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Homework Help: Cryptographic system

  1. Jun 2, 2010 #1
    4. Consider a cryptographic system in which a message is list of 5 real numbers: n = [n_1, ... n_5].
    The numbers are encrpyted by multiplication with a fixed 5x5 encryption matrix M:
    e=[M ]∗n
    where "e" is a vector containing the encrypted numbers.
    Given
    e = [19, 3 , 6 ,11 , 23 ]
    and
    M=[3 2 1 0 0
    0 1 -1 0 1
    0 0 1 1 0
    1 1 0 1 0
    0 5 2 0 -1]
    is it possible to find n?
    And if yes, find it.

    my first thought was just to use row reduction of the matrix:

    M=[3 2 1 0 0 19
    0 1 -1 0 1 3
    0 0 1 1 0 6
    1 1 0 1 0 11
    0 5 2 0 -1 23]

    but a couple of steps later on it just screws up ;(

    can anyone help here ?
     
  2. jcsd
  3. Jun 2, 2010 #2
    What is the condition for the message to be decrypatble? What did you with M to the original message? What do you need to do to get back to it? How would you do that? How do check if it can be done?
     
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