[SOLVED] CS MATH/CSCI 4116 Cryptography Sample Midterm Exam

MATH/CSCI 4116 Cryptography Sample Midterm Exam
This was an actual 60-minute midterm, written the last time I taught this course.
Please keep in mind that this was a closed-book, in-class exam. So, while the material is a fair representation of what you can expect, some questions would not be suitable for an open-book exams.
Since this exam was written later in the term, it included the material required to answer Question 7. Please disregard it.
The value of each question is given in brackets. [Total: 25]
*****************************************
1. [2]
Describe the differences between a code and a cipher.
2. [3]
The Vigen`ere cipher, the Hill cipher, and the permutation cipher are not secure. Explain why.
3. [4]
(a) Find all the invertible residue classes mod 12 and their inverses.
(b) Determine the group of units and the zero divisors of Z/16Z.
4. [3]
Is security of the affine cipher with a given modulus m increased if one encryption is followed by a second encryption with a different key? Give details.
5. [5]
(a) State the definition (not a formula) of Eulers -function.
(b) Find (2016). [Here you may use an appropriate formula].
(c) We know that (ab) = (a)(b) whenever gcd(a, b) = 1. Give an example that shows
that the identity is, in general, not true when gcd(a, b) = 1.
6. [4]
Suppose that you know that a Hill cipher with alphabet Z26 and block length 2 is being used, and you have obtained the ciphertext string (7, 0, 13, 3), along with the corresponding plaintext string (5, 14, 14, 19). Find the key.
7. [4] [Disregard]
(a) Show that the polynomial x2 + x + 1 is irreducible over Z/2Z.
(b) Construct the multiplication table for the finite field GF(22), using the irreducible polynomial f(x) = x2 + x + 1.