1. Assume pseudorandom permutations exist. Show that there exists a function F’ that is a…

1. Assume pseudorandom permutations exist. Show that there exists a function F’ that is a pseudorandom permutation but is not a strong pseudorandom permutation.

2. Let F be a pseudorandom permutation, and define a fixed-length encryption scheme (Enc, Dec) as follows: On input m ∈ {0, 1} n/2 and key k ∈ {0, 1}n, algorithm Enc chooses a uniform string r ∈ {0, 1} n/2 of length n/2 and computes c := Fk(r||m).

Show how to decrypt, and prove that this scheme is CPA-secure for messages of length n/2. (If you are looking for a real challenge, prove that this scheme is CCA-secure if F is a strong pseudorandom permutation.)

 

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