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

View Answer

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

2. ᶲ(37)=

a) 24

b) 22

c) 13

d) 36

View Answer

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

3. ᶲ(35)=

a) 24

b) 25

c) 22

d) 18

View Answer

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

View Answer

Explanation: ᶲ(21)= 6 x 2 =12.

5.7^{3} mod 19 =

a) 18

b) 1

c) 14

d) 12

View Answer

Explanation: 7

^{3}mod 19 = 1.

6. 7^{(3+j)} mod 19 =

a) 7^{j} mod 19

b) 1 mod 19

c) 7^{3} + 7^{j} mod 19

d) All of the mentioned are true

View Answer

Explanation: 7

^{(3+j)}mod 19 = 7

^{3}* 7

^{j}mod 19 = 7

^{j}mod 19 ( since 7

^{3}mod 19 = 1 ).

7. What is the period of 7^{m} mod 19?

a) 2

b) 3

c) 4

d) 5

View Answer

Explanation: Period is 3. It is the smallest positive integer for which 7

^{m}mod 19 = 1.

8. ᶲ(19)=

a) 14

b) 13

c) 18

d) 17

View Answer

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

View Answer

Explanation: 11

^{3}(mod 19) = 1.

10. What is the period of 17 (mod 19)

a) 5

b) 7

c) 9

d) 11

View Answer

Explanation: 17

^{9}( mod 19) = 1.

11. What is the period of 9 (mod 19)

a) 12

b) 10

c) 11

d) 9

View Answer

Explanation: 9

^{9}(mod 19) = 1.

12. How many primitive roots does Z<19> have?

a) 5

b) 8

c) 7

d) 6

View Answer

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(y^{r}) – 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

View Answer

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

**Sanfoundry Global Education & Learning Series – Cryptography and Network Security.**

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