Knapsack Cryptosystem Pre Test

• Question 1: For the given sequence: 4, 8, 15, 29, 61, 125, 247, 500
  1. prove that the given sequence is superincreasing
  2. choose the M = 1009 and W = 91 to generate the public key
  3. use the public key that you just generated to encrypt the plaintext message: 10111001
  4. find a multiplicative inverse of W mod 1009
  5. decrypt the message that you got in 4 to get an original plaintext
• Question 2: The following sequence is superincreasing: 2, 3, 6, 12, 25, 40, 98
  1. TRUE
  2. FALSE

• Question 3: For the given sequence 1, 3, 5, 10, 20, 40 and the plaintext 101001 the ciphertext is:
  1. 79
  2. 33
  3. 46
  4. all previous answers are wrong

• Question 4: For the superincreasing sequence 1, 3, 5, 10, 20, 40 and knapsack value 53 the solution is:
  1. 110011
  2. 010101
  3. 101010
  4. all previous answers are wrong

  Additional Questions

  • Give an example of superincreasing sequence and not-superincreasing sequence
  • Give an example of not-superincreasing sequence and the knapsack value that has two possible solutions
  • Give an example of superincreasing sequence and knapsack value that solution doesn't exist