Question: Let G be a pseudorandom generator that maps n-bit inputs to (n+ 1)-bit outputs, and define G0 (s1, . . . , sn) = G(s1,

Let G be a pseudorandom generator that maps n-bit inputs to (n+ 1)-bit outputs, and define G0 (s1, . . . , sn) = G(s1, . . . , sn)||(s1 s2). Here s1, . . . , sn are the bits of the seed s, and || denotes concatenation. Is G0 a pseudorandom generator

Let F be a pseudorandom function (PRF) that takes an n-bit key and maps n-bit inputs to n-bit outputs. (We will cover pseudorandom functions in class on September 17th.) Which of the following derived PRFs are secure? Justify your answer.

(a) F 1 k (x) = Fk(x)||0

(b) F 2 k (x, y) = Fk(x) Fk(y)

(d) F 4 k (x) = Fk(x)||Fk(Fk(x))

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