COMP3223 School of Computing: assessment brief Module title Cryptography Module code COMP3223 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 1 1. Assignment guidance Provide answers to the three exercises below. Answer all three exer- cises. 2. 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 ab g = , c d 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 1 1 cipher in G. [1 mark] 12 (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 A = Aadj = 2 ab c d d −b −c a 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] 3 3. 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. 4. 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. 5. 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. 6. 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). 4 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. 7. 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. 8. 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