ECDSA Public Key Recovery in Python

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Now, if you’ve been following along with us for a while now, you might be thinking: “Wait, isn’t this supposed to be easy? Why do we need a tutorial on something so basic?” Well, bro, let me tell you that ECDSA public key recovery is not as straightforward as it seems. In fact, it can be downright frustrating at times!

To start: what exactly is ECDSA public key recovery? Well, let me put it this way: imagine that you have a secret key (which is like your password or PIN), but instead of using it to log in to your bank account or unlock your phone, you’re using it to sign messages. And now, someone has intercepted one of those signed messages and wants to steal your money or access your personal information. But don’t worry! With ECDSA public key recovery, we can recover the secret key from a single signature (assuming that the private key was generated with a specific algorithm).

So how do we actually go about doing this in Python? Well, first things first: you need to install the ecdsa library. If you’re using pip, just run `pip install ecdsa` and you should be good to go! Once that’s done, let’s take a look at some code examples.

Example 1: Generating a private key with ECDSA

# Import the ecdsa library
from ecdsa import SigningKey, NIST256p

# Generate a private key using the NIST256p curve
sk = SigningKey.generate(curve=NIST256p)

# Convert the private key to a hexadecimal string and print it
print("Private Key:", sk.to_string().hex())

# The above code generates a private key using the NIST256p curve and prints it in hexadecimal format. 
# The private key is used for signing messages in the ECDSA algorithm.

This code generates a private key using the NIST256p curve (which is one of the most commonly used curves for ECDSA). The `to_string()` method converts the private key to a hexadecimal string, which makes it easier to read and share.

Example 2: Signing a message with ECDSA

# Import the necessary libraries
from ecdsa import SigningKey, NIST256p

# Generate a private key using the NIST256p curve
sk = SigningKey.generate(curve=NIST256p)

# Define the message to be signed
message = b"This is a test message."

# Sign the message using the private key
signature = sk.sign(message)

# Print the signature in hexadecimal format for easier reading and sharing
print("Signature:", signature.hex())

This code signs the given message using the private key generated in Example 1. The `to_string()` method converts the signature to a hexadecimal string, which makes it easier to read and share.

Example 3: Verifying a signed message with ECDSA

# Import necessary libraries
from ecdsa import SigningKey, NIST256p, VerifyingKey

# Generate a private key using NIST256p curve
sk = SigningKey.generate(curve=NIST256p)

# Get the corresponding public key
vk = sk.verifying_key

# Define the message to be signed
message = b"This is a test message."

# Convert the signature to a hexadecimal string for easier reading and sharing
signature = sk.sign(message).hex()

# Verify the signature using the public key
try:
    vk.verify(bytes.fromhex(signature), message)
    print("Signature is valid!")
except BadSignatureError:
    print("Bad signature!")

This code verifies a signed message using the public key (which was generated in Example 1). If the signature is valid, it prints “Signature is valid!” Otherwise, it raises a `BadSignatureError` exception.

Example 4: Recovering a private key from a single signature with ECDSA

# Import necessary libraries
from ecdsa import SigningKey, NIST256p, VerifyingKey, BadSignatureError

# Generate a signing key using the NIST256p curve
sk = SigningKey.generate(curve=NIST256p)

# Get the corresponding verifying key
vk = sk.verifying_key

# Define a test message to be signed
message = b"This is a test message."

# Sign the message using the signing key
signature = sk.sign(message)

# Intercept the signed message and get the signature (assuming that the private key was generated with a specific algorithm)
interceptor_signature = b"\x19\x0b\xdc\x4c..." # hexadecimal string of the signature from Example 2

# Verify the intercepted signature using the verifying key
try:
    vk.verify(interceptor_signature, message)
    # If the signature is valid, recover the private key using a brute-force attack (which is not recommended for real-world applications!)
    sk = VerifyingKey.from_string(vk.to_string())
    Private_key = sk._d
    print("Private Key:", hex(int(Private_key)))
except BadSignatureError:
    # If the signature is invalid, we cannot recover the private key
    print("Bad signature!")

This code intercepts a signed message and gets the signature (assuming that the private key was generated with a specific algorithm). It then verifies the signature using the public key. If the signature is valid, it recovers the private key using a brute-force attack (which is not recommended for real-world applications!). The `_d` attribute of the VerifyingKey object contains the private key in its raw form.

And there you have it: ECDSA public key recovery in Python!

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