Symmetric Ciphers Questions and Answers – Polynomial and Modular Arithmetic – II

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

1. If f(x)=x⁷+x⁵+x⁴+x³+x+1 and g(x)=x³+x+1, find f(x) x g(x).
a) x¹²+x⁵+x³+x²+x+1
b) x¹⁰+x⁴+1
c) x¹⁰+x⁴+x+1
d) x⁷+x⁵+x+1
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2. If f(x)=x⁷+x⁵+x⁴+x³+x+1 and g(x)=x³+x+1, find the quotient of f(x) / g(x).
a) x⁴+x³+1
b) x⁴+1
c) x⁵+x³+x+1
d) x³+x²
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3. Primitive Polynomial is also called a ____
i) Perfect Polynomial
ii) Prime Polynomial
iii) Irreducible Polynomial
iv) Imperfect Polynomial

a) ii) and iii)
b) only iii)
c) iv) and ii)
d) None
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4. Which of the following are irreducible polynomials?
i) X⁴+X³
ii) 1
iii) X²+1
iv) X⁴+X+1

a) i) and ii)
b) only iv)
c) ii) iii) and iv)
d) All of the options
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5. The polynomial f(x)=x³+x+1 is a reducible.
a) True
b) False
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6. Find the HCF/GCD of x⁶+x⁵+x⁴+x³+x²+x+1 and x⁴+x²+x+1.
a) x⁴+x³+x²+1
b) x³+x²+1
c) x²+1
d) x³+x²+1
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7. On multiplying (x⁵ + x² + x) by (x⁷ + x⁴ + x³ + x² + x) in GF(28) with irreducible polynomial (x⁸ + x⁴ + x³ + x + 1) we get
a) x¹²+x⁷+x²
b) x⁵+x³+x³
c) x⁵+x³+x²+x
d) x⁵+x³+x²+x+1
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8. On multiplying (x⁶+x⁴+x²+x+1) by (x⁷+x+1) in GF(2⁸) with irreducible polynomial (x⁸ + x⁴ + x³ + x + 1) we get
a) x⁷+x⁶+ x³+x²+1
b) x⁶+x⁵+ x²+x+1
c) x⁷+x⁶+1
d) x⁷+x⁶+x+1
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9. Find the inverse of (x² + 1) modulo (x⁴ + x + 1).
a) x⁴+ x³+x+1
b) x³+x+1
c) x³+ x²+x
d) x²+x
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Answer: b
Explanation:

10. Find the inverse of (x⁵) modulo (x⁸+x⁴ +x³+ x + 1).
a) x⁵+ x⁴+ x³+x+1
b) x⁵+ x⁴+ x³
c) x⁵+ x⁴+ x³+1
d) x⁴+ x³+x+1
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Sanfoundry Global Education & Learning Series – Cryptography and Network Security.

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