# Asymmetric Ciphers Questions and Answers – Number Theory – III

This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Number Theory – 3”.

1. gcd( 18,300) =
a) 4
b) 12
c) 8
d) 6

Explanation: gcd( 18,300) = 6. Find the common factors to compute GCD/HCF.

2. ᶲ(37)=
a) 24
b) 22
c) 13
d) 36

Explanation: 37 is a prime number hence ᶲ(37) = 36.

3. ᶲ(35)=
a) 24
b) 25
c) 22
d) 18

Explanation: ᶲ(36) = 24 = 6 x 4. These are the numbers which are relatively prime –
1,2,3,4,6,8,9,11,12,13,16,17,18,19,22,23,24,26,27,29,31,33,34.

4. ᶲ(21)=
a) 10
b) 12
c) 8
d) 14

Explanation: ᶲ(21)= 6 x 2 =12.

5.73 mod 19 =
a) 18
b) 1
c) 14
d) 12

Explanation: 73 mod 19 = 1.
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6. 7(3+j) mod 19 =
a) 7j mod 19
b) 1 mod 19
c) 73 + 7j mod 19
d) All of the mentioned are true

Explanation: 7(3+j) mod 19 = 73 * 7j mod 19 = 7j mod 19 ( since 73 mod 19 = 1 ).

7. What is the period of 7m mod 19?
a) 2
b) 3
c) 4
d) 5

Explanation: Period is 3. It is the smallest positive integer for which 7m mod 19 = 1.

8. ᶲ(19)=
a) 14
b) 13
c) 18
d) 17

Explanation: 19 is a prime no. hence ᶲ(19)= 18.

9. What is the period of 11 (mod 19)
a) 2
b) 3
c) 4
d) 5

Explanation: 113 (mod 19) = 1.

10. What is the period of 17 (mod 19)
a) 5
b) 7
c) 9
d) 11

Explanation: 179 ( mod 19) = 1.

11. What is the period of 9 (mod 19)
a) 12
b) 10
c) 11
d) 9

Explanation: 99 (mod 19) = 1.

12. How many primitive roots does Z<19> have?
a) 5
b) 8
c) 7
d) 6

Explanation: Z<19> has the primitive roots as 2,3,10,13,14 and 15.

13. Which of the below properties are correct?
Consider the following Logarithmic Properties –
i) y = x(log_x(y))
ii) log_x(1) = 1
iii) log_x(x) = 0
iv) log_x(yz) = log_x(y) + log_x(z)
v) log_x(yr) – r x log_x(y)

a) 1st 2nd and 4th
b) 2nd 3rd and 5th
c) 2nd 4th and 5th
d) 1st 4th and 5th

Explanation: log_x(1) = 0 ; log_x(x) = 1 are the correct versions of ii) and iii).

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