Pari functions for elliptic curves are very general and work for finite fields as well. A finite field elements is represented by a modular polynomial modulo an irreducible modular polynomial. For instance, a representation of the finite fields with 7^3 elements consists of elements of this form (in Pari notation):
Mod( Mod(1, 7)*a*x^2 + Mod(1, 7)*b*x + Mod(1, 7)*c, Mod(1, 7)*x^3 + Mod(1, 7)*x + Mod(1, 7) )
You get all elements by varying a, b and c from 0 to 6. See this recent thread for more examples.

Building an efficient finite field library starting from big integers is fun, but quite demanding, and you'd probably prefer to focus on the higher level algorithms. In this case, I suggest you try and play a bit with Pari under the GP environment (which is interactive and has online help). Once you have understood what functions serve your purpose, you can assemble them into a C program or a GP script, which will be invoked from your program, or integrate them directly into your program (via Math::Pari).

Have fun

Antonio

The stupider the astronaut, the easier it is to win the trip to Vega - A. Tucket

In reply to Re: Re: Re: Elliptic Curves in polynomial groups by abell
in thread Elliptic Curves in polynomial groups by John M. Dlugosz

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