Results 1 to 2 of 2

Math Help - derangements and permutations in cryptography

  1. #1
    Newbie
    Joined
    Mar 2014
    From
    Melbourne, Australia
    Posts
    2

    derangements and permutations in cryptography

    hi, i have a problem that i am having a bit of trouble with;

    we are given a partial key (missing 11 letters) for a mono-alphabetic substitution cipher and asked to calculate the number of possible keys given that no plaintext letter can be mapped to itself.


    ordinarily, the number of possible keys would be the number of derangements of the missing letters (!11), however 5 of the plaintext letters that are missing mappings already exist as mappings in the partial key, so logically it shouldnt matter what the mapping of those plaintext letters is, because they can never map to themselves.


    so shouldnt the number of possible keys be 5! * !6, ie. (the number of permutations of the 5 already mapped free letters) * (the number of derangements of the remaining 6)?


    the problem is that 5! * !6 = 31800 which is much less than !11 = 39916800


    intuitively the set of derangements should be a smaller subset of !11, shouldnt it?


    am i just getting something wrong in my arithmetic? or am i completely missing the concepts? any help would be greatly appreciated


    thanks gus
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2014
    From
    Melbourne, Australia
    Posts
    2

    Re: derangements and permutations in cryptography

    sorry, the value for !11 should be 14684570, not 39916800 which is the value of 11!..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. number of derangements
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 28th 2013, 02:45 PM
  2. Mathematical Thinking: 2 Derangements/proof questions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 11th 2010, 04:48 AM
  3. Replies: 2
    Last Post: December 10th 2010, 11:38 AM
  4. Derangements(help me asap)
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 13th 2010, 01:07 AM
  5. Number of derangements of n objects
    Posted in the Math Challenge Problems Forum
    Replies: 10
    Last Post: February 10th 2010, 08:16 AM

Search Tags


/mathhelpforum @mathhelpforum