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authorJ08nY2018-02-04 19:20:08 +0100
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# Curves
+ECTester contains a collection of elliptic curve/point parameters, these parameters either come from standards or
+were generated manually or using [ecgen](https://github.com/J08nY/ecgen).
-## SECG
+These parameters can be found in the [cz.crcs.ectester.data](/src/cz/ectester/data/) package.
+
+
+## Standard
+
+### SECG
SEC 2: Recommended Elliptic Curve Domain Parameters version 2.0 January 27, 2010
[Source](http://www.secg.org/sec2-v2.pdf)
-## NIST
+### NIST
RECOMMENDED ELLIPTIC CURVES FOR FEDERAL GOVERNMENT USE July 1999
[Source](http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf)
-## x962
+### x962
ANSI X9.62 example curves.
-## Brainpool
+### Brainpool
ECC Brainpool Standard Curves and Curve Generation v. 1.0 19.10.2005
[Source](http://www.ecc-brainpool.org/download/Domain-parameters.pdf)
-## anssi
+### anssi
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
+### GOST
GOST R 34.10-2001: RFC5832 curves.
[Source](https://tools.ietf.org/html/rfc5832)
-## anomalous
+
+## Generated
+
+### anomalous
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](https://dspace.jaist.ac.jp/dspace/bitstream/10119/4464/1/73-61.pdf), others were generated using [ecgen](htps://github.com/J08nY/ecgen).
-## invalid
+### invalid
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](https://www.nds.rub.de/media/nds/veroeffentlichungen/2015/09/14/main-full.pdf).
-Generated using [ecgen](https://github.com/J08nY/ecgen)
+Generated using [ecgen](https://github.com/J08nY/ecgen).
-## composite
+### composite
Contains curves of composite order, with small order points.
-Generated using [ecgen](https://github.com/J08nY/ecgen)
+Generated using [ecgen](https://github.com/J08nY/ecgen).
+
+### wrong
+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.
-## wrong
-Contains parameters that are not elliptic curves(over Fp and F2m), such as `p` parameter that is not prime, irreducible polynomial that is not irreducible and similar.
+### twist
+Contains pre-generated points on twists of known named curves from NIST, SECG.
+These points can be used to attack some implementations.
-Generated manually. \ No newline at end of file
+Generated using [ecgen](https://github.com/J08nY/ecgen). \ No newline at end of file