Question

Note: It is possible to encrypt/decrypt problems 2-5 using online calculators. For this reason, it is
important that sufficient work is shown in order to demonstrate your understanding of the material.
Answers which simply include the final encrypted/decrypted message but do not include all necessary
steps will be awarded no credit.

1. Find the following Euler Totients using Euler’s Theorem, as explained on p.409 of the
text (10 points each):
a.ϕ(13)
b.ϕ(81)
c.ϕ(100)
d.ϕ(102)

2. Use a Hill Cipher to encode the following message: “BATTLESHIP SUNK.” Use the
following matrix as your key (15 points):
4 6 0
3 2 2
7 1 2

3. Bob is arguing that if you use output feedback (OFB) mode twice in a row to encrypt a
long message, M, using the same key each time, it will be more secure. Explain why Bob
is wrong, no matter what encryption algorithm he is using for block encryption (15
points).

4. Suppose you wish to encrypt the message, M = 42 using RSA encryption. Given a public
key where p = 23 and q = 11 and the relative prime e = 7. Find n, and show all necessary
steps to encrypt your message (42). (Hint: check p.411 of the text for information on
public key RSA) (15 points)

5. Now suppose you receive an encrypted message, C = 287. Given that p = 13 and q =
29 and that e = 5, show all necessary steps to decrypt the message, and then give the
final plaintext decryption of the message. (15 points)

Answer 1

Answer:

1.

2.

3&4&5