Information Technology (IT) Department Principles of Cybersecurity (CYS 232) Assignment #1 Faculty of Information Technology and Computer Sciences Yarmouk University, Irbid Jordan Spring 2021 Theory and programming assignment Description: You need to answer the following questions and write down your answers using your hand written. Due date is March 17th, of 2021. The deadline for submitting the assignment is March 17th, 2021. After that date no assignments will evaluated 1) 2) 3) 4) 5) 6) 7) If b|a (a divides b), what is the gcd( a, b) ? what is the gcd( a, 0) ? Shaw the steps to find the gcd( 70, 38 ), justify your answer. Shaw the steps to find the gcd( 8, 17 ), justify your answer. Shaw the steps to find the gcd(40902, 24140), justify your answer. Write down the code in python for gcd, Show a screen shot for the run. Write down the code in python for extended Euclidean algorithm. Show a screen shot for the run. 8) List four properties of divisibility discussed in this chapter. Give an integer with only one divisor. Give an integer with only two divisors. Give an integer with more than two divisors. 9) Find the general solution of the Diophantine equations: (a) 3x + 4y = 26; (b) 6x - 9y = 12; (c) 15x + 20y = 65. 10) For each of the following linear congruences, either find all the solutions (expressed in the form x ≡ s mod m) or show that no solutions exist. When solutions do exist, find the smallest positive integer solution in each case. (a) 3x ≡ 7 (mod 11). (b) 8x ≡ 96 (mod 124). (c) 5x ≡ 13 (mod 30). (d) 5x ≡ 64 (mod 81). (e) 12x ≡ 30 (mod 66). 11) Using the extended Euclidean algorithm, find the greatest common divisor of the following pairs and the value of s and t. a) 4 and 7 b) 291 and 42 c) 84 and 320 d) 400 and 60 12) Find the particular and the general solutions to the following linear Diophantine equations. a. 25x + 10y = 15 b. 19x + 13y = 20 c. 14x + 21y = 77 d. 40x + 16y = 88