How to do multiplication in Galois Fiels(2^8)?

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Expression for Galois Fiels(2^8) multiplication:-

Which of the following expression is the correct one? please suggest.

Exp[ ( Log A + Log B )Mod 255]
OR
[Exp( Log A + Log B )] Mod 255

Posted 8-Feb-12 20:25pm

Ratika Agarwal

Updated 14-Feb-12 19:07pm

v5

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Sergey Alexandrovich Kryukov 9-Feb-12 2:30am

What, no language tagged, nothing? This is off-topic. Do you need to learn mathematics? Learn it. Matrices is a really simple topics (but of course you will need a lot more). This is a wrong forum.
--SA

Ratika Agarwal 9-Feb-12 2:40am

I think you should do a bit homework on the questions posted in forums. B'coz you may be the only one who is not able to understand some term of it. If you know the ans.then post it. Else, let others help the needy ones.

Sergey Alexandrovich Kryukov 9-Feb-12 2:49am

Please do me a favor to decide by myself if I decide to post or not. Please don't take my words as an accusation in poor knowledge in mathematics or something like that. I just don't know it from your question. And to help you, I need to know what exactly you are missing. In this case, do you know the algorithm or not? Is there anything related to computer science or programming you need help with? I still don't understand it. Are you talking about matrix multiplication or something else?
--SA

Ratika Agarwal 9-Feb-12 2:33am

I don't need a language specific answer. I just want its logic and idea. It is a part of advance Mathematics, that's why I have tagged is as mathematics too.

Sergey Alexandrovich Kryukov 9-Feb-12 2:43am

Advanced..? He-he... :-)
--SA

Ratika Agarwal 9-Feb-12 2:47am

Quote me... "You are here to ask for help or to help somebody. Not to make fun of what you don't know about."

Sergey Alexandrovich Kryukov 9-Feb-12 2:50am

May I ask you why? :-)
You are talking as if this is something bad... :-)
--SA

Sergey Alexandrovich Kryukov 9-Feb-12 3:09am

Please, don't post non-solution as a solution. No one will see it anyway unless she or he loads this page, so it could not help you. And you are not answering my questions. Not to many people are dealing with this branch of mathematics anyway, so don't get hysterical. So far, your are the one who gets the most opportunities to find out the solution, but you still expect some help...
--SA

Ratika Agarwal 9-Feb-12 3:13am

What is your ques?? tell me.

Sergey Alexandrovich Kryukov 9-Feb-12 3:19am

:-)

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Sergey Alexandrovich Kryukov · Answer 1 · 2012-02-08T20:30:00

Solution 1

http://en.wikipedia.org/wiki/Matrix_%28mathematics%29[^].

[EDIT]

This looks like an interesting work, but I'm not sure it's detailed enough: http://www.google.com/url?sa=t&rct=j&q=%28%22finite+field%22+OR+%22galois+field%22%29+matrix+multiplication&source=web&cd=3&ved=0CC8QFjAC&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.83.5873%26rep%3Drep1%26type%3Dpdf&ei=lH8zT-LYMIfa0QHnqaS5Ag&usg=AFQjCNGxSfwGU1_1obUpSMfEsOAq62AiwA[^].

—SA

Posted 8-Feb-12 20:30pm

Sergey Alexandrovich Kryukov

Updated 8-Feb-12 21:18pm

v2

Comments

Ratika Agarwal 9-Feb-12 2:35am

I know matrix operations very well. But my problem is to multiply in GALOIS FIELD(2 power n).

Sergey Alexandrovich Kryukov 9-Feb-12 2:41am

Good for you. I apologize then. But what tells you that Galois field requires matrix multiplication which is different. I think matrix multiplication is matrix multiplication. Please explain to me if I'm wrong.

And what's your problem? Is it programming or mathematics?
--SA

Ratika Agarwal 9-Feb-12 2:49am

A simple matrix mult.is not same as in Galois Field(2 power n). That is what I am asking here for, how to do it..

Sergey Alexandrovich Kryukov 9-Feb-12 2:55am

Sound surprising... do you know just the definition of the operation you need? I don't... "How" goes next...
--SA

Sergey Alexandrovich Kryukov 9-Feb-12 3:12am

Is it Vandermonde matrix multiplication over finite field?
--SA

Ratika Agarwal 9-Feb-12 3:22am

Yes. It is the multiplication over a Galois finite Field, but not over vandermonde.

Sergey Alexandrovich Kryukov 9-Feb-12 3:38am

I understand what's "over a finite field" but not "over Vandermonde" :-)
--SA

Sergey Alexandrovich Kryukov 9-Feb-12 3:40am

OK, where is the definition of a particular operation over a finite field and why you need that operation and not another?
--SA

Ratika Agarwal 9-Feb-12 3:45am

I need this particular operation for "Mix rows /columns operation of AES/Whirlpool algorithms" of cryptography.

Sergey Alexandrovich Kryukov 9-Feb-12 3:53am

There are a lot of open-source implementations of this algorithm...
--SA

Sergey Alexandrovich Kryukov 9-Feb-12 3:58am

This algorithm is more or less explained here, but I'm afraid, may be not in all detail:

http://books.google.com/books?id=WEyWx0k-jLQC&pg=PA43&lpg=PA43&dq=%28finite+OR+Galois%29+field+whirlpool&source=bl&ots=8inQ1kRJ12&sig=thNSa11KdoDqDD8_nwS7pxg9aaI&hl=en&sa=X&ei=uokzT8SNIoKN0QHY7p3IAg&ved=0CCwQ6AEwAQ#v=onepage&q=%28finite%20OR%20Galois%29%20field%20whirlpool&f=false

--SA

Ratika Agarwal 9-Feb-12 3:30am

Thanks for help. But I have already searched a lot before coming to code project. I too came across this PDF, but it's not helpful.

Sergey Alexandrovich Kryukov 9-Feb-12 3:37am

Yes, that was my guess...
--SA

Espen Harlinn 9-Feb-12 8:44am

5'ed! - quite an effort :)

Sergey Alexandrovich Kryukov 9-Feb-12 12:21pm

Not at all, but thank you.
--SA