|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 fields. 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. Cheers, Bill.