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Solution of systems of equations over finite fields

I need to invert a rather large (n> 1000) system of equations in a finite field (more precisely, modulo 2 ^ 32-5). Are there libraries that can do this efficiently? Preferably in Java, but C is fine (we already have some JNI bindings).

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I would go for fflas-ffpack , this is a C ++ library, the developers are super-friendly and the project is constantly being updated.

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