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Package FiniteFields

In a Mathematica session, I evaluate: Needs["FiniteFields`"]; fld = GF[2]; Now, for example, I'd like to compute $a^3+a^5$ for $a \in{Z_2}$. The result I'd like ...
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Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
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Elliptic curve cryptography in Mathematica

I can find no resources for doing elliptic curve cryptography. I have used the finite field package, but I find it cumbersome and it does not seem to have any builtin methods for ECC. How can I get ...