# how to find key matrix in hill cipher

I want to solve this problem but there are 3 known plaintext-ciphertext pairs.

The key of Hill cipher is a 3*3 matrix as k=[k1,k2,3; k4,k5,k6; k7,k8,k9] where the unknown ki={0,1,...25}={A,B,...,Z} can be solved given a sufficient number (at least three are needed) known plaintext-ciphertext pairs. It is given that Ek(sky)=BAA, Ek(sun)=ABA, Ek(hat)=AAB. Find the decryption matrix, that is, the inverse k^-1 of the key matrix K.

• Welcome to crypto.se! $\;$ Your question is a straight dump of homework, and thus off topic. You are supposed to try solving the problem, and ask us only when you hit an issue, and tell us which. $\;$ As for any problem of this kind, I suggest that you 1) identify appropriate unknowns 2) identify what the givens tell you about these unknowns 3) try to apply your bag of mathematical tools. – fgrieu Oct 8 '14 at 12:09
• the problem is that I can solve this problem just for 1 known plaintext-ciphertext pair. and I put all pairs in one matrix and I have doubt that is true or false. – teardrop Oct 8 '14 at 12:47
• No you can't solve this problem with a single known plaintext-ciphertext pair (where plaintext and ciphertext are 3 characters): that's $3\cdot\log_2(26)$ bits worth of information, when the matrix holds nearly $9\cdot\log_2(26)$ bits of information (not quite, because it is known invertible; but close). $\;$ Again, write down what known plaintext-ciphertext pairs tell you about the unknowns; the rest will follow. – fgrieu Oct 8 '14 at 12:55