How are matrices used in cryptography?

Answer 1

Suppose you had a secret message you needed to give someone. You can use a matrix to make it unreadable to anyone except the recipient.

First, you must have an encoding matrix. Let's suppose your encoding matrix is...

-2 2 3

-1 3 2

2 1 3

And your message is... I like matrices

You must then write you message with numbers.

Suppose you use the code A=1, B=2, C=3 etc. Spaces are 27.

That would make your message this:

9 27 12 9 11 5 27 13 1 20 18 9 3 5 19

You translate this into a matrix, going down the columns. The matrix must have three rows to be able to multiply.

9 9 27 20 3

27 11 13 18 5

12 5 1 9 19

When you multiply the two, you get...

72 19 -25 23 61

96 34 14 52 50

81 44 70 85 68

To find the original message, you multiply by the inverse

of the encoding matrix--the decoding matrix. You will find the first pattern of numbers and be able to find the message.

(Sorry, I don't know how to make matrix brackets. You'll just have to deal with it. I tried to make it pretty clear.)