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This term I have many cryptography courses treating finite fields. I was wondering if there is any good software that could help doing basic operations in galois fields etc. I already googled but found nothing appropriate.

What I would need: A tool/software that can calculate in arbitrary galois fields gf(p^n)

(+,-,*,/,gcd, inverse)

In addition to that I would need a function to generate an irreducible polynomial for a given field. (parameters could get big e.g. 2^100)

I already considered matlab generating a irreducible polynomial for gf(2^103), but computation takes too long.

Do you have any recommendations and do you know any good programs for calculation in finite fields?


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closed as off-topic by DrLecter, Gilles, Maeher, figlesquidge, AFS Dec 31 '13 at 0:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

Sorry, but reference requests are off-topic. However, Sage is a popular and free tool. – DrLecter Dec 30 '13 at 16:01
As DrLecter says, this question will probably be closed as off-topic. My recommendation would be MAGMA. – figlesquidge Dec 30 '13 at 21:08
okay, but where would have been the right place to ask? – Thorben Dec 30 '13 at 21:18
Discussion of mathematical software is on-topic at Math.SE, as are reference requests (if that's an issue). – hardmath Jan 1 '14 at 18:14
up vote 1 down vote accepted

You can use Sage or MATLAB. Among the two sage is free and uses python as the programming language.

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Looks very promising, I will give it a try, thx – Thorben Dec 30 '13 at 16:10
Sage seems to be the perfect tool for this. The docs belonging to the topic can be found under… – Thorben Dec 30 '13 at 21:21

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