Assignment title
Coursework 1
Assignment type and description
Coursework assignment
Rationale
Learning the mathematical basis of symmetric cryp- tosystems
Weighting
20% of total mark
Submission dead- line
March 6th 2023 at 09:00
Submission method
Turnitin submission through Minerva
Feedback provision
Feedback provided on Minerva
Learning outcomes assessed
(i) Understand and apply in practice the fundamental principles of cryptography and information security. (ii) Analyse and evaluate the strengths and weaknesses of cryptosystems. (iii) Apply mathematical analysis to un- derstand how symmetric cryptosystems are constructed.
Module lead
Dr Toni Lassila
- Assignment guidance
Provide answers to the three exercises below. Answer all three exer-
cises.
- Assessment tasks
Exercise 1: Alice and Bob use the Hill cipher over Z3 to communicate. (a) Let G = (Z2×2, ·) be the multiplicative group of 2×2 matrices with
3
elements in Z3, i.e. matrices of the form
where a,b,c,d ∈ Z3 and det(g) = ad ? bc ∈ Z?3. What is the
order of the group |G|? Explain how you can count the number
of elements in the group. [4 marks] ??
12
(b) Show that the key K = a valid encryption key for the Hill
(c) Find the inverse key K?1 for the key K = ? ? in G. Hint:
?1 1? The inverse matrix A?1 of a 2 × 2 matrix
??
can be expressed as A?1 = det(A)?1Aadj where the adjoint matrix
is defined as
and all the computations are performed in Z3. [3 marks] Exercise 2: Alice and Bob communicate using the autokey cipher and
the plaintext is encoded in the 26-character alphabet.
(a) Bob receives the ciphertext‘PVMXWPIHUUNEOEKGMXHQM- FIOG’and knows that the encryption key is‘TRADE’. Explain the steps of how Bob performs decryption in the autokey cipher and find the plaintext. [3 marks]
(b) Explain why the autokey cipher is not vulnerable to a frequency attack even if the key length is known. Mention two other ciphertext- only attacks that can be used against the autokey cipher when the key length is short. [3 marks]
Exercise 3: Alice and Bob use the DES block cipher for secure com- munication.
(a) The 3DES cipher involves three rounds of DES applied succes- sively with a total key length of 168 bits. Explain why 4DES using four rounds of DES does not increase the security com- pared to 3DES when the attacker has access to a known plaintext- ciphertext pair and explain the method of attack. [4 marks]
(b) Alice and Bob use DES in the cipher feedback (CFB) mode. Sup- pose that during transmission, one bit in the i’th ciphertext block Ci is flipped. How many plaintext blocks will be affected during decryption and how? Justify your answer by appealing to the CFB decryption algorithm diagram below. [2 marks]
- General guidance and study support
The MS Teams group for COMP3223 Cryptography will be used for general support for this assignment. If your question would reveal parts of the answer to any problem, please send instead a private message to the module leader on MS Teams.
- Assessment criteria and marking process
Assessment marks and feedback will be available on Minerva within three weeks of the submission deadline. Late submissions are allowed, standard late penalties apply.
- Presentation and referencing
When writing mathematical formulas, use similar notation and sym- bols as during the lectures and tutorials. Hand-written sections for mathematical notation are acceptable but need to be clearly readable.
You may assume theorems and other results that have been presented during lectures and tutorials as known. Any other theorems need to be cited using standard citation practice.
- Submission requirements
This is an individual piece of work. Submit your answers through Tur-
nitin as one PDF document (generated either in Word or with LaTeX).
You may use hand-written and scanned pages for mathematical formu- las, but these need to be clearly legible and the document must contain at least some typeset text or Turnitin will reject it. All submissions will be checked for academic integrity.
- Academic misconduct and plagiarism
Academic integrity means engaging in good academic practice. This involves essential academic skills, such as keeping track of where you find ideas and information and referencing these accurately in your work.
By submitting this assignment you are confirming that the work is a true expression of your own work and ideas and that you have given credit to others where their work has contributed to yours.
- Assessment/marking criteria grid
Total number of marks is 20, divided as follows:
Exercise 1 (Hill cipher): 8 marks
Exercise 2 (Autokey cipher): 6 marks
Exercise 3 (DES and block cipher operation modes): 6 marks