Simple Data Encryption with Applied Algebra

by Pyrotech

In order to perform encryption of this kind you will require some basic knowledge of linear algebra or a program such as matlab or mathematica that will perform any operations you need.

The idea behind this form of encription is as follows; a number is assigned to each letter, number and symbol required for the data transfer (any number will do, and dont forget to assign a number for spaces between words). The letters contained in the message are then replaced by the numbers assigned to them as shown in the example:

space=27
a=1
b=2
c=3
and so on

hence 'hello mate'=8 5 7 7 15 27 13 1 20 5

We can then form a matrix of any number of dimensions. Here I will form a 3 by 4 matrix

8 5 7 7
15 27 13 1
20 5 27 27

(Extra spaces are placed at the end to ensure the shape of the matrix).

We then left multiply this matrix by any 3 by 3 invertible matrix. The size of this invertible matrix (which is your 'encryption key') corresponds to the number of rows of the data matrix. Once this multiplication is completed the data is encripted and can be sent safetly to a thirs party. To decrypt it they must left multiply the encripted data matrix by the matrix inverse of the encription matrix.

All that remains to be done is substitute the letters back in, and the decryption is complete. As you can see, it is very difficult to decrypt such a code without the matrix key.