Cryptographic Arithmetic Toolbox/Software 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? 

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