Bill Allombert on Thu, 07 Jun 2012 12:16:17 +0200

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New experimental GP interface for elliptic curves over finite fields

Dear PARI developers,

I have added a new experimental interface for elliptic curves over finite
A new function ellffinit is provided to create curves over finite fields:

Create a curves over F_7:
? E=ellffinit([1,3],7);

Create a curves over F_101^3:
? a=ffgen(ffinit(101,3),'a);
? E=ellffinit([1,a^3],a);

(for technical reasons, the characteristic must be >3. This will be fixed eventually.)
ellffinit precomputes the structure of the group E(F_q).
ellffinit data is suitable for all functions expecting small ellinit data.

Dedicated algorithms for curves over Fq:
point counting (ellcard): both Shanks-Mestre and SEA are implemented over Fq.
group structure (ellgroup)
group generators (ellgenerators)
pairings (elltatepairing,ellweilpairing)
point order (ellorder)
discrete logarithms FF_elllog

There are some limitation currently (SEA only work for char p>1000).

Please experiment and tell us what you would need.