Interactive RSA Cryptography Demo

This is a fully browser-based web application that demonstrates the RSA encryption/decryption process. It uses the Square and Multiply algorithm for efficient modular exponentiation and is designed as an educational tool.

Live Demo: [Link to your GitHub Pages URL]

Technologies Used

• HTML5
• CSS3
• Vanilla JavaScript (with BigInt for large number arithmetic)

Features

• RSA Key Generation: Input two primes p and q to generate a public/private key pair.
• Encryption/Decryption: Encrypt a numeric message with the public key and decrypt it with the private key.
• Square and Multiply: The application uses and displays the step-by-step process of the Square and Multiply algorithm for all exponentiation operations.
• Input Validation: Ensures that inputs are prime and that messages are valid.
• No Backend: All computations are performed in the client's browser.

Setup Instructions

To run this project locally:

1. Clone the repository: git clone https://github.com/<your-username>/<your-repo-name>.git
2. Navigate to the project directory: cd <your-repo-name>
3. Open the index.html file in your web browser.

Explanation of a Key Algorithm

Square and Multiply

The Square and Multiply algorithm (also known as binary exponentiation) is used to compute b^e mod m efficiently. Instead of performing e-1 multiplications, it reduces the complexity significantly.

The algorithm works by processing the bits of the exponent e from left to right.

1. Start with a result of 1.
2. For each bit in the binary representation of e: a. Square the current result: result = (result * result) mod m. b. If the bit is 1, multiply the result by the base: result = (result * b) mod m.
3. After iterating through all bits, the final result is the answer.

This implementation uses JavaScript's native BigInt to handle the large numbers that are common in RSA.