Question

Question #6dc14

Answer 1

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 :