1. Suppose the variables X and Y in the following Bare Bones program have the values 3 and 2, respectively, when execution begins. What will be the value of Z when the program terminates? (PLEASE EXPLAIN WHY)

clear Z

while X not 0:

decr X

incr Z

while Y not 0:

decr Y

incr Z

2. If x^a mod n = c and x^b mod n = d then x^a+b mod equals (PLEASE EXPLAIN WHY)

A. c + d mod n

B. c*d mod n

C. c^d mod n

D. None of the above

3. Use the two primes 11 and 19, one possible encryption (e) and decryption (d) key is 13 97 since (13*97)-1 = 7*180 which of the following would be another suitable encryption key (e) and a decryption key (d) (PLEASE EXPLAIN WHY)

A e == 19 d == 19 B e == 17 d == 53 C. e == 15 d == 103

D e == 3 d == 47 E. e == 29 d == 143 F. e == 31 d == 53

a: A B

b: A B F

c: B C

d: A

4. Is the following congruence equation true ? (PLEASE EXPLAIN WHY)

7823 = -3 mod 77

A: Yes

B: No

C: Cannot be determined

5. Knowing the public keys to the RSA public-key encryption are n = 77 and e = 7, what are the private keys. (PLEASE EXPLAIN WHY)

A: 41

B: 43

C: 7

D: None of the above

6. Which of the following statement(s) are true.

A: P is contained in NP.

B: All solvable problems are in P.

C: The traveling salesman problem is in NP.

D: The traveling salesman problem is not solvable.

Z == 6

Z == 5

Z == 4

None of the above