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Information Assurance: Homework 3 Solution
Due February 19, 2009 on compass.
1. In a monoalphabetic cryptosystem, LKZLP can be the cipher text for which of the following plain texts?
a) array
b) atlas
c) ample
d) angry
Because the cryptosystem is monoalphabetic, the first and the fourth letters must be the same in the plaintext, but not other letters. (slide # 14 of lecture 4)
2. An English word has been encrypted to QAOPERTYEIAS. What type of cipher is used?
a) Transposition Cipher
b) Substitution Cipher
In English words, Q is always followed by U. There is no U in this word, so it must be a substitution cipher. (slide # 39 of lecture 4)
3. In the Vigenere cryptosystem, what is the cipher text corresponding to the plaintext “HELLO WORLD” and the key “ENG”?
a) PLOOK WKQOI
b) LWRRT ILSRT
c) LRRPB CSERH
d) DRFHB QKEFZ
H+E=L, E+N=R, L+G=R, E+L=P, etc. (slide # 24 of lecture 4)
4. In the DES cryptosystem, S-boxes are:
a) Non-linear and one-to-one functions
b) Linear and one-to-one functions
c) Non-linear and many-to-one functions
d) Linear and many-to-one functions
(slide # 19 of lecture 5)
S-Boxes get 6-bit inputs and output 4-bits, so they are many-to-one and non-linear functions. Also a counter example for non-linearity:
S1(1)=0
S1(2)=4
S1(3)=15
S1(1+2)=S1(3)=15
S1(1)+S1(2)=4
S1(1+2)!=S1(1)+S1(2) , so it is non-linear. (slide # 20 of lecture 5)
5. Which property of the f function in a Feistel network is crucial to its working and security:
a) Invertible
b) Non-linear
c) Both a and b
d) None of the above
The elegance of the Fiestel network is that f can be non-invertible. Non-linearity, on the other hand, is crucial because otherwise the entire network will be linear and easily breakable. (slide # 11 and 19 of lecture 5)
6. The text “Brain: an apparatus with which we think we think” is encrypted using a block cipher to “FGRJIJUPO LPUZSUYTJ HGTLKYQTR KOUJFCZAQ GZRALKJUK PKIOPUXSA LOSREKHTA PKIOPUXSA LOSREKHTA”. Which block cipher mode was used? (Assume that the block size is a word of 9 letters. If a word is shorter, it is padded to 9 letters)
a) ECB
b) CBC
“We think” is repeated twice in the plaintext. The corresponding cipher text “PKIOPUXSA LOSREKHTA” is also repeated twice, so the mode cannot be CBC. (slide # 32 of lecture 5)
7. In a 128-bit LFSR which of the following is true about its period?
a) Period is 2128-1
b) Period is 264-1
c) Period can be larger than 2128-1
d) Period cannot be determined with the information provided
Period depends on the feedback function. (slide # 43 of lecture 5)
8. In a Diffie-Hellman key exchange session, if p=73, public key of Alice=18, private key of Alice=34, and private key of Bob=23, what is the shared key?
a) 36
b) 43
c) 57
d) The information is not enough; we have to know the value of g
Shared key = 1823 mod 73 = 36. (slide # 10 of lecture 6)
Note that you don’t need g to calculate the shared key.
You can use Windows Calculator (scientific mode) for such calculations.
9. Which of the following is true for an integer w>0:
a) Φ(w) = w-1 (Φ denotes the Totient function)
b) w can be used as the modulus in the RSA algorithm
c) If s is prime number (w<s), then ws ≡ w (mod s)
d) All of the above
(a) is only true when w is a prime and (b) is only true when p is a product of two primes. (c) is always true (Fermat’s theorem). (slide # 8 of lecture 6)
10. In an RSA cryptosystem, p=23, q=5, Alice’s public key= (5, 115), and Alice’s private key=53. Bob wants to send a number to Alice which only Alice can read. He encrypts it and sends the encrypted number 96 to Alice. What is the plaintext number?
a) 33
b) 34
c) 35
d) 36
Bob encrypts the message with Alice’s public key. Alice must decrypt it with her private key. (slide # 16 of lecture 6)
M=cd mod n = 9653 mod 115 = 36