Cryptography: Diffie-Hellman Key Exchange - Example

 

•Key exchange is based on the use of the prime number q = 353 and a primitive root of 353, in this case a = 3. A and B select secret keys XA = 97 and XB = 233, respectively. Each computes its public key:

A computes YA = 397 mod 353 = 40.

B computes YB = 3233 mod 353 = 248.

•After they exchange public keys, each can compute the common secret key:

A computes K = (YB)XA mod 353 = 24897 mod 353 = 160.

B computes K = (YA)XB mod 353 = 40233 mod 353 = 160.

•We assume an attacker would have available the following information:

q=353; a=3; YA =40; YB =248

In this simple example, it would be possible by brute force to determine the secret key 160. With larger numbers, the problem becomes impractical. 

•What kind of attacks is possible here?

–Man-in-the-middle attack.

•Why is it vulnerable to MITM?

•The key exchange protocol is vulnerable to such an attack because it does not authenticate the participants.

•How to get protected?

•This vulnerability can be overcome with the use of digital signatures and public-key certificates