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Question 1 (6 marks) A description of RSA cryptography is given at the end of the lecture notes for Section B1.(Numbers). The topic is there described as non-assessed. I should have added that the description relates to examinations and regular weekly assignments, but that it is a suitable topic for a deeper graduate assignment. So please tackle the following with slides 32 and 33 of the B1 notes in front of you and using the free online calculator WolframAlpha for the arithmetic
. (a) Encode m=1091060694, using RSA with(e,n)=(2547688103, 2745928813) (b) For the same RSA parameters as in (a) decode c=1434356023. You will ﬁrst need to calculate the (supposedly secret) decoding exponent d. For both parts write out, exactly, the input to, and output from, Wolfram Alpha, that you used to arrive at your answer.
Question 2 (6 marks) F(c) Based on your answers to (a) propose a formula for an. Hint: Consider values of an n .
(d) Use mathematical induction to prove that your proposed formula for (c) is correct.
MATH1005 Graduate Assignment B 2019 Page 2 of 3 Question 3 (8 marks) About 700 students take our exam. After grading, the scripts have to be sorted into ID order. How will we do this? One way is described below, followed by some questions. For simplicity, assume there are exactly 704 scripts.
1. Count oﬀ the scripts into 64 piles of 11 each.