Diffie-Hellman Key Exchange Algorithm

The Diffie-Hellman key exchange algorithm, also known as the Diffie-Hellman protocol, enables secure key sharing between two parties over an insecure communication channel. It allows both parties to agree upon a shared secret key without directly transmitting it.

How it Works

1. Initialization:

   • Both parties, let's call them Alice and Bob, agree on two public parameters: a prime number ( p ) and a base ( g ), where ( g ) is a primitive root modulo ( p ). These parameters are publicly known.

2. Key Generation:

   • Each party generates their own private key. Alice chooses a private key ( a ) and Bob chooses a private key ( b ). These private keys are kept secret.

3. Public Key Calculation:

   • Alice computes her public key ( A = g^a \mod p ) and sends it to Bob.
   • Bob computes his public key ( B = g^b \mod p ) and sends it to Alice.

4. Shared Secret Calculation:

   • Upon receiving the public key from the other party, each party computes the shared secret using their own private key and the received public key.
   • Alice computes ( s = B^a \mod p ) and Bob computes ( s = A^b \mod p ).
   • Both parties arrive at the same shared secret ( s ), which can be used as the encryption key for secure communication.

Implementation Details

This implementation consists of the following components:

• KeyChanging Class:

  • Represents the structure required for the Diffie-Hellman key exchange algorithm, including public prime number, public generator number, and private secret number.

• SquareAndMultiply Function:

  • Implements the square and multiply algorithm to perform modular exponentiation efficiently, which is a crucial part of the Diffie-Hellman key exchange.

• decryptTheKey Function:

  • Performs the key exchange process between two parties, Alice and Bob, based on their private and public parameters.

Usage

1. Enter the public prime number (( p )) and public generator number (( g )).
2. Enter the private keys for both Alice and Bob.
3. The program will calculate the shared secret key for both parties and display the results.

About

This implementation serves as a demonstration of the Diffie-Hellman key exchange algorithm in action, providing a practical understanding of how secure key sharing can be achieved in cryptographic protocols.