Verifying Elliptic Curve Cryptography

[James Cloos <cloos@jhcloos.com>]

I've read examples in sage, but pari/gp is more readily available
on my systems, so:

Does anyone have any sample code in gp for working with modern curves?

I'm interested in the math for things like ecdh or eddsa using
"safe" curves (cf: http://safecurves.cr.yp.to).

I take it that sage's EllipticCurve() uses pari's ellinit(), yes?

I haven't done much with pari's elliptic curve support.

In particular, how can one use a curve like e:521:

  x^2+y^2 = 1-376014x^2y^2
  modulo p = 2^521 - 1

given that ellinit doesn't take an x²y² coefficient?

-JimC
-- 
James Cloos <cloos@jhcloos.com>         OpenPGP: 0x997A9F17ED7DAEA6