Given the key displayed below 4x4 key Pick a plain text mess

Given the key displayed below 4x4 key. Pick a plain text message (three words, no spaces; meetmetonight, for example—or use something else!), go through the detailed steps of the Hill cipher explained in the textbook (Chapter 2 and any supporting material), and encrypt it. Then reverse the encryption (again in a detailed, step-by-step fashion) and recover the plaintext.

Here is the key matrix:

8              6              9              5

6              9              5              10

5              8              4              9

10           6              11           4

Solution

message = \"soyerandtext\"

breaking the message into pieces of 4 since the key is 4X4.

message = [s o y e]\' [r a n d]\' [t e x t]\'

message in numbers = [18 14 24 4]\' [17 0 13 3]\' [19 4 21 19]\'

Then multiplying the key matrix and message matrix to get the resulting array using a python program given below:

import numpy as np
key = [[8, 6, 9, 5], [6, 9, 5, 10], [5, 8, 4, 9], [10, 6, 11, 4]]
message = [18, 14, 24, 4]
print np.dot(key, message)

Result:

[464 394 334 544], [268 197 164 325] and [460 445 382 521]

Taking modulo 26 of all these resulting arrays:

= [22 4 22 24], [8 15 8 13] and [18 3 18 1]

Therefore, message = [W E W Y]\', [I P I N]\' and [S D S B]\'

Hence, encrypted message = wewyipinsdsb

Getting back the plain text,

Inverse of the key matrix:

[ -3 20 -21   1]
[ 2 -41 44   1]
[ 2 -6   6 -1]
[ -1 28 -30 -1]

this mod 26 =

[ 23 20 5 1]
[ 2 11 44   1]
[ 2 20 6 25]
[ 25 2 22 25]

Now, multiplying this with our cipher text using the same python code:

[720 1080 856 1642]\' , [537 546 689 731]\' and [565 862 229 877]\'

Now, finally taking modulo 26 of these matrices:

[18 14 24 4]\', [17 0 13 3]\' and [19 4 21 19]\'

Which is \"soyerandtext\" which was our initial message.