RSA Implementation in TypeScript

This is a simple implementation of the RSA algorithm in TypeScript by John Gonsalves. The implementation includes key generation, encryption, decryption, and digital signature functionalities.

Prerequisites

• Node.js (v12.0.0 or higher)
• npm (Node Package Manager)

Setup

1. Clone or download this repository
2. Install the dependencies:

npm install

Running the Tests

The repository includes a test file (test.ts) that demonstrates both RSA encryption/decryption and digital signatures with example values.

To run the tests:

npx tsc && node dist/test.js

Modifying the Test Values

You can modify the test values in test.ts to try different numbers. Keep in mind:

• p and q should be prime numbers
• e should be coprime with (p-1)(q-1)
• The message should be a positive number less than n (where n = p * q)

Implementation Details

The implementation includes several key functions:

• gcd: Calculates the Greatest Common Divisor using the Euclidean algorithm
• multInverse: Calculates the Multiplicative Inverse using the Extended Euclidean algorithm
• keySchedule: Generates public and private key pairs
• rsaEncrypt: Encrypts a message using the public key
• rsaDecrypt: Decrypts a ciphertext using the private key
• RSA: Main function that demonstrates the complete encryption/decryption process
• RSA_DIGITAL_SIGNATURE: Function that demonstrates digital signature creation and verification

The implementation uses BigInt for handling large number calculations, which is necessary for real-world RSA operations.

Digital Signatures

The implementation includes a digital signature function that:

1. Creates a signature by encrypting a message with the private key
2. Verifies the signature by decrypting it with the public key
3. Compares the result with the original message to verify