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Trying to Develop a Decryption Scheme for a Given Encryption

  1. Sep 17, 2011 #1
    Hello PF friends!

    Earlier this week a friend of mine (both of us are in the same mathematics department) posed an encryption mapping to me and I have thus far not been able to solve it. Here's the map of the k+1 layer:

    [itex]\lambda_n^{k+1} = (\sum_{i=1}^{n} \lambda_i^{k})\; mod\; 27,[/itex]

    where [itex]\lambda_i^{k}[/itex] is the numerical representation (A=0,B=1,...,' '=27) of the ith letter of the kth layer.

    Clearly this encryption is punctuation-free and does not act on numbers. Let me show you what the process looks like:

    Plaintext: H-E-L-L-O T-H-E-R-E
    # Repr. : 7-4-11-11-14-26-19-7-4-17-4
    Encrypt : 7-11-22-6-20-19-11-18-22-12-16

    So far, I have shown that because the first number in the code never changes, determining the second letter reduces to solving a modular equation if we know how deeply encrypted the data is (a requisite for decrypting this in full, I think).

    The first part I am working on is trying to show if it is Uniquely Decipherable or not--I haven't found a counter-example to it, but am also not sure how to apply the theorems of Sardinas and Kraft to this code.

    Finally, if it is uniquely decipherable, I wonder if this code is at best probabilistically decipherable.

    Any insight or thoughts would be great...I don't want to work on writing an encryption algorithm if I can't find a way to decrypt it!
  2. jcsd
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