RSA Encryption and Decryption Program

Introduction

This program is a demonstration of the RSA (Rivest-Shamir-Adleman) encryption and decryption algorithm, a widely utilized public-key cryptosystem. The RSA algorithm involves the use of two keys: a public key for encryption and a private key for decryption.

Features

• Key Generation: The program generates public and private keys based on user-input prime numbers (p and q).
• Encryption: Converts each character of the input message into its ASCII value and encrypts it using the RSA algorithm.
• Decryption: Decrypts the encrypted values back to ASCII and reconstructs the original message.

Usage

1. Prime Numbers:

   • Enter two prime numbers (p and q) to generate the public and private keys.
   • The program checks the primality of the provided numbers.

2. Key Generation:

   • The program computes the public key (e, n) and the private key d.

3. Encryption:

   • Each character of the input message is converted to its ASCII value.
   • The ASCII values are encrypted using the public key.

4. Decryption:

   • The encrypted values are decrypted using the private key.
   • The decrypted ASCII values are converted back to characters.

5. Security Note:

   • The program provides a simplified demonstration for educational purposes.
   • Real-world RSA implementations involve more sophisticated key generation and security measures.

How it Works

Key Generation

• Calculate n = p * q, where p and q are prime numbers.
• Compute Euler's totient function: phi = (p-1) * (q-1).
• Find a public exponent e such that 1 < e < phi and gcd(e, phi) = 1.
• Calculate the private exponent d as the modular multiplicative inverse of e modulo phi.

Encryption

• Convert each character of the input message to its ASCII value.
• Encrypt each ASCII value using the public key (e, n) with the formula: ciphertext = (plaintext^e) mod n.

Decryption

• Decrypt each encrypted ASCII value using the private key d with the formula: plaintext = (ciphertext^d) mod n.
• Convert each decrypted ASCII value back to its character representation.

Security Considerations

• The program uses a simplified method to calculate d, which may not be secure for real-world applications.
• In practice, secure key generation and management are critical aspects of RSA implementation.

How to Run

1. Compile and Run:

   • Compile the program using a C++ compiler.
   • Run the compiled executable.

2. User Input:

   • Follow the prompts to enter prime numbers (p and q) and a message for encryption.

3. Output:

   • Observe the encrypted and decrypted messages.

Feel free to explore and modify the code to enhance your understanding of RSA encryption.