ECTester contains a collection of elliptic curve/point parameters, these parameters either come from standards or were generated manually or using ecgen.
These parameters can be found in the cz.crcs.ectester.data package.
SEC 2: Recommended Elliptic Curve Domain Parameters version 2.0 January 27, 2010
RECOMMENDED ELLIPTIC CURVES FOR FEDERAL GOVERNMENT USE July 1999
ANSI X9.62 example curves.
ECC Brainpool Standard Curves and Curve Generation v. 1.0 19.10.2005
Agence nationale de la sécurité des systèmes d'information: Publication d'un paramétrage de courbe elliptique visant des applications de passeport électronique et de l'administration électronique française. 21 November 2011
GOST R 34.10-2001: RFC5832 curves.
Barreto-Naehrig curves from: A Family of Implementation-Friendly BN Elliptic Curves
An assortment of some other curves. Montgomery curves transformed into short Weierstrass form from https://eprint.iacr.org/2013/647.pdf
Curve25519 transformed into short Weierstrass form.
These prime field curves have the same order as the field order, and are susceptible to attacks reducing ECDLP over a multiplicative group of the curve, to DLP over an additive group of the underlying field, which is easy (linear time).
Some of these are from Atsuko Miyaji's paper, others were generated using ecgen.
This category contains pre-generated invalid curves for a large subset of NIST, SECG and Brainpool curves. Invalid curves for a given curve, are short Weierstrass curves with all parameters equal to the given curve except the b
parameter. These curves can be used to attack some implementations.
Generated using ecgen.
Contains curves of composite order, with small order points.
Generated using ecgen.
Contains parameters that are not elliptic curves(over Fp and F2m), such as p
parameter that is not prime or an irreducible polynomial that is not irreducible.
Generated manually.
Contains pre-generated points on twists of known named curves from NIST, SECG. These points can be used to attack some implementations.
Generated using ecgen.
Contains pre-generated points on the line Y: x = 0
. These points are constructed from elements of prime
order in the multiplicative group F_p given a curve over it.
Generate manually using PARI/GP.
Contains curves that are composite order, with points not on the subgroup generated by the generator.
Generated using ecgen.
Contains supersingular curves, over F_p with order equal to p + 1. These have embedding degree equal to 2.
Generated using ecgen.
Contains some test vectors from the google/Wycheproof project.