Diffie-Hellman Key Exchange

 1. Diffie-Hellman Key Exchange :

It is a kind of method of securily exchanging the cryptographic key over a public channel. Figure 1 explains the functionality of proposed algorithm.


Fig. 1: The Diffie-Hellman Key Exchange

Note 1. In Diffie-Hellman algorithm the key exchange by both the person say Bob and Alice are same. 

Since We know that

K = (Yb)^(Xa) mod q                                { as we know Yb = α^(Xb) mod q)}

 = ((α^(Xb) mod q))^(Xa) mod q

 = α^(XaXb) mod q

 = (α^(Xa) mod q)^(Xb) mod q

 = (Ya^(Xb) mod q)

Hence, above calculation shows that both keys are same. 

 

1.1 Man-in-the-Middle Attack 

Since if the value is small then it can be easily break with brute force approach. 

The protocol depicts in diffie hellman algorithm is insecure against a man in middle attack. Suppose Alice and Bob wish to exchange keys, and Darth is the adversary. The attack proceeds as follows.(as shown in Fig. 2).


Fig. 2 Man-in-Middle Attack

Bob and Alice think that they shares a secret key, but instead Bob and Darth share secret key K1 and Alice and Darth shares secret key K2. All future communication between Bob and Alice is compromised in the following way.

1. Alice sends an encrypted message M: E(K2,M).

2. Darth intercepts the encrypted message and decrypts it to recover M.

3. Darth sends Bob E(K1,M) or E(K1,M'), where M' is any message. In the first case, Darth simply wants to eavsedrop on the communication without altering it. In the second case, Darth wants to modify the message going to Bob. 


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