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diff --git a/docs/CURVES.md b/docs/CURVES.md index 4a80d49..a417035 100644 --- a/docs/CURVES.md +++ b/docs/CURVES.md @@ -1,47 +1,95 @@ # 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 +### Barreto-Naehrig +Barreto-Naehrig curves from: A Family of Implementation-Friendly BN Elliptic Curves + +[Source](https://eprint.iacr.org/2010/429.pdf) + +### Other +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. + + +## 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. + +### twist +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](https://github.com/J08nY/ecgen). + +### degenerate +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](http://pari.math.u-bordeaux.fr/). + +### cofactor +Contains curves that are composite order, with points not on the subgroup generated by the generator. + +Generated using [ecgen](https://github.com/J08nY/ecgen). + +### supersingular +Contains supersingular curves, over F_p with order equal to p + 1. These have embedding degree equal to 2. + +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. +## Other -Generated manually.
\ No newline at end of file +### Wycheproof +Contains some test vectors from the [google/Wycheproof](https://github.com/google/wycheproof) project.
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