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Decrypt the Derivation Path of a Bitcoin Address

Hello, fellow Bitcoiners.

While studying Bitcoin, I came across a problem that I wanted to ask: how can I determine with which derivation path a given Bitcoin address 1xxxxxxxxxxxx was created? In this article, I will explain how to deduce the derivation path of a given address.

Understanding the Bitcoin Address Format

Before we dive into the derivation path, let’s take a quick look at the structure of Bitcoin addresses. A Bitcoin address consists of eight hexadecimal characters, divided into three parts:

• Version: The first four characters represent the version of the Bitcoin protocol.

• Checksum: The next two characters are a checksum, which is used to verify the integrity of the transaction data.

• Index

  

  : The last four characters represent the index in the blockchain.

Derivation Paths

Bitcoin uses a cryptographic technique called Elliptic Curve Diffie-Hellman (ECDH) to derive private keys from public keys. The derivation path is based on the following rules:

• For each derivation step, we need two actions:

+
Public key: x

+
Shared secret: y

Deduce the derivation path from the address

Now let’s apply these rules to deduce the branch path from a given address.

• Check if the first four characters are a version number (0x…). If not, the address is unlikely to be valid.

• Extract the checksum (the last two characters) and verify its integrity using tools like the gethash command in the terminal or by checking with your local Bitcoin client.

If both checks pass, we can proceed to extract the index from the next four characters:

• Take the last four characters (xxxxxxxxxx) as input for the ECDH derivation.

• Compute the corresponding shared secret y using a key generator like secp256k1-gen.

Once you have y, you can obtain the public key x by performing modular exponentiation with p-1 (where p is the maximum block weight of the network). This will give you another random number.

Example for demonstration

Let’s assume we have a valid address 1234567890abcdef, where:

*The first four characters are not a version number.

• The checksum is correct.

• Extract the index from xxxxxxxxxxxx.

Here is how we can calculate the shared secret and public key using Python code:

import hashlib

Set ECDH settings
p = 1_000_000_007 
Maximum network block weight (256 bits)
q = p * p
n = q - 1
e = 65537
d = e ** (-1)

Deduce the shared secret y using the BLS signature scheme
y = hashlib.blake2b((p, n) + ((hashlib.sha256(b'') + bytes([x])).digest(),)).digest()[:32]

Calculate the public key x by modular exponentiation with p-1
public_key_x = pow(y, d, p - 1)

The derived private key is our input for further derivation

Conclusion

In In conclusion, deciphering the derivation path of a Bitcoin address requires knowledge of the ECDH algorithm and tools like gethash to verify the checksum. By following these steps, you can deduce the derivation path of a given address, which can be useful in various applications such as wallet verification or private key management.

However, please note that this is just an example explanation and may not cover all possible scenarios or edge cases. Always consult experts or use trusted sources when dealing with crypto systems.

I hope this article was helpful to you! Do you have any questions or want to learn more about Bitcoin?