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)=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
View Answer
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
View Answer
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
View Answer
Explanation: Perform polynomial addition.
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
View Answer
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
View Answer
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
View Answer
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
View Answer
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
View Answer
Explanation: The respective 8-bit word is 01100111.
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