Cryptopgraphy is extremely benifical to people, enabling them to keep certain information private, it has been a very imporatant matter all throughout history and till this very day.
You Probably Wonder how can matrices possibly be used Cryptography!
Well it is quite simple to say that due to the existence of matrices their multiplication and their inverse, The idea of cryptoghraphy was made possible.
Here is an example I found demonstrating how cryptography can be use to hide certain information using matrices multiplyong them and then finding their inverses, if you are intrested enough check this link to expand your understanding on how the following example was made Possible.
EXAMPLE:
Consider the Following Matrix Reffered to as the Encoding Matrix:
{-3,-3,-4;0,1,1;4,3,4} ( the comma seperates the entries in the rows and the semicolon seperates the columns)
Let the message we want to send be: Prepare to negotiate.
Assing every letter of the alphabet to a number ex: A-1 B-2 C-3 etc...
By Decoding the Matrix above and finding its inverse relate every entery in the Inverse matrix to the approtpriate letter and you will find your message.
Check out the Link To Deepen your understanding of Cryptography using matrices and their inverses. http://aix1.uottawa.ca/~jkhoury/cryptography.htm
Thank You,
Oliver Chlela
waw, that was a really intresting way of using matrices, I never thought that nations use them to encode/decode messages. It's cool to find out that by transforming a message into numbers,then into a matrix, and by multiplying it by an encoding matrix, you actually create a well protected coded message!! Moreover, to decode it, the inverse of the encoding matrix is used, now that's one super thing! Very nice post Oliver!
ReplyDeleteI found it also intresting nothing to add to what alessandra said. A new way maybe to say merry christmas through a matrix notation.
ReplyDeleteOliver,
ReplyDeleteThanks a lot! Very interesting indeed! I think decoding and encoding is a very useful applications on matrices!
Enjoy your vacations!
Zeina
it's probably the most interresting post yet
ReplyDeleteso thx oliver
and a
10 66 24 77 37
1 25 5 25 18 (HAPPY NEW YEAR)
48 81 69 15 81
TO ALL
and the encoding matrix is:
1 2 0
0 1 0
0 0 3
Thanks for the post. i think it is fairly interesting to find out about such things. I think that this system of encryption is being used these days in video games and other entertainment related subjects. So, good work and thanks again.
ReplyDeleteAntoine Bou Nader
LAU
i tried to search on the web about its uses in our major as biology students and found out that it can be used by physicians to calculate the progression of the disease in patients.. pretty interesting..i like
ReplyDeleteGeorge Ghanameh
LAU
to emphasize on what i previously stated, Scientists can also use linear algebra matrices to predict future outbreaks of a disease. Scientists who track and document and make predictions of future outbreaks of disease must use their skills in linear algebra to validate their findings.. (what is meant by outbreaks of diseases, is that similar to the outbreak of H1N1 last year and based on that they will work harder on finding ways to prevent such a catastrophic event before taking place)
ReplyDeleteGeorge Ghanameh
LAU