RSA

A Python-based exploration of RSA public-key cryptography and integer factorization. Includes tools to generate large primes, create RSA key pairs, encrypt/decrypt files, and test factorization vulnerabilities using Brute Force and Fermat's method. Created as a high school final project.

RSA Encryption & Factorization Explorer

🚀 Project Overview

This repository contains my final high school project, focusing on the mechanics of RSA public-key cryptography. It is a hands-on implementation of how RSA encryption works under the hood, accompanied by mathematical factorization algorithms designed to test how these keys can be broken.

📁 Features & Modules

Core Cryptography

• makePublicPrivateKeys.py: Generates RSA public and private key files using randomly generated large primes.
• publicKeyCipher.py: Encrypts standard text into block integers and decrypts it back to readable text using the generated key files.

Mathematical Utilities

• primeNum.py: Handles prime number logic, including a Sieve of Eratosthenes and the Rabin-Miller primality test for generating secure keys.
• cryptomath.py: Contains essential mathematical functions, such as finding the Greatest Common Divisor (Euclid's Algorithm) and modular inverses (Extended Euclidean Algorithm).

Factorization & Cracking Tools

• bruteForce.py: A brute-force trial division script with a timer to test how long it takes to factorize a given modulus.
• fermat.py & fermat.sage: Implementations of Fermat's factorization method in both Python and SageMath to efficiently find factors of odd positive integers.

⚙️ How to Use

1. Generate Keys: Run makePublicPrivateKeys.py to create your public (_pubkey.txt) and private (_privkey.txt) keypair files.
2. Encrypt & Decrypt: Run publicKeyCipher.py in the same directory as your key files. You can toggle the mode variable inside the script to either 'encrypt' a message to a file or 'decrypt' an existing file.
3. Test Factorization: Run bruteForce.py or fermat.py to time how long it takes your machine to factorize large integers.

📚 Acknowledgments

• Core cryptography logic and mathematical utilities are based on the BSD-licensed Cracking Codes with Python by Al Sweigart.
• The Python implementation of Fermat's factorization was inspired by GeeksforGeeks.