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Is there any popular robust implementation for a finite field in java? (An implementation of prime fields ,i.e. $GF(p)$ might also be good.

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You could look at Givaro c++ library for finite fields (I used it, and it is quite okay, and source code is accessible), and try to adapt it to java, because for java I am afraid you have nothing analogue. (Last time I looked for this, I found only some buyable library, and for $p=2$ only.)

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  • $\begingroup$ Can you post a link? C++ might be okay also, I can use JNI. Forgot to mention, I need to use it with very large fields (for cryptography matters), does it efficient enough? $\endgroup$ – Bush Oct 31 '14 at 17:34
  • $\begingroup$ I don't know if it would suit your need, as I was using it to construct quasi-numbers. A link ? Google is your friend, and typing "Givaro c++" in it may surprise you. $\endgroup$ – Olórin Oct 31 '14 at 17:36
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You can check Rings Java library (http://ringsalgebra.io). It has quite efficient support for Galois fields $GF(p, k)$ (both for small and for arbitrary large $p$).

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