Consider the following key exchange protocol:

a) Alice chooses uniform k,r {0,1}n , and sends s = kr to Bob.

b) Bob chooses uniform t {0,1}n , and sends u = st to Alice.

c) Alice computes w = ur and sends it to Bob.

d) Alice outputs k and Bob outputs wt.

Show that Alice and Bob output the same key.

Analyze the security of this scheme: Either prove its security or show a concrete attack.