Asymmetric Ciphers Questions and Answers - Knapsack/ Merkle - Hellman/ RSA Cr...

This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Knapsack/ Merkle – Hellman/ RSA Cryptosystem”.

1. Find the ciphertext for the message {100110101011011} using superincreasing sequence { 1, 3, 5, 11, 35 } and private keys a = 5 and m=37.
a) C = ( 33, 47, 65 )
b) C = ( 65, 33, 47 )
c) C = ( 47, 33, 65 )
d) C = ( 47, 65, 33 )
View Answer

Answer: c
Explanation: {vi} = { 1, 3, 5, 11, 35 }
a = 5 and m = 37
Public key generation:
{wi} = avi mod m
wi = {5, 15, 25, 18, 27}
Break the message into k-bit tuple i.e. 5-bit tuple
10011 01010 11011
Encoding of M as follows:
M Ci
10011 47
01010 33
11011 65

Ciphertext sent will be: C = (47, 33, and 65).

2. Suppose that plaintext message units are single letters in the usual 26-letter alphabet with A-Z corresponding to 0-25. You receive the sequence of ciphertext message units 14, 25, 89. The public key is the sequence {57, 14, 3, 24, 8} and the secret key is b = 23, m = 61.
Decipher the message. The Plain text is
a) TIN
b) INT
c) KIN
d) INK
View Answer

Answer: b
Explanation: Solve using Knapsack Cryptosystem.
Wi = {57, 14, 3, 24, 8}
b = 23 and m = 61
a = b-1 mod m
61 = 2 x23 + 15
23 = 1x 15 + 8 Therefore 1= 8 x 23 – 3 x 61
15 = 1x 8 + 7 b-1 = 23-1= 8
8 = 1x 7 + 1 a = 8
v_i=a^(-1) w_i mod m
=bw_i mod m
v_i={ 30, 17, 8, 3, 1}

Cipher text V = bC mod m Plaintext
14 23 x 14 mod 61 = 17 01000 = 8 = I
25 23 x 25 mod 61 = 26 01101 = 13 = N
89 23 x 89 mod 61 = 34 10011 = 19 = T.

3. RSA is also a stream cipher like Merkel-Hellman.
a) True
b) False
View Answer

Answer: a
Explanation: RSA is a block cipher system.

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4. In the RSA algorithm, we select 2 random large values ‘p’ and ‘q’. Which of the following is the property of ‘p’ and ‘q’?
a) p and q should be divisible by Ф(n)
b) p and q should be co-prime
c) p and q should be prime
d) p/q should give no remainder
View Answer

Answer: c
Explanation: ‘p’ and ‘q’ should have large random values which are both prime numbers.

5. In RSA, Ф(n) = _______ in terms of p and q.
a) (p)/(q)
b) (p)(q)
c) (p-1)(q-1)
d) (p+1)(q+1)
View Answer

Answer: c
Explanation: Ф(n) = (p-1)(q-1).

6. In RSA, we select a value ‘e’ such that it lies between 0 and Ф(n) and it is relatively prime to Ф(n).
a) True
b) False
View Answer

Answer: b
Explanation: gcd(e, Ф(n))=1; and 1 < e < Ф(n).

7. For p = 11 and q = 19 and choose e=17. Apply RSA algorithm where message=5 and find the cipher text.
a) C=80
b) C=92
c) C=56
d) C=23
View Answer

Answer: a
Explanation: n = pq = 11 × 19 = 209.

8. For p = 11 and q = 19 and choose d=17. Apply RSA algorithm where Cipher message=80 and thus find the plain text.
a) 54
b) 43
c) 5
d) 24
View Answer

Answer: c
Explanation: n = pq = 11 × 19 = 209.
C=M^e mod n ; C=5¹⁷ mod 209 ; C = 80 mod 209.

9. USENET falls under which category of public key sharing?
a) Public announcement
b) Publicly available directory
c) Public-key authority
d) Public-key certificates
View Answer

Answer: a
Explanation: Many users have adopted the practice of appending their public key to messages that they send to public forums, such as USENET newsgroups and Internet mailing lists.

Perform encryption on the following PT using RSA and find the CT.

10. p = 3; q = 11; M = 5
a) 28
b) 26
c) 18
d) 12
View Answer

Answer: b
Explanation: n = 33; f(n) = 20; d = 3; C = 26.

11. p = 5; q = 11; M = 9
a) 43
b) 14
c) 26
d) 37
View Answer

Answer: b
Explanation: n = 55; f(n) = 40; d = 27; C = 14.

12. p = 7; q = 11; M = 8
a) 19
b) 57
c) 76
d) 59
View Answer

Answer: b
Explanation: n = 77; f(n) = 60; d = 53; C = 57.

13. p = 11; q = 13; M = 7
a) 84
b) 124
c) 106
d) 76
View Answer

Answer: c
Explanation: n = 143; f(n) = 120; d = 11; C = 106.

14. p = 17; q = 31; M = 2
a) 254
b) 423
c) 128
d) 523
View Answer

Answer: c
Explanation: n = 527; f(n) = 480; d = 343; C = 128.

15. n = 35; e = 5; C = 10. What is the plaintext (use RSA) ?
a) 3
b) 7
c) 8
d) 5
View Answer