Diffie Hellman Key Exchange

Enter Prime Number P:

Enter Primitive Root G:

Alice's Private Key A:

Bob's Private Key B:

Introduction

The Diffie Hellman (DH) Algorithm is a key-exchange protocol that enables two parties communicating over public channel to establish a mutual secret without it being transmitted over the Internet.
This revolutionary algorithm was proposed by Whitfield Diffie and Martin Hellman in 1976, enabling two entities to agree upon a secret key without prior arrangements, even in the presence of potential eavesdroppers.

Working of Diffie-Hellman Key Exchange

Alice and Bob must agree upon two number:
- A large prime number P.
- A generator G, which is the primitive root of P.
Alice and Bob randomly chose a private key, say A and B for Alice and Bob respectively.
- These private keys are kept secret and not being shared.
Both Alice and Bob perform a calculation to generate their corresponding public keys.
- Alice's Public Key → X_A = G^AmodP
- Bob's Public Key → Y_B = G^BmodP
- The public key are then shared with each other, X_A is shared with Bob and Y_B is shared with Alice.
Both Alice and Bob then calculates the Shared Secret Key using the public key received.
- Alice's Secret Key → K_A = Y^A_BmodP
- Bob's Secret Key → K_B = Y^B_AmodP
K_A = K_B, Alice and Bob now both have shared secret keys, which can be used for encryption and decryption of information using symmetric key algorithms.

Security

The security of the Diffie-Hellman key exchange is dependent on how it is implemented, as well as the numbers that are chosen for it. Diffie-Hellman has no means of authenticating the other party by itself, but in practice other mechanisms are used to ensure that the other party in a connection is not an impostor. As long as it is implemented alongside an appropriate authentication method and the numbers have been selected properly, it is not considered vulnerable to attack.