RSA

Introduction

The RSA Public Key Encryption System is a Haskell-based implementation of the RSA algorithm, showcasing key generation, encryption, and decryption. Named after its inventors Rivest, Shamir, and Adleman, this system uses a public and a private key to demonstrate public key cryptography and data security practices.

Project Structure

This project includes several components:

• Haskell Modules:

  • Main.hs: Contains the main executable logic, handling user inputs and orchestrating the encryption and decryption processes.
  • RSA.hs: Provides all the necessary cryptographic functions, including key generation, encryption, decryption, and helper functions for handling integers and strings.

• Cabal Configuration:

  • RSA-public-key-encryption-system.cabal: Configures the Haskell project, dependencies, and build information.

• Text Files:

  • public_key.txt and private_key.txt: Files where the public and private keys are stored.
  • messages.txt: This file stores encrypted messages in a persistable format.

• Additional Files:

  • LICENSE: Provides the licensing information.
  • CHANGELOG.md: Documents the chronological development and updates of the project.

Function Descriptions

RSA.hs Functions

• gcd: Computes the greatest common divisor of two integers using Euclid's algorithm, ensuring they are coprimes.
• extendedEuclid: Implements the Extended Euclidean Algorithm to find integers x and y such that they satisfy the equation ax + by = gcd(a, b).
• modInverse: Calculates the modular inverse of an integer e modulo φ, essential for deriving the private key in RSA.
• randomPrime: Generates a random prime number within a specified range, crucial for creating the RSA modulus.
• isPrime: Checks if a number is prime, a basic utility used during the generation of prime numbers for RSA.
• generateKeys: Generates a pair of RSA keys (public and private) using random prime numbers.
• findCoprime: Identifies an integer coprime to a given number, used to find a suitable public key exponent.
• powMod: Performs modular exponentiation, which is fundamental for RSA encryption and decryption operations.
• encrypt: Encrypts an integer message using a public key, applying the RSA encryption formula.
• decrypt: Decrypts an encrypted integer using a private key, reversing the RSA encryption process.
• stringToInts: Converts a string to a list of integers based on ASCII values, preparing text for encryption.
• intsToString: Converts a list of integers back to a string, reconstructing text from decrypted ASCII values.
• encryptString: Encrypts a string by converting it to integers and encrypting each integer.
• decryptString: Decrypts a list of encrypted integers to a string, combining decryption and ASCII conversion.

Main.hs Functions

• main: Initializes the application, generates keys, and starts the interactive encryption/decryption session.
• mainLoop: Manages user interaction for ongoing encryption and decryption tasks within a loop.
• savePublicKeyToFile: Saves the RSA public key to a file.
• savePrivateKeyToFile: Saves the RSA private key to a file.
• loadPublicKeyFromFile: Loads the RSA public key from a file.
• loadPrivateKeyFromFile: Loads the RSA private key from a file.
• saveMessagesToFile: Saves encrypted messages to a file for persistent storage.
• loadMessagesFromFile: Loads encrypted messages from a file, allowing for decryption or review.

Setup

To set up the RSA Public Key Encryption System, ensure you have the GHC (Glasgow Haskell Compiler) and Cabal installed. Proceed with the following steps:

1. Clone the repository:

   git clone https://github.com/ibrahimrl/RSA-Encryption.git

2. Navigate to the project directory:

    cd RSA-Encryption

3. Build the project using Cabal:

   cabal build

4. Run the executable::

   cabal run

Usage

Key Generation

Upon initial startup, the system automatically generates a public and private key, saving them in public_key.txt and private_key.txt.

Encrypting Messages

1. Run the application.

2. Select 'encrypt' by typing e when prompted.

3. Enter the message you wish to encrypt and press enter.

4. The encrypted message will be displayed and saved to messages.txt.

Decrypting Messages

1. Run the application.

2. Select 'decrypt' by typing d when prompted.

3. Enter the encrypted message. Copy this from messages.txt or your previous output.

4. The program will display the decrypted message, revealing the original text.

Managing Keys

• View Keys: Open public_key.txt and private_key.txt to view your RSA keys.

• Regenerate Keys: Delete the existing key files and restart the application to generate new keys.

Additional Information

• Security Note: This implementation is intended for demonstration purposes. The generated keys may need to be larger for secure applications.

Contact

For queries or contributions, please contact the project maintainer at ibrahim.rahimli20016@gmail.com

License

This project is licensed under the MIT License.