Bill Allombert on Thu, 16 Feb 2017 00:06:24 +0100 |
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Re: Verifying Elliptic Curve Cryptography |
On Wed, Feb 15, 2017 at 05:26:53PM -0500, James Cloos wrote: > 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? What is a "modern curve" ? Is it modern like in "modern dance" ? > 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? You can use ellfromeqn() to compute an Weierstrass equation for the curve. ? e=ellfromeqn(x^2+y^2-(1-376014*x^2*y^2)) %3 = [0,376013,0,1504056,565544608728] ? p=2^521 - 1; ? E=ellinit(e,p); ? ellcard(E) %6 = 6864797660130609714981900799081393217269435300143305409394463459185543183397654701903506606654631398546774636260936570417277131794810169271973685174680434092 Cheers, Bill.