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Welcome to the Number Theory and Finite Fields MCQs Page

Dive deep into the fascinating world of Number Theory and Finite Fields with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Number Theory and Finite Fields, a crucial aspect of Cryptography and Network Security. In this section, you will encounter a diverse range of MCQs that cover various aspects of Number Theory and Finite Fields, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Cryptography and Network Security.

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Check out the MCQs below to embark on an enriching journey through Number Theory and Finite Fields. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Cryptography and Network Security.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Number Theory and Finite Fields. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Number Theory and Finite Fields MCQs | Page 4 of 10

Q31.
-5 mod -3 =

a.

3

b.

2

c.

1

d.

5

Discuss
Answer: (c).1
Q32.
Multiply 00100110 by 10011110 in GF(2^8) with modulus 100011011.The result is
Discuss
Answer: (a).00101111
Q33.
Find the inverse of (x^7+x+1) modulo (x^8 + x^4 + x^3+ x + 1).
Discuss
Answer: (c).x^7
Q34.
7x = 6 mod 5. Then the value of x is

a.

2

b.

3

c.

4

d.

5

Discuss
Answer: (b).3
Q35.
State whether the following statement is true or false over a field.

The product of monic polynomials is monic.
Discuss
Answer: (a).True
Q36.
State whether the following statement is true or false over a field.

The product of polynomials of degrees m and n has a degree m+n+1.
Discuss
Answer: (b).False
Q37.
State whether the following statement is true or false over a field.

The sum of polynomials of degrees m and n has degree max[m,n].
Discuss
Answer: (c).Can’t Say
Q38.
Is x^3 + 1 reducible over GF(2)
Discuss
Answer: (a).Yes
Q39.
Is x^3 + x^2 + 1 reducible over GF(2)
Discuss
Answer: (b).No
Q40.
Is x^4 + 1 reducible over GF(2)
Discuss
Answer: (a).Yes
Page 4 of 10

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