. Let G: {0, 1}^→ {0, 1}³ be a secure length-tripling PRG. For each function below, state whether it is also a secure PRG. If the function is a secure PRG, give a proof. If not, then describe a successful distinguisher and explicitly compute its advantage. When we write a||b||c := G(s), each of a, b, c have length 1. H(s): (a) x|ly||z := G(s) return G(x)||G(z) H(s): (b) xyz = G(s) return x|ly (c) H(s): x := G(s) y := G(s) return x|ly (d) (e) H(s): x := G(s) y := G(0¹) return x||y H(s): x := G(s) y := G(0¹) return x + y

. Let G: {0, 1}^→ {0, 1}³ be a secure length-tripling PRG. For each function below, state whether it is also a secure PRG. If the function is a secure PRG, give a proof. If not, then describe a successful distinguisher and explicitly compute its advantage. When we write a||b||c := G(s), each of a, b, c have length 1. H(s): (a) x|ly||z := G(s) return G(x)||G(z) H(s): (b) xyz = G(s) return x|ly (c) H(s): x := G(s) y := G(s) return x|ly (d) (e) H(s): x := G(s) y := G(0¹) return x||y H(s): x := G(s) y := G(0¹) return x + y