrs28Qm7waiCcAVoF93Nn', '1BMKGYmgjrvmSDtvLZvKjyVMnbi6FLmcVi'

Hope this will help you.

Note: it will give you the WIF format too.

Full output:

PRIVATE KEY:     E41B45E722251672C01A28E4FADA590471FEA09F90D13B143033ED3A1107EF49
('04417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3BAAA3251D2587D4E57ACBCE7991B72355EA33C44DBCF260D09B6C921879A61AA4', '02417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3B')

PREPENDED:                               80E41B45E722251672C01A28E4FADA590471FEA09F90D13B143033ED3A1107EF49
PRIV_UNCOMP+CHECKSUM:                    80E41B45E722251672C01A28E4FADA590471FEA09F90D13B143033ED3A1107EF496CB6A884
Private_key_WIF_uncompressed_Base58:     5KYkFr9FMmBVcwjLbJinAw94b985tgyt4PL9Jhcjsk6J6ZRfxjM
PRIV_COMP+CHECKSUM:                      80E41B45E722251672C01A28E4FADA590471FEA09F90D13B143033ED3A1107EF4901070CD9AC
Private_key_WIF_compressed_Base58:       L4s7vXuQNe1KKeZsURDQNqxaqgrGb9U4MwZVf8GkEyCNTKyEk3iK
('5KYkFr9FMmBVcwjLbJinAw94b985tgyt4PL9Jhcjsk6J6ZRfxjM', 'L4s7vXuQNe1KKeZsURDQNqxaqgrGb9U4MwZVf8GkEyCNTKyEk3iK')
Public address uncompressed:     12sF1DbBbPaoNYrs28Qm7waiCcAVoF93Nn
Public address compressed:       1BMKGYmgjrvmSDtvLZvKjyVMnbi6FLmcVi

Editing original code by Jon Do request

import ecdsa
import hashlib
import base58

def bytes_to_hex_string(b: bytes):
    return ''.join('{:02x}'.format(x) for x in b).upper()

def get_prepend_if_even_or_odd_for_compressed(x_point):
    y = int(x_point[64:], 16)
    if y % 1 == 1:
        return "03"  # odd
    return "02"  # even

private_key = "e41b45e722251672c01a28e4fada590471fea09f90d13b143033ed3a1107ef49"

# Convert hex private key to bytes
private_key = bytes.fromhex(private_key)
print(f"Private key hex string: \t\t {bytes_to_hex_string(private_key)}")
print(f"Private key bytes: \t\t\t {private_key}")
# Derivation of the private key
signing_key = ecdsa.SigningKey.from_string(private_key, curve=ecdsa.SECP256k1)

verifying_key = signing_key.get_verifying_key()
print(f"Verifying key, x and y points (bytes):\t{verifying_key.to_string()}", type(verifying_key.to_string()))

x_point = bytes_to_hex_string(verifying_key.to_string())
print(f"Uncompressed private key (hex):\t\t 04{x_point.upper()}")

even_odd = get_prepend_if_even_or_odd_for_compressed(x_point)
print(f"Compressed private key in (hex):\t {even_odd}{x_point.upper()[:64]}")

# public_key = bytes.fromhex("04") + verifying_key.to_string()  # this is error, you're using uncompressed private key
public_key = bytes.fromhex(even_odd) + verifying_key.to_string()[:32]

# Hashes of public key
sha256_1 = hashlib.sha256(public_key)  # now public_key contains compressed private key
ripemd160 = hashlib.new("ripemd160")
ripemd160.update(sha256_1.digest())

# Adding prefix to identify Network
hashed_public_key = bytes.fromhex("00") + ripemd160.digest() # hashed_private_key is public key

# Checksum calculation
checksum_full = hashlib.sha256(
    hashlib.sha256(hashed_public_key).digest()).digest()
checksum = checksum_full[:4]

# Adding checksum to hashpubkey
bin_addr = hashed_public_key + checksum

# Encoding to address
address = str(base58.b58encode(bin_addr))
final_address = address[2:-1]  # change 2

print(f"Public compressed key (hex): \t\t {final_address}")

The new output is:

Private key hex string:                  E41B45E722251672C01A28E4FADA590471FEA09F90D13B143033ED3A1107EF49
Private key bytes:                       b'\xe4\x1bE\xe7"%\x16r\xc0\x1a(\xe4\xfa\xdaY\x04q\xfe\xa0\x9f\x90\xd1;\x1403\xed:\x11\x07\xefI'
Verifying key, x and y points (bytes):  b'AzUA=\x94\x8dy\xf5\x19O\x1f,\xd6p\xf0x\xcb\x7fm:/+\x12\xe8\xcd\xf9\xa3&\x8c\xad;\xaa\xa3%\x1d%\x87\xd4\xe5z\xcb\xcey\x91\xb7#U\xea3\xc4M\xbc\xf2`\xd0\x9bl\x92\x18y\xa6\x1a\xa4' <class 'bytes'>
Uncompressed private key (hex):          04417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3BAAA3251D2587D4E57ACBCE7991B72355EA33C44DBCF260D09B6C921879A61AA4
Compressed private key in (hex):         02417A55413D948D79F5194F1F2CD670F078CB7F6D3A2F2B12E8CDF9A3268CAD3B
Public compressed key (hex):             1BMKGYmgjrvmSDtvLZvKjyVMnbi6FLmcVi