# How can I decode a Hill Cipher without a key? [duplicate]

On my exam, we had to solve this problem:

message matrix is: [20, 19, 14; 17, 0 10]
and the ciphertext matrix is: [18, 15, 16; 3, 24, 24].
Find key matrix.

I couldn't solve this problem, because I tried to find key matrix by multiplying [20, 19, 14; 17, 0 10]^-1 and [18, 15, 16; 3, 24, 24], but I wasn't able to calculate [20, 19, 14; 17, 0 10]^-1, because it's not a square matrix.

How can I decode a Hill Cipher without a key?

## marked as duplicate by e-sushi, fgrieu, Gilles, AFS, rathApr 26 '14 at 16:15

• There's a comma missing after the first 0, and perhaps some other parts of the statement (as is, by an entropy argument, it seems plausible that several keys could match). – fgrieu Apr 24 '14 at 12:17