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1. Assume secure MACs exist. Prove that there exists a MAC that is secure (by Definition 4.2) but is not strongly secure (by Definition 4.3).

2. Consider the following MAC for messages of length ℓ(n) = 2n − 2 using a pseudorandom function F: On input a message m0||m1 (with |m0| = |m1| = n − 1) and key k ∈ {0, 1} n, algorithm Mac outputs t = Fk(0||m0) k Fk(1||m1). Algorithm Vrfy is defined in the natural way. Is (Gen, Mac, Vrfy) secure? Prove your answer.