*Matrix Cryptography*by David Stanley

Cryptography,
put simply, is the art of encoding messages.
It serves to answer the simple question of how you get a message to a
friend without your enemy being able to read it. Cryptography has been used for centuries by
militaries and intelligence agencies to send important messages, while insuring
that the information the messages contain does not fall into enemy hands.

Although there are many forms of
cryptography, one of the simplest yet most effective forms of encryption still
utilizes the simple

**matrix**.The message is placed in matrix form, and then multiplied by a random square matrix or**encoding matrix**.
The first step is to write down the message
that you wish to send. I will use this
completely true and totally non-brown nosing message as an example:

**Mr Roer is the best math teacher ever in the history of humanity.**

Secondly, you must create an

**encoding matrix**. This matrix must be a square matrix. An example of this would be:

In this kind of encryption, letters are
assigned numbers for their place in the alphabet. A would be 1, B would be 2, C would be 3 and
so on. Spaces are assigned the number
27, as their are only 26 letters in the alphabet. So the message in matrix form would be:

Notice how my encoding matrix has the
same amount of columns as the message matrix does rows. This is required or else they cannot be
multiplied. All that is left to do is to
multiply the encryption matrix by the message matrix. This gives you:

Now
if you received this in the mail, you would have no idea at all what it
said. In order to figure this out in a
timely manner, you would have to have the decoding matrix. The decoding matrix is the inverse of the
encoding matrix. This can easily be
found on your calculator. The decoding
matrix for this problem is quite long, so I will round to four decimal
places.

The exact elements in the decoding matrix have more digits and would give the exact numbers as the original message. Using this rounded decryption matrix gives numbers that can all be rounded to the original message, though occasionally a letter might be slightly off.

In summary, the encoding process written in
calculator language when

[A] is the encoding matrix,

[B] is the original
message,

and [C] is the encoded message is [A]x[B]=[C].

The process of decoding the message is ([A]^-1)x[C]=[B].

And there you have it. That is matrix cryptography in a
nutshell.

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