Read the following Notes before proceeding:
It is important that you show all working out and explain your steps. Marks are given for this.
Do not include extraneous Maple code in your submission.
Do not copy or plagiarise. Read the University position on plagiarism – it is a serious matter. People who do this are given 0 for the question.
Number all pages of your assignment.
Put your name on each page.
Please keep a copy of your assignment as sometimes, the one you submit may go missing.
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______________________________________________________________ The first four questions should be done without Maple. The last two should be done using Maple.
For a string of bits S, let S* denote the complementary string obtained by changing all the 1s to 0s and all the 0s to 1s. Show that if the DES key K encrypts P to C, then K* encrypts P* to C*. (Hint: This has nothing to do with the structure of the S-boxes. To do the problem, just work through the encryption algorithm.) 9 marks
Suppose the key for round 0 in AES consists of 128 bits, each of which is 1. Determine the key components W(4), W(5), W(6), W(7), for the end of the first round. 10 marks
Given an RSA modulus of 55 and encryption exponent 3: (a) find the decryption modulus d; 2 marks (b) show, efficiently, that for a message m encrypted to c using this scheme, we have cd ≡ m (mod 55). 3 marks
Let p = 123456791, q = 987654323 and e = 127. Let the message m = 14152019010605. Using Maple, compute me (mod q); then use the Chinese remainder theorem to combine these to get me ≡ c (mod pq). Verify by computing me and c (mod pq) directly. 6 marks
Use a Maple procedure for the Baby Step, Giant Step algorithm to solve 8576 ≡ 3x (mod 53047). 10 marks
TOTAL: 40 marks
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