Given the key displayed below 4x4 key. Pick a plain text message (three words, n
ID: 3932633 • Letter: G
Question
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
Explanation / Answer
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.
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