# Symmetric Ciphers Questions and Answers – Polynomial and Modular Arithmetic- I

This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Polynomial and Modular Arithmetic”.

1. A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication.
a) True
b) False

Explanation: GF(2) is the set {0, 1} with two operations, addition and multiplication

2. Multiplication / Division follow which operation?
a) XOR
b) NAND
c) AND
d) OR

Explanation: Multiplication / Division is the same as the AND operations.

3. What do the above numbers correspond to?
0 1 2 3 4
0 4 3 2 1

0 1 2 3 4
– 1 3 2 4

b) Both Multiplicative Inverses
c) Additive and Multiplicative Inverse respectively
d) Multiplicative and Additive Inverses respectively

Explanation: The top set of numbers correspond to Additive Inverses and the bottom set of numbers correspond to Multiplicative Inverse.
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4. How many numbers cannot be used in GF(p) in 2n where n=4?
a) 2
b) 5
c) 3
d) 1

Explanation: If n=4, the largest prime less than 24 is 13. This means that we cannot use the integers 13, 14 and 15.

5. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) + g(x)
a) x3+2x2-x+3
b) x3+x2+3
c) x3+x+1
d) x2+2x+4

Explanation: We get the solutions via basic polynomial addition.

6. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) – g(x)
a) x3+x+4
b) x3+x+1
c) x3+x2+3
d) x3+3x+2

Explanation: We get the solutions via basic polynomial subtraction.

7. If f(x)=x4+x3+2 and g(x)=x3-x+6, find: f(x) + g(x)
a) 2x4+2x3+x+8
b) x4+2x3-x+8
c) x4+x2+x+8
d) x4+x3+8

8. If f(x)=x4+x2-x+2 and g(x)=x2-x+1, find: f(x) – g(x)
a) x4+1
b) x2+1
c) x2+2x+6
d) x4-1

Explanation: Perform polynomial subtraction.

9. If f(x)=x3+x2+2 and g(x)=x2-x+1, find the quotient of f(x) / g(x)
a) x+3
b) x2+4
c) x
d) x+2

Explanation:We get the solution via basic polynomial division.

10. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) x g(x)
a) x4+x2+2x+2
b) x5+2x3+2x+3
c) x5+3x2-2x+2
d) x4+x2+x+1

Explanation: We get the solution via basic polynomial multiplication.

11. Find the 8-bit word related to the polynomial x5 + x2 + x
a) 00010011
b) 01000110
c) 00100110
d) 11001010

Explanation: The respective 8-bit word is 00100110.

12. Find the 8-bit word related to the polynomial x6 + x5 + x2 + x +1
a) 00010011
b) 11000110
c) 00100110
d) 01100111

Explanation: The respective 8-bit word is 01100111.

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