Diffie-Hellman Key Exchange Eve, an attacker, can alter messages that Alice and
ID: 3855246 • Letter: D
Question
Diffie-Hellman Key Exchange
Eve, an attacker, can alter messages that Alice and Bob send to each other without their knowing. To do this she intercepts (and makes some changes to) the exchanges Alice and Bob make with each other. Discover this method and describe it to me. Hint: You should be attacking the key-exchange. Find a method so that Alice and Eve have shared keys and Eve and Bob have shared keys (even though Alice thinks she is communicating with Bob and Bob thinks he is communicating with Alice). And remember that Eve can intercept any message Alice sends to Bob and vice versa. This means that she can stop the message from reaching its destination and send another in its place.
Explanation / Answer
Eve, an attacker can alter messages that Alice and Bob send to each other without knowing. To do this, Eve intercepts the exchanges Alice and Bob make with each other. A method so that Alice and Eve have shared keys and Eve and Bob have shared keys is as follows:
The method uses Diffie-Hellman key exchange protocol to generate a shared key between Alice and Eve, Eve and Bob using a public channel.
Let there be a prime number p and r be the generator, both of p and r are publicly known parameters. Let the random number selected by Alice be a. The message sent by Alice to Bob is . Let the random number selected by Bob be b and sends the message to Alice.
The shared key is . This shared key is computed by Alice as and Bob as . The encrypted message is as follows: where M is the message.