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1. The basic Diffie-Hellman key exchange protocol is vulnerable to a "man-in-the-middle" attack, as explained in the textbook. Describe this attack.

2. Consider a cryptographic hash function f:{0,1}ⁿ -> {0,1}^h that satisfies the preimage resistance property and second preimage resistance property, even though it only works on fixed-size input blocks. Joe needs a function like this, but it has to work on pairs of n-bit inputs, so he defines g:{0,1}ⁿ×{0,1}ⁿ -> {0,1}^h as

   g(x,y) = f(x XOR y) .

   Is this function preimage resistant? Does it satisfy the second preimage resistance property? Justify both answers!

3. Prove that a hash function that satisfies the collision resistance property also satisfies the second preimage resistance property. (Hint: Write the statement you're trying to prove as an implication, and then prove the logical contrapositive.)