Given the key displayed below 4x4 key. Given phrase \"meetmetonight\" go through

Question

Given the key displayed below 4x4 key.    Given phrase "meetmetonight" 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

No other informaiton is given on this question.

Explanation / Answer

given text=meetmetonight

given key matrix=8 6 9 5

                          6 9 5 10

                           5 8 4 9

                           10 6 11 4

first we should encrypt the text

for that we have to write plain text 4*1 form

m    12    m 12    n    13     t    19

e      4      e 4      i    8       z    25

e      4       t 19    g    6      z    25

t       19     o    14   h    7     z    25

we have got our key M and each of these plaintext converted into 4*1 ismutilplied with that

                          8 6 9 5          12

                          6 9 5 10 *        4

                           5 8 4 9            4

                           10 6 11 4          19

we get code rgte

similarly for other we get code

xfit

hqim

cmwn

the ciphertext is

rgtexfithqimcmwn

for decryting this we find the inverse of the key modulo 26

which comes out be

23 20 5 1

2 15 18 1

2 20 6 25

25 2 22 25

now multiplying this inverse key with the cipher text 4*1 matrix we get plaintext.

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