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
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2. Multiplication / Division follow which operation?
a) XOR
b) NAND
c) AND
d) OR
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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
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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
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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
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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
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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
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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
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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
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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
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11. Find the 8-bit word related to the polynomial x⁵ + x² + x
a) 00010011
b) 01000110
c) 00100110
d) 11001010
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12. Find the 8-bit word related to the polynomial x⁶ + x⁵ + x² + x +1
a) 00010011
b) 11000110
c) 00100110
d) 01100111
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Sanfoundry Global Education & Learning Series – Cryptography and Network Security.

To practice all areas of Cryptography and Network Security, here is complete set of 1000+ Multiple Choice Questions and Answers.