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

1. ᶲ(231)=

a) 230

b) 60

c) 80

d) 120

View Answer

Explanation: ᶲ(231) = ᶲ(3) x ᶲ(7) x ᶲ(11) = 2 x 6 x 10 = 120.

2. n is prime if and only if n divides (2^{n} – 2).

a) True

b) False

View Answer

Explanation: This isn’t true for all cases. Take for example 341 which is non prime.

3. Find x for the CRT when x= 2 mod 3; x= 3 mod 5; x = 2 mod 7

a) 33

b) 22

c) 23

d) 31

View Answer

Explanation: We have M = 3 x 5 x 7 = 105; M/3 = 35; M/5 = 21; M/7 = 15.

The set of linear congruences

35 x b1 = 1 (mod 3); 21 x b2 = 1 (mod 5); 15 x b3 = 1 (mod 7)

has the solutions b1 = 2; b2 = 1; b3 = 1. Then,

x = 2 x 2 c 35 + 3 x 1 x 21 + 2 x 1 x 15 = 233 (mod 105) = 23.

4. Consider a function: f(n) = number of elements in the set {a: 0 <= a < n and gcd(a,n) = 1}. What is this function?

a) Primitive

b) Totient

c) Primality

d) All of the mentioned

View Answer

Explanation: Such a set is known as Totient.

5. The inverse of 49 mod 37 is –

a) 31

b) 23

c) 22

d) 34

View Answer

Explanation: 49

^{-1}mod 37 = 34.

6. Six teachers begin courses on Monday Tuesday Wednesday Thursday Friday and Saturday, respectively, and announce their intentions of lecturing at intervals of 2,3,4,1,6 and 5 days respectively. Sunday lectures are forbidden. When first will all the teachers feel compelled to omit a lecture? Use CRT.

a) 354

b) 371

c) 432

d) 213

View Answer

Explanation: Use CRT to get the answer as 371.

7. How many primitive roots are there for 25?

a) 4

b) 5

c) 7

d) 8

View Answer

Explanation: 2, 3, 8, 12, 13, 17, 22, 23 are the primitive roots of 25.

Given 2 as a primitive root of 29, construct a table of discrete algorithms and solve for x in the following –

8. 17 x^{2} = 10 ( mod 29 )

a) x = 3, 22 (mod 29)

b) x = 7, 28 (mod 29)

c) x = 2, 27 (mod 29)

d) x = 4, 28 (mod 29)

View Answer

Explanation: On solving we get x = 2, 27 (mod 29).

9. x

a) x = 6, 24 (mod 29)

b) x = 9, 24 (mod 29)

c) x = 9, 22 (mod 29)

d) x = 6, 22 (mod 29)

View Answer

Explanation: On solving we get x = 9, 24 (mod 29).

10. x^{7} = 17 (mod 29)

a) x = 8, 9, 12, 13, 15, 24, 28 (mod 29)

b) x = 8, 10, 12, 15, 18, 26, 27 (mod 29)

c) x = 8, 10, 12, 15, 17, 24, 27 (mod 29)

d) x = 8, 9, 13, 15, 17, 24, 28 (mod 29)

View Answer

Explanation: On solving we get x = 8, 10, 12, 15, 18, 26, 27 (mod 29).

11. The inverse of 37 mod 49 is –

a) 23

b) 12

c) 4

d) 6

View Answer

Explanation: 37

^{-1}mod 49 = 4.

12. How many primitive roots are there for 19?

a) 4

b) 5

c) 3

d) 6

View Answer

Explanation: 2, 3, 10, 13, 14, 15 are the primitive roots of 19.

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

To practice all areas of Cryptography, __here is complete set of 1000+ Multiple Choice Questions and Answers__.