Asymmetric Ciphers Questions and Answers – Number Theory – IV

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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

Answer: a
Explanation: log_10(7) mod 19 = 12.
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2. 3201 mod 11 =
a) 3
b) 5
c) 6
d) 10
View Answer

Answer: a
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 310 = 1 (mod 11). Therefore
3^201 = (310)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

Answer: c
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

Answer: b
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

Answer: d
Explanation: log_15(9) mod 19 = 4.
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6. Find a number x between 0 and 28 with x85 congruent to 6 mod 35.
a) 6
b) 32
c) 8
d) 28
View Answer

Answer: a
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

Answer: c
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

Answer: c
Explanation: log_2(7) mod 19 = 6.

9. ᶲ(41)=
a) 40
b) 20
c) 18
d) 22
View Answer

Answer: a
Explanation: 41 is a prime.
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10. ᶲ(27)=
a) 6
b) 12
c) 26
d) 18
View Answer

Answer: d
Explanation: ᶲ(27) = ᶲ(33) = 33 – 32 = 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

Answer: b
Explanation: Use Eulers Theorum.

12. ᶲ(440)=
a) 200
b) 180
c) 160
d) 220
View Answer

Answer: c
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

Answer: a
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.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn