SIT 281 TRIMESTER 2 2020
1. You have found two plaintext-ciphertext pairs which you know are from an affine
cipher based on the English alphabet. The pairs are (1,7) and (0,2).
(a) Find the equation of the cipher.
(b) Use Maple and the resultant affine cipher to encrypt the sentence “My
student ID is xxx, and I am now working on Assignment 1a”, and verify the
result is correct by decryption (replace “xxx” with your real student ID, delete
the blank and punctuation, and capital and lower-case letter are the same).
2. Instead of modulo 2, Alice have a LFSR works with modulo 3. The formula of this
LFSR is xn+3 = xn + 2xn+1+2xn+2 (mod 3), where the initial values are x0=0, x1=1,
(a) Compute first 20 outputs (including x0, x1 and x2) of the
(b) What is the period? What is the largest period of a LFSR with 3 registers
under modulo 3?
3. By hand, use the Extended Euclidean algorithm to write the gcd of 4951 and 4369
as their linear combination.
4. By hand, find the last four digits of 118012
5. Find all the roots of the equation x
2 = 35 (mod 23*43) by hand (4 marks), and then
verify the result with Maple (1 mark).
TOTAL: 20 marks
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