# 伪代码代写 | SIT 281 TRIMESTER 2 2020 ASSIGNMENT

SIT 281 TRIMESTER 2 2020
ASSIGNMENT
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.
2 marks
(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 marks

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,
x2=2.
(a) Compute first 20 outputs (including x0, x1 and x2) of the
above LFSR.

2 marks
(b) What is the period? What is the largest period of a LFSR with 3 registers
under modulo 3?
2 marks
3. By hand, use the Extended Euclidean algorithm to write the gcd of 4951 and 4369
as their linear combination.
3 marks
4. By hand, find the last four digits of 118012
.
4 marks
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 E-mail: vipdue@outlook.com  微信号:vipnxx 