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

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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

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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.

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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