Diffie-Hellman Algorithm - Simple Overview

Diffie-Hellman Algorithm allows two parties to agree on a Shared Secret Key while exchanging messages in Public.

Diffie Hellman is ONLY used for Key-Establishment. 

These keys might be used for any purpose depending on the protocol.

Diffie Hellman does not authenticate, so its possible to establish a Secret-Key with a Bad-Guy.

Technical Details

Diffie-Hellman relies on the difficulty of calculating Discrete Logarithms. 

• p is a Prime Number
• g is a Primitive Root of P
• (Primitive Root means -  p^k mod g  will return ALL values from (1, 2 , 3.....p-1) for the first p-1 values of k)
• p & g are public and can be intercepted during communication.

Protocol

1. Alice chooses private key "a"   

    Bob chooses private key "b"

2. A computes a public value A = p^a mod g

    B computer a public value B = p^b mod g

3. A and B are exchanged publicly 

4.  Alice calculates    K = B^a mod g  = p^ab mod g

     Bob calculates      K = A^b mod g  =p^ab mod g

5. K is the shared secret between Alice & Bob

Alice and Bob can now use K for whatever purpose they want.

Vulnerabilities

An attacker could be doing a man in the middle attack, by establishing two separate keys with Bob & Alice and then being the middleman in their conversation.

Solution: Authenticated Diffie Hellman Exchange.

1. Encrypt the Diffie-Hellman Exchange communication with a PRE-SHARED SECRET KEY.
2. Encrypt the Diffie-Hellman Value, with other side's public key.
3. Sign the Diffie-Hellman Value, with your side's private key.
4. Transmit a HASH(DiffieHellmanValue, Name, Pre-Shared-Secret) to the other side.