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@@ -4,20 +4,48 @@ Tool for generating Elliptic curve domain parameters. ### Usage -#### ecgen -The main binary of the tool, does the hard work. - 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. - - `-p/--prime` requests the curve order to be prime. - `-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/> - `-o/--output=FILE` writes output to `FILE`. - `-f/--input=FILE` reads input from `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. + +##### 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 + +##### 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) + + ### Build |