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

View Answer

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

View Answer

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

a) Both Additive Inverses

b) Both Multiplicative Inverses

c) Additive and Multiplicative Inverse respectively

d) Multiplicative and Additive Inverses respectively

View Answer

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

View Answer

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)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) + g(x)

a) x^{3}+2x^{2}-x+3

b) x^{3}+x^{2}+3

c) x^{3}+x+1

d) x^{2}+2x+4

View Answer

Explanation: We get the solutions via basic polynomial addition.

6. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) – g(x)

a) x^{3}+x+4

b) x^{3}+x+1

c) x^{3}+x^{2}+3

d) x^{3}+3x+2

View Answer

Explanation: We get the solutions via basic polynomial subtraction.

7. If f(x)=x^{4}+x^{3}+2 and g(x)=x^{3}-x+6, find: f(x) + g(x)

a) 2x^{4}+2x^{3}+x+8

b) x^{4}+2x^{3}-x+8

c) x^{4}+x^{2}+x+8

d) x^{4}+x^{3}+8

View Answer

Explanation: Perform polynomial addition.

8. If f(x)=x^{4}+x^{2}-x+2 and g(x)=x^{2}-x+1, find: f(x) – g(x)

a) x^{4}+1

b) x^{2}+1

c) x^{2}+2x+6

d) x^{4}-1

View Answer

Explanation: Perform polynomial subtraction.

9. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find the quotient of f(x) / g(x)

a) x+3

b) x^{2}+4

c) x

d) x+2

View Answer

Explanation:We get the solution via basic polynomial division.

10. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) x g(x)

a) x^{4}+x^{2}+2x+2

b) x^{5}+2x^{3}+2x+3

c) x^{5}+3x^{2}-2x+2

d) x^{4}+x^{2}+x+1

View Answer

Explanation: We get the solution via basic polynomial multiplication.

11. Find the 8-bit word related to the polynomial x^{5} + x^{2} + x

a) 00010011

b) 01000110

c) 00100110

d) 11001010

View Answer

Explanation: The respective 8-bit word is 00100110.

12. Find the 8-bit word related to the polynomial x^{6} + x^{5} + x^{2} + x +1

a) 00010011

b) 11000110

c) 00100110

d) 01100111

View Answer

Explanation: The respective 8-bit word is 01100111.

**Sanfoundry Global Education & Learning Series – Cryptography and Network Security.**

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