privFIND.md

Classes and Methods:

ECPoint Class (Imported):

• Represents a point on an elliptic curve.
• Attributes:
• • x (int): The x-coordinate of the point.
• • y (int): The y-coordinate of the point.
• • infinity (bool): A flag indicating whether the point is the point at infinity (neutral element for group operation on the curve).

Secp256k1 Class (Extended):

• Represents the secp256k1 elliptic curve and provides methods for elliptic curve operations.

• New Method Added:

• • find_private_key: Attempts to find the private key given a public key and a generator point using a brute force approach.

find_private_key Method:

• Purpose: To find the private key (d) given a public key (public_key) and a generator point (generator_point) on the secp256k1 elliptic curve.

• Parameters:

• • public_key (ECPoint): The public key point.
• • generator_point (ECPoint): The generator point G of the secp256k1 curve.

• Returns: The private key d if found, otherwise None.

• Process:

• • Initializes current_point at the point at infinity.
• • Iterates over possible scalar values d.
• • Performs point addition on the curve and checks if the resulting point matches the given public_key.
• • Returns d if a match is found, indicating the private key corresponding to the given public key.

Example Usage:

• The example demonstrates how to use the find_private_key method to attempt to find the private key corresponding to a given public_key and generator_point.
• It initializes an example public_key with specific x and y coordinates.
• It calls the find_private_key method and prints the result.

Important Notes:

• The find_private_key method implements a brute force approach and is computationally infeasible for large-scale numbers typical in real-world elliptic curve cryptography (like secp256k1).
• This code is for educational purposes to demonstrate the concept of the discrete logarithm problem in elliptic curve cryptography.
• In actual cryptographic practice, private keys are kept secret, and finding a private key from a public key is intentionally computationally infeasible.
• Always use secure, well-tested cryptographic libraries for real-world applications.

This documentation provides an overview of the code, its structure, the functionality of each part, and important notes regarding its use and the limitations of the approach used in the find_private_key method.