Question #6dc14

1 Answer
Trevor Ryan.
Sep 18, 2015

MATH is encoded as WEVN.
GTXIOHHPLM is decoded as BESTBUDDYZ.

Explanation:

Since the key matrix K is used to encode elements #(x,y)inZZ_(26)xxZZ_(26)#, the inverse matrix #K^(-1)# will decode back to the original plain text.

Using the normal definition and remembering that we work in the field modulo 26, we get that

#K^(-1)=1/(det(K))*adj(K)=[(4,7),(9,22)]#

Performing this calculation we in fact fine that K is involutory, ie, equal to its own inverse. That is #K^2=I_2 and K=K^(-1)#

We may now use the Hill encoding and decoding function with the same key matrix K, and on the given codewords to yield :

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