2. New Pseudorandom Function Family. (7+8+10) Let G be a length-doubling PRG G: {0, 1}B - {0, 1}2. Recall the basic GGM PRF construction presented below. . Define G(x) = (Go(x), G1(x)) where Go, G1 : {0, 1} B -> {0, 1}B . We define gid (X1, X2, . . . In) as Gan (. . . Gx2 (Gx, (id)) ...) where id {0, 1}, for a fixed value of n when the key id is picked uniformly at random from the set {0, 1} . (a) (7 points) Why is the above-mentioned GGM construction not a pseudorandom function family from the domain {0, 1}* to the range {0, 1}"? (Note that {0, 1}* means that the length of the input to the PRF is arbitrary) Solution