Let G be a PRG that stretches the input by two (i.e., G : {0,1} ...

Transcribed Image Text:

Let G be a PRG that stretches the input by two (i.e., G : {0,1}" → {0, 1}2n). Consider the following function F and show it is not a PRF. The function F takes an n bit key and a 2n bit input x and is defined as follows: F₁(x) = = x G(xLXRk) where are the left n bits of x and æ are the right n bits of x. Do this by constructing a distinguisher and computing P(DF(-) = 1) and P(Dƒ() = 1) and showing the difference between the two probabilities is large. f() is a random function. Let G be a PRG that stretches the input by two (i.e., G : {0,1}" → {0, 1}2n). Consider the following function F and show it is not a PRF. The function F takes an n bit key and a 2n bit input x and is defined as follows: F₁(x) = = x G(xLXRk) where are the left n bits of x and æ are the right n bits of x. Do this by constructing a distinguisher and computing P(DF(-) = 1) and P(Dƒ() = 1) and showing the difference between the two probabilities is large. f() is a random function.