# Elliptic Curve Primality Proving for Pari/GP
# [Atelier home](http://pari.math.u-bordeaux.fr/wiki/)

## People involved

- Jared Assuncion
- Jean-Pierre Flori
- Dana Jacobsen

## Tasks

Jared has an initial implementation.  Will be released in a branch <? when ?>.  Currently working on using better class groups.

## Comments from Dana

- My standalone GMP ECPP:  [ecpp-dj](http://sti15.com/nt/ecpp-dj.tar.gz).  This seems to be the fastest open source implementation, and is competitive with Pari's APR-CL to ~2000 digits.  See, for example: [graph of performance](http://probableprime.org/images/primality-times-v3.png).  The biggest downside (IMO) is hard-coded class polynomials.  This ships with Perl's ntheory module, so is easily available on Windows and most Linux distributions (though with the default Perl installation it uses a very small set of polynomials).

- Pari has a plethora of functions dealing with class polynomials, including getting one or all roots, finding the j-invariant, etc.  This should be a massive help for implementing ECPP.

- Also included is a verifier in C that understands Primo, Primo 4.1, and MPU certificate formats.  There is a description of the MPU format.  If Pari/GP chooses a different certificate format, it should be a relatively simple matter to add to this verifier or make a converter (assuming the certificate has numbers similar to Morain's papers or a well-written description of how to easily obtain them, like Primo does).

- Important to me as a user is that the certificate be well specified.  Please include a single line header with format name and version number.  Without that it's impossible for a program to determine what is being given to it, or to change the output later.  For running a verifier for a certificate you've just created is one application, storing these certificates for use many years later is a critical application, and if the output is just a jumble of numbers then it's basically useless.