DUBLIN CITY UNIVERSITY SEMESTER 1 EXAMINATIONS 2014/2015

DUBLIN CITY UNIVERSITY
SEMESTER 1 EXAMINATIONS 2014/2015
MODULE:
CA642 - Cryptography and Number Theory
PROGRAMME(S):
MCM - M.Sc. in Computing
ECSA - Study Abroad (Engineering and Computing)
YEAR OF STUDY:
1,X
EXAMINERS:
Dr Geoffrey Hamilton (Ext:5017)
Dr. Ning Zhang
TIME ALLOWED:
3 hours
INSTRUCTIONS:
Answer all questions. All questions carry equal marks.
PLEASE DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO
The use of programmable or text storing calculators is expressly forbidden.
Please note that where a candidate answers more than the required number of questions,
the examiner will mark all questions attempted and then select the highest scoring ones.
Requirements for this paper (Please mark (X) as appropriate)
X
X
X
X
Log Tables
Graph Paper
Dictionaries
Statistical Tables
X
X
X
X
CA642–Cryptography and Number Theory
Semester 1 EXAMINATIONS 2014/2015
Thermodynamic Tables
Actuarial Tables
MCQ Only - Do not publish
Attached Answer Sheet
Page 1 of 4
QUESTION 1
[Total marks: 20]
1(a)
[5 Marks]
Calculate 4/71 (mod 119).
1(b)
[5 Marks]
Evaluate the least significant decimal digit of 1098737951
1(c)
[5 Marks]
Calculate the quadratic residues in Z∗19 .
1(d)
[5 Marks]
Evaluate all the square roots of 4 mod 77.
[End Question 1]
QUESTION 2
[Total marks: 20]
2(a)
[5 Marks]
Block ciphers are usually designed to provide confusion and diffusion. Explain what is
meant by each of these properties, and give examples of the features of block ciphers
which are used to provide them.
2(b)
[10 Marks]
Describe the Advanced Encryption Standard (AES) with reference to the following
(use diagrams if necessary):
• Encryption algorithm
• Decryption algorithm
• Block size
• Key size
• Number of rounds
• Robustness against attacks
Describe how AES provides confusion and diffusion.
2(c)
[5 Marks]
What are the minimum recommended block size and key size which should be used
for a block cipher? What attacks could be mounted against the block cipher if either of
these sizes is less than recommended? What are the implications of this for AES?
[End Question 2]
CA642–Cryptography and Number Theory
Semester 1 EXAMINATIONS 2014/2015
Page 2 of 4
QUESTION 3
[Total marks: 20]
Using the diagram below, explain in detail the steps required to launch a successful
differential cryptanalysis attack on the FEAL-4 block cipher.
[20 Marks]
[End Question 3]
CA642–Cryptography and Number Theory
Semester 1 EXAMINATIONS 2014/2015
Page 3 of 4
QUESTION 4
[Total marks: 20]
4(a)
[8 Marks]
Describe the Merkle Damgård construction which is often used in the implementation of hash functions (use diagrams if necessary). What properties are required for a
hash function to be considered to be cryptographically secure and why?
4(b)
[7 Marks]
Describe how hash functions can be used for message authentication. How do Message Authentication Codes (MACs) differ from Manipulation Detection Codes (MDCs)?
Describe how a MAC can be constructed from a block cipher, and how a MAC can be
constructed from a MDC.
4(c)
[5 Marks]
If a MAC with secret key k were created from a MDC as MACk (m) = MDC(k||m), show
how you could make use of the Merkle Damgård construction to compute MACk (m||m0 )
without knowing k.
[End Question 4]
QUESTION 5
[Total marks: 20]
5(a)
[6 Marks]
Define the RSA problem which must be solved in order to break RSA. Show that this
problem is no harder than the integer factorisation problem.
5(b)
[7 Marks]
Show how the Pollard ρ method (not to be confused with the Pollard p − 1 method)
for integer factorisation works and use it to find the factors of 187.
5(c)
[7 Marks]
Describe how RSA decryption can be performed more efficiently with knowledge of
the prime factors of the modulus. Use the described method to decrypt the ciphertext
124 using decryption exponent 23 and modulus 187.
[End Question 5]
[END OF EXAM]
CA642–Cryptography and Number Theory
Semester 1 EXAMINATIONS 2014/2015
Page 4 of 4