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diff --git a/docs/CURVES.md b/docs/CURVES.md index d1749df..4a80d49 100644 --- a/docs/CURVES.md +++ b/docs/CURVES.md @@ -1,15 +1,47 @@ # Curves -## anomalous +## SECG +SEC 2: Recommended Elliptic Curve Domain Parameters version 2.0 January 27, 2010 + +[Source](http://www.secg.org/sec2-v2.pdf) + +## NIST +RECOMMENDED ELLIPTIC CURVES FOR FEDERAL GOVERNMENT USE July 1999 + +[Source](http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf) + +## x962 +ANSI X9.62 example curves. ## 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 +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 R 34.10-2001: RFC5832 curves. + +[Source](https://tools.ietf.org/html/rfc5832) + +## 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 +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). -## NIST +Generated using [ecgen](https://github.com/J08nY/ecgen) -## nonprime +## composite +Contains curves of composite order, with small order points. -## SECG +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, irreducible polynomial that is not irreducible and similar. + +Generated manually.
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