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).

-------------

4x4 plaintext

aist

rmes

cego

hdoe

& the associated plain text numeric matrix

[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

The decrypted message:

archimedesgotsoexcitrdbecausehesblveqtheproblemtua thnzfjjlezpnrnnazfkmyvetcxpfni

with spacing:

archimedes got so excitrd because he sblveq the problem tuat hnzfjjlezpnrnnazfkmyvetcxpfni

From this it appears thatthe ciphertext was not proof readwhen entered.

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