This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Number Theory – 4”.

1. What is the Discrete logarithm to the base 10 (mod 19) for a =7?

a) 12

b) 14

c) 8

d) 11

View Answer

Explanation: log_10(7) mod 19 = 12.

2. 3^{201} mod 11 =

a) 3

b) 5

c) 6

d) 10

View Answer

Explanation: Use Fermats Theorum. Fermat’s Theorem states that if p is prime and a is a positive integer not divisible

by p, then a

^{(p–1)}= 1 (mod p). Therefore 3

^{10}= 1 (mod 11). Therefore

3^201 = (3

^{10})

^{20}x 3 = 3 (mod 11).

3. Find a number x between 0 and 28 with x^85 congruent to 6 mod 29.

a) 22

b) 12

c) 6

d) 18

View Answer

Explanation: Use Fermats Theorum.

4. What is the Discrete logarithm to the base 13 (mod 19) for a =13?

a) 14

b) 1

c) 8

d) 17

View Answer

Explanation: log_13(13) mod 19 = 1.

5. What is the Discrete logarithm to the base 15 (mod 19) for a =9?

a) 3

b) 7

c) 12

d) 4

View Answer

Explanation: log_15(9) mod 19 = 4.

6. Find a number x between 0 and 28 with x^{85} congruent to 6 mod 35.

a) 6

b) 32

c) 8

d) 28

View Answer

Explanation: Use Eulers Theorum.

7. Find a number ‘a’ between 0 and 72 with ‘a’ congruent to 9794 mod 73.

a) 53

b) 29

c) 12

d) 37

View Answer

Explanation: Use Fermats Theorum.

8. What is the Discrete logarithm to the base 2 (mod 19) for a =7?

a) 3

b) 4

c) 6

d) 9

View Answer

Explanation: log_2(7) mod 19 = 6.

9. ᶲ(41)=

a) 40

b) 20

c) 18

d) 22

View Answer

Explanation: 41 is a prime.

10. ᶲ(27)=

a) 6

b) 12

c) 26

d) 18

View Answer

Explanation: ᶲ(27) = ᶲ(33) = 3

^{3}– 3

^{2}= 27 – 9 = 18.

11. Find a number ‘a’ between 0 and 9 such that ‘a’ is congruent to 7^1000 mod 10.

a) 2

b) 1

c) 3

d) 4

View Answer

Explanation: Use Eulers Theorum.

12. ᶲ(440)=

a) 200

b) 180

c) 160

d) 220

View Answer

Explanation: ᶲ(440) = ᶲ(2^3) x ᶲ(5) x ᶲ(11) = (2^3 – 2^2) x 4 x 10 = 160.

13. GCD(n,n+1) = 1 always.

a) True

b) False

View Answer

Explanation: If p were any prime dividing n and n + 1 it would also have to divide (n + 1) – n = 1. Thus GCD of 2 consecutive numbers is always 1.

**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__.