ECDLP_Pollard_Rho

Elementary Pollard's Rho for ECDLP

This repository contains a basic, elementary implementation of Pollard's Rho algorithm for solving the Elliptic Curve Discrete Logarithm Problem (ECDLP). The code is designed to be simple and clear for educational purposes.

⚠️ Security Warning: For Educational Use Only ⚠️

This code is intended for learning and demonstration purposes only. It is a simplified, "textbook" implementation and is NOT CRYPTOGRAPHICALLY SECURE. Real-world elliptic curve cryptography relies on the difficulty of solving the ECDLP; this code is an attack on that problem and demonstrates how it can be broken for small parameters. DO NOT use this code in any production environment, for real-world applications, or with sensitive data. Key limitations include:

• It is not optimized and is only feasible for curves with a very small group order.
• It lacks necessary safeguards and may fail or crash on certain inputs.
• It is not a robust or reliable cryptographic tool.

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Purpose

The primary goal of this repository is to provide a straightforward example of how Pollard's Rho algorithm can be applied to solve the ECDLP. It is a learning tool for students and enthusiasts interested in elliptic curve cryptography and number theory algorithms.

Usage

The elliptic curve parameters (such as the prime field, curve coefficients, and base point order) and the points $P$ and $Q$ must be defined within the script itself. Once the parameters are configured in the code, you can execute the script.