Fundamental Security Properties and Mechanisms
Assignment 1
Issued: 17 November 2022
Copyright By Assignmentchef assignmentchef
Deadline for submission via MOLE: 1500on 15 December 2022.
Total Marks Available 100.
The marks available for this assignment make up 50%
of the total marks available for the COM6014 module
Answer both questions.
Any queries on this assignment should be raised via the Assessment discussion forum.
Question 1. Substitution Permutation Network Cipher and Differential Cryptanalysis (70 Marks)
A simple 3-round substitution permutation network (SPN) cipher inspired by the Heys cipher is shown in Figure 1.
The cipher operates on 8-bit blocks. Key mixing is simple bitwise XOR. The 8-bit plaintext block P is XOR-ed bitwise with the 8-bit key K1 before the resulting 8-bit block enters the two first-round S-boxes. The remaining key mixing operations are handled similarly.
A substitution box (S-box) is shown in Figure 2. This S-box is used throughout the cipher shown in Figure 1, i.e. all 6 S-boxes are identical.
The permutation part of the first two rounds is as shown in Figure 1. The final (third) round does not implement any permutation; the outputs from the final round S-boxes are simply XOR-ed bitwise with the key K4 to produce ciphertext C.
256 plaintext-ciphertext (P-C) pairs have been generated using the 3-round cipher and four secret keys (K1, K2, K3, K4). The 256 P-C pairs are given in the file 256PC-pairs.txt that accompanies this assessment.Plaintexts and ciphertexts are given as integers with the natural binary interpretation, e.g. the integer 5 represents the 8-bit block 00000101, 129 represents the 8-bit block 10000001, and so on.
You are required to carry out Linear Cryptanalysis on the P-C pairs provided to recover the final round key K4.
You will need to:
a) develop one or two suitable 2-round linear approximations for the system. You should:
i. identify the active S-boxes in your approximation(s) and their biases. Indicate how you obtained these figures. [10 Marks]
ii. state clearly the overall 2-round approximation(s). These will involve bits from plaintexts P, bits from intermediate ciphertexts U3, and various key bits. Formulate also related approximations that do not involve any key bits [10 Marks]
iii. Calculate the strength of each 2-round approximation.Give the absolute value of the bias of each 2-round linear approximation derived and show how they were calculated.[8 Marks]
iv. Identify clearly which final round key bits are targeted by each approximation. [2 Marks]
v. Justify your specific choices made above. [5 Marks]
The above allows for using one or two approximations. Different approximations may allow different final round key bits to be targeted. An approximation may allow the full 8 bits of the final round key to be targeted, or a subset of those bits (in which case you will need another approximation to discover any remaining final round bits.
Note: you should not overcomplicate your answers. You are NOT expected to do the step-by-step algebraic manipulations given in the lecture on Linear Cryptanalysis (which serve to show why linear cryptanalysis works). In answering the above, you should include a copy of Figure 1 in your submitted script. It should be possible to tell at a glance which S-boxes are active (participating in the approximation), what individual S-box approximations have been used, and what K4 key bits are targeted. You should supplement your annotated figure with text where necessary. You should indicate any active S-box approximations both visually AND textually.
The above is the theoretical/analytical part of the question.You need to complete this part to inform the practical part of the question immediately below.
b) Use the results above to recover the key K4. Show the results of your work. You will need to implement code to:
i. read-in the P-C pairs. [5 Marks]
ii. carry out the (partial) decryption of ciphertexts (of PC-pairs) for a given (possibly partial) K4 key guess (trial), i.e., to obtain the appropriate U3 bits. [8 Marks]
iii. carry out the linear approximation checking between appropriate P bits and U3 bits. [8 Marks]
iv. identify promising candidates for K4. You should state in your answer why identified candidate(s) are particularly promising. [5 Marks]
c) Outline how you would recover all remaining keys, i.e. K1 , K2 , and K3. (You are NOT expected to actually recover them, just outline how you would do this.) [5 Marks]
d) How might small changes to the algorithm shown in figure 1 improve security? [4 Marks]
Figure 1. Simple Very Small SPN Cipher
Figure 2. Specification of the Common S-Box
Question 2Side Channels (30 Marks)
This question is concerned with the use of so-called side channels to attack cryptographic systems. Write a short report (800 words max) on the topic of cryptographic side channels. You should:
a) Explain what is meant by the term side channel in the context of cryptosystems. [5 Marks]
b) Give brief descriptions of particular side channels. [10 Marks]
c) Describe countermeasures to those side channels and assess those countermeasures in terms of how effective they are and how practical it is to implement them. [10 Marks]
d) Research available literature on side channels and use it to inform your answer. [5 Marks]
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