ECB  Elliptic Curve Builder  is a generator of ordinary elliptic curves.
The curves over the Galois fields GF(P), GF(2^{N}) and GF(3^{N}) are built
using the socalled complex multiplication method.
Even if, for some reasons, one does not trust the curves produced with ECB, they
remain useful in order to test and/or to tune ECC applications.
Executable for Linux 64bit (Ubuntu 18.04/x8664 architecture)
Compiled with Free Pascal 3.0.4 and
Lazarus 1.8.2

Properties of a curve created with ECB
 over GF(P)
 equation y^{2} = x^{3} + Ax + B;
 the order is U = R*K with R prime and K < R;
 the binary size of the prime modulus P may be any in 30..1536.
 over GF(2^{N})
 equation y^{2} + xy = x^{3} + Ax^{2} + B;
 the order is U = R*K with R prime and K < R;
 the field degree N may be any in 30..1024;
 the basis of the field GF(2^{N}) may be polynomial or normal.
 over GF(3^{N})
 equation y^{2} = x^{3} + Ax^{2} + B;
 the order is U = R*K with R prime and K < R;
 the field degree N may be any in 20..768;
 the basis of the field GF(3^{N}) may be polynomial or normal.
Here are three examples of use with the three Galois fields:
v2.0.5 (April 28, 2019)
Previous changes
The ECB software may be used free of charge but it might be a good idea to read the
EndUser License Agreement before downloading and using it.
