UNIVERSITY OF UYO
DEPARTMENT OF ELECTRICAL/ELECTRONICS & COMPUTER ENGINEERING
SESSION: 2019/2020 SEMESTER: SECOND
COURSE CODE/TITLE: CPE 823 ADVANCED CRYPTOGRAPHY AND DATA
SECURITY
INSTRUCTION: ANSWER FIVE QUESTIONS ONLY
Time: 3hrs
Question 1
a.
b.
c.
d.
e.
f.
What are the essential ingredients of a symmetric cipher?
What are the two basic functions used in encryption algorithms?
How many keys are required for two people to communicate via a cipher?
What is the difference between a block cipher and a stream cipher?
What are the two general approaches to attacking a cipher?
A generalization of the Caesar cipher, known as the affine Caesar cipher,
has the following form: For each plaintext letter p, substitute the ciphertext
letter C:
C = E([a, b], p) = (ap + b) mod 26
A basic requirement of any encryption algorithm is that it be one-toone. That is, if p _ q, then E(k, p) _ E(k, q). Otherwise, decryption is
impossible, because more than one plaintext character maps into the
same ciphertext character. The affine Caesar cipher is not one-to-one
for all values of a. For example, for a = 2 and b = 3, then E([a, b], 0) =
E([a, b], 13) = 3.
i. Are there any limitations on the value of b? Explain why or
why not.
ii.
Determine which values of a are not allowed.
iii. Provide a general statement of which values of a are and are
not allowed. Justify your statement.
Question 2
a. What is the OSI security architecture?
b. What is the difference between passive and active security threats?
c. List and briefly define categories of passive and active security attacks.
d. List and briefly define categories of security services.
e. List and briefly define categories of security mechanisms.
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Question 3
a.
b.
c.
d.
e.
Why is it important to study the Feistel cipher?
What is the difference between a block cipher and a stream cipher?
What is a product cipher?
What is the difference between diffusion and confusion?
Consider a block encryption algorithm that encrypts blocks of length n,
and let N = 2n. Say we have t plaintext–ciphertext pairs Pi, Ci = E(K, Pi),
where we assume that the key K selects one of the N! possible mappings.
Imagine that we wish to find K by exhaustive search. We could generate
key K_ and test whether Ci = E(K_, Pi) for 1 … i … t. If K_ encrypts each
Pi to its proper Ci, then we have evidence that K = K_. However, it may be
the case that the mappings E(K, #) and E(K_, #) exactly agree on the t
plaintext–cipher text pairs Pi, Ci and agree on no other pairs.
i. What is the probability that E(K, #) and E(K_, #) are in fact
distinct mappings?
ii. What is the probability that E(K, #) and E(K_, #) agree on
another t_ plaintext–ciphertext pairs where 0 … t_ … N - t?
Question 4
a. Suppose the DES F function mapped every 32-bit input R, regardless of the
value of the input K, to i) 32-bit string of one, ii) bitwise complement of R
Hint: Use the following properties of the XOR operation:
1. What function would DES then compute?
2. What would the decryption look like?
(A_ B) _ C = A_ (B _ C)
A_ A = 0
A_ 0 = A
A_ 1 = bitwise complement of A
Where A, B, C are n-bit strings of bits 0 is an n-bit string of zeros, 1 is an n-bit
string of one
b. What is the difference between diffusion and confusion?
c. Which parameters and design choices determine the actual algorithm of a
Feistel cipher?
d. Explain the avalanche effect.
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Question 5
a.
b.
c.
d.
Briefly define a group.
Briefly define a ring.
Briefly define a field.
For the group Sn of all permutations of n distinct symbols,
i. What is the number of elements in Sn?
ii.
show that Sn is not abelian for n > 2.
e. A modulus of 0 does not fit the definition but is defined by convention as
follows:
a mod 0 = a. With this definition in mind, what does the following expression
mean: a K b (mod 0)?
Question 6
a. What was the original set of criteria used by NIST to evaluate candidate
AES ciphers?
b. What was the final set of criteria used by NIST to evaluate candidate AES
ciphers?
c. What is the difference between Rijndael and AES?
d. What is the purpose of the State array?
e. In the discussion of Mix Columns and InvMixColumns, it was stated that
b(x) = a-1(x)mod (x4 + 1)
where a(x) = {03}x3 + {01}x2 + {01}x + {02} and b(x) = {0B}x3 +
{0D}x2 + {09}x +{0E}. Show that this is true.
Question 7
a.
b.
c.
d.
What is triple encryption?
What is a meet-in-the-middle attack?
How many keys are used in triple encryption?
Why is the middle portion of 3DES a decryption rather than an
encryption?
e. Why do some block cipher modes of operation only use encryption while
others use both encryption and decryption?
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f. You want to build a hardware device to do block encryption in the cipher
block chaining (CBC) mode using an algorithm stronger than DES. 3DES
is a good candidate. Figure 1 shows two possibilities, both of which follow
from the definition of CBC. Which of the two would you choose:.
i.
For security?
ii.
For performance?
iii.
Can you suggest a security improvement to either option
in Figure 1, using only three DES chips and some number
of XOR functions? Assume you are still limited to two
keys.
Fig 1: Use of Triple DES in CBC
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