Let N be a large integer and let K = M = C = Z/NZ. For each of the functions e: K times M rightarrow C listed in (a) - (c), answer the following questions: Is e an encryption function? If e is an encryption function, what is its associated decryption function d? If e is not an encryption function, can you make it into an encryption function by using some smaller, yet reasonably large, set of keys? e_k(m) k - m (mod N). e_k(m) k middot m (mod N). e_k(m) (k + m)^2 (mod N).

Use a physical stopwatch to record the length of time it takes to run the program. calculate the difference obtained by calls to the method system.currenttimemillis() just before the start of the algorithm and just after the end of the algorithm. calculate the difference obtained by calls to the method system.currenttimemillis() at the start of the program and at the end of the program so that the elapsed time includes the display of the result. use the value returned by the method system.currenttimemillis() just after the end of the algorithm as the elapsed time.