1. ## Cryptography....

Hello...

"Z c s f f b e u a s s o x c z w u x b s n b h a o g y m q h m x z l r e c z m s i c x j k z f c x z e x q c h s k y f n w u v a y j b h t h c g f u a z t d p m t q g p r x g d s a d c y x n q t k h i v f o e b k l e b a l r j e s p b w i "

was encrypted with a (4 X 4) Hill cipher and the first 16 bits decrypted to:
" a r c h i m e d s e g o t s o e"

1) We need to find the (4 X 4 ) matrices A and B such that A.M = B, where M is the encryption matrix...

2) Use M to decrypt the entire message...

thanks for the help!

2. Originally Posted by Vedicmaths
Hello...

"Z c s f f b e u a s s o x c z w u x b s n b h a o g y m q h m x z l r e c z m s i c x j k z f c x z e x q c h s k y f n w u v a y j b h t h c g f u a z t d p m t q g p r x g d s a d c y x n q t k h i v f o e b k l e b a l r j e s p b w i "

was encrypted with a (4 X 4) Hill cipher and the first 16 bits decrypted to:
" a r c h i m e d s e g o t s o e"

1) We need to find the (4 X 4 ) matrices A and B such that A.M = B, where M is the encryption matrix...

2) Use M to decrypt the entire message...
!
The Hill Cipher was developed and published in 1929. Mr. Hill (& company) invented a hardware device -- for which he got a patent. The product did not become a killer app -- not because it had problems -- but in the 1930 depression era, data security was not a high priority.

The Hill cipher can use matrices of 2x2, 3x3, 4x4, 5x5, 6x6, etc. for the encryption/decryption process.

In this example above, the fundamental pieces of information about the Hill cipher are given.
1) A 4x4 encryption matrix.
2) The plain text and the matching cipher text.
3) Only 26 letters in the system [using MOD 26]

Some of the information supplied:
Ciphertext= "zcsffbeuassoxczwuxbsnbhaogymqhmxzlreczmsicxjkzfcx zexqchskyfnwuvayjbhthc..."
Plaintext = "archimedsegotsoe..."
--------------
4x4 ciphertext in columns of 4 row depth
zfax
cbsc
sesz
fuow

The ciphertext letters (ascii code) transformed to numeric values a=0, z=25 (mod 26 matrix).

$C = \begin{bmatrix}25 & 05 & 00 & 23 \\
02 & 01 & 18 & 02 \\
18 & 04 & 18 & 25 \\
05 & 20 & 14 & 22 \\
\end{bmatrix}$

-------------
4x4 plaintext
aist
rmes
cego
hdoe

& the associated plain text numeric matrix

$P= \begin{bmatrix}00 & 08 & 04 & 19\\17 & 12 & 18 & 18\\02 & 04 & 06 & 14\\07 & 03 & 14 & 04\\ \end{bmatrix}$

[The detailed explanation has been abridged]*
With a transpose of the 4x4 Ciphertext adjacent to a 4x4 transpose of the plaintext,
making a 4 row x 8 column matrix. The Ciphertext was row-reduced modulo 26 to reduced
echelon form, then forming an identity matrix for the left half, thus the right half
was a transpose of the inverse matrix.
That matrix was used to decrypt the data supplied.
Something didn't work as expected.
There was a typo in the supplied PLAINTEXT data.
The 9th & 10th letters of the plain text appeared to be swapped, since the
accepted spelling of the greek math man is "ARCHIMEDES".
I changed the plaintext & recomputed. This is the resulting decryption matrix and
the supplied ciphertext decoded.
===================
A decryption matrix

$M= \begin{bmatrix}24 & 02 & 17 & 00\\ 23 & 11 & 23 & 04\\ 21 & 05 & 05 & 21\\19 & 16 & 15 & 02 \end{bmatrix}$

The decrypted message:
archimedesgotsoexcitrdbecausehesblveqtheproblemtua thnzfjjlezpnrnnazfkmyvetcxpfni
with spacing:
archimedes got so excitrd because he sblveq the problem tuat hnzfjjlezpnrnnazfkmyvetcxpfni
From this it appears that the ciphertext was not proof read when entered.

*It makes little sense to have a full explanation of how it works when the data is invalid.

3. WoW !

Thanks a lot for the help Sir!

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### hill cipher 4x4 example

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