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Thread: Cryptography questions

  1. #1
    Oct 2009

    Cryptography questions

    Explain why not all encryptors have corresponding decryptors, providing at least two examples of cncryptors wihch cannot be decrypted.

    of the (26)^2=676 possible encryptors, determine precisely which have decryptors and which don't. How many decryptable encryptors are there?

    Explain a procedure indicating how to find a decryptor, that is, if one exists for any given encryptor

    Help would be greatly appreciated

    For these problems we are using linear congruences. A linear encryptor is a function of the form E(w)=Aw+B (mod N)
    Last edited by MichaelG; Nov 9th 2009 at 04:33 PM. Reason: More Detail
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  2. #2
    MHF Contributor chisigma's Avatar
    Mar 2009
    near Piacenza (Italy)
    From the encryption law...

    $\displaystyle E(w)= A\cdot w + B \mod N$ (1)

    ... we derive the 'decryption law'...

    $\displaystyle w = A^{-1}\cdot (E - B) \mod N$ (2)

    The problem in this case is represented by the term $\displaystyle A^{-1}$, that is the 'multiplicative inverse' of the element $\displaystyle A \in W$. But $\displaystyle N=26$ is not prime so that not all the $\displaystyle A \in W$ do have multiplicative inverse...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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