1. Let Ex(): P → C and Dk(): C → P satisfy (2.1).

(a) Show that the function Ex(): P → C is injective; that is, show for all M, M' ε

P that the equation Ex (M) = EK (M') implies M = M'.

(b) Explain why and under which circumstances an encryption function should be injective.

(c) Assume that P equals C and is finite. Show that Ex (DK (C)) = C holds for all C ε C. Thus, if Dx (+) cannot be computed from Ex(), such a scheme could be used for digital signatures.