Alice and Bob use the Diffie-Hellman to create two keys k1 and k2. In generating

Question

Alice and Bob use the Diffie-Hellman to create two keys k1 and k2. In generating k1, Alice selects a random number x and computes SA = gx mod p. Bob selects a random number y and computes SB = gy mod p. Alice and Bob exchange SA and SB, and k1 = gxy mod p. In generating k2. Alice chooses another random number x’ but Bob still uses the same random number y. Suppose an eavesdropper knows that x and x’ differ each other by t (i.e., either x-x’ = t or x’-x=t). Given the knowledge of k1 and a pair of plaintext M and ciphertext C encrypted by k2, can the eavesdropper find out k2?

Explanation / Answer

Solution:

Yes, the evesdropper can find k2 since he has the info about x and x',

he can easily intercept k2, and if the k2 to intercepted then based on the knowledge of that, k1 can be intercepted as well. since Bob has used the same random number y.

after k1 is intercepted, the eavesdropper will be able to figure out the SA and SB as well.

Hence the k2 key is also compromised.

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