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51. In knapsack cryptosystem, suppose a' = (1, 3, 5, 10), w = 7, m = 20 and x = 1101. Then what cipher text?

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52. In a RSA system, the public key of a given user is e = 31, n = 3599. What is the private key user?

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53. Given the following input (4322, 1334, 1471, 9679, 6171, 6173, 4199) and the has function = x mod 10, which of the following statement(s) is (are) true?
i. 1471, 6171 has to the same value
ii. All elements has to the same value
iv. Each element hashes to a different value

  • Option : D
  • Explanation :
    Hash function given is mod(10).
    9679, 1989 and 4199 all these give same hash value i.e 9
    1471 and 6171 give hash value 1
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54. Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?

  • Option : A
  • Explanation :
    Simple Uniform hashing function is a hypothetical hashing function that evenly distributes items into the slots of a hash table. Moreover, each item to be hashed has an equal probability of being placed into a slot, regardless of the other elements already placed.
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55. Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for i ranging from 0 to 2020?

  • Option : C
  • Explanation :
    Using concept of power of cycle:
    (A) (0,1,4,9,6,5,6,9,4,1,0) repeated
    (B) (0,1,4,9,6,5,6,9,4,1,0) repeated
    (C) (0,1,8,7,4,5,6,3,2,9) repeated
    (D) (0,2,4,6,8) repeated
    So, only h(i) =i3 mod 10 covers all the digits from 0 to 9.
    Option (C) is correct.
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Computer Networks Section 1