## ecgen [![Build Status](https://travis-ci.org/J08nY/ecgen.svg?branch=master)](https://travis-ci.org/J08nY/ecgen) [![GitHub release](https://img.shields.io/github/release/J08nY/ecgen.svg)](https://github.com/J08nY/ecgen/releases/latest)

Tool for generating Elliptic curve domain parameters.

### Usage

	ecgen --fp/--f2m -r -p BITS

 - `--fp`/`--f2m` specifies the field type (prime/binary).
<br/><br/>
 - `-r/--random` requests a random curve to be generated.
 - `-s/--seed=[SEED]` requests to generate a curve based on the ANSI X9.62 generation process and seed `SEED`.
 - `-k/--koblitz` requests to generate a Koblitz curve.
 - `-p/--prime` requests the curve order to be prime.
 - `-n/--order=ORDER` requests the curve to have a (prime) order `ORDER`.
 - `-i/--invalid` requests that invalid curves of small prime orders be generated.
<br/><br/>
 - `-v/--verbose=[FILE]` turns on verbose output (to file).
 - `-t/--format=[FORMAT]` sets format to output in. One of \[csv,json\], default is json.
 - `-f/--input=FILE` reads input from `FILE`.
 - `-o/--output=FILE` writes output to `FILE`.
 - `-a/--append` appends to output file (doesn't overwrite it).
<br/><br/>
 - `-d/--datadir=DIR` specifies the PARI/GP datadir containing the `seadata` package.

### Generation methods
Three different EC curve parameters generation methods are implemented.

[Efficient Algorithms for Generating Elliptic Curves over Finite Fields Suitable for Use in Cryptography - [Baier]](https://www.cdc.informatik.tu-darmstadt.de/reports/reports/harald_baier.diss.pdf)

[Generation Methods of Elliptic Curves - [Baier, Buchmann]](https://www.ipa.go.jp/security/enc/CRYPTREC/fy15/doc/1030_Buchmann.evaluation.pdf)

##### Random approach
 - Generates field and equation parameters:
   - randomly
   - using ANSI X9.62 verifiably random method(from seed), until a curve with requested properties appears.
   - given input
 - Can generate curves repeatedly until one satisfies requested properties:
   - `-p/--prime` generates curves until a prime order curve is found.
   - `-k/--koblitz` generates a curve with fixed *A = 0* parameter.

##### Invalid curve generation
 - Generates *invalid* curves for a given curve.
 - These curves have the same field, and *A* parameter in the short Weierstrass equation.
 - Multiplication using some(most?) scalar multiplication algorithm proceeds the same way multiplication on the input curve would.
 - Used with the `-i / --invalid` option
 - [Validation of Elliptic Curve Public Keys - [Antipa, Brown, Menezes, Struik, Vanstone]](https://www.iacr.org/archive/pkc2003/25670211/25670211.pdf)
 - [Differential Fault Attacks on Elliptic Curve Cryptosystems - [Biehl, Mayer, Muller]](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.107.3920&rep=rep1&type=pdf)
 - [Practical Invalid Curve Attacks on TLS-ECDH - [Jager, Schwenk, Somorovksy]](http://euklid.org/pdf/ECC_Invalid_Curve.pdf)

##### Complex multiplication
 - Capable of generating a curve of a given (prime) order.
 - Generates a subset of all Elliptic Curves over a given field.
 - Used with the `-n / --order` option
 - [Constructing elliptic curves of prime order - [Broker, Stevenhagen]](https://arxiv.org/abs/0712.2022)
 - [Generating Elliptic Curves of Prime Order - [Savas, Schmidt, Koc]](http://people.oregonstate.edu/~schmidtt/ourPapers/SavasKoc/ches01curve.pdf)


### Build


	git clone https://github.com/J08nY/ecgen.git
	cd ecgen
	make

### Requirements

 - PARI/GP
 - parson

ecgen uses the [PARI/GP](http://pari.math.u-bordeaux.fr/) library for elliptic
curve arithmetic and it's SEA point counting algorithm implementation. It also requires the 
additional [seadata](http://pari.math.u-bordeaux.fr/packages.html) package (seadata and seadata-big recommended for large curves).

[parson](https://github.com/kgabis/parson) is used to output curve parameters in JSON format.

### License

	This program is free software: you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with this program.  If not, see <http://www.gnu.org/licenses/>.


*© Eastern Seaboard Phishing Authority*