Overview

ECB - Elliptic Curve Builder - is a generator of ordinary elliptic curves. The curves over the Galois fields GF(P), GF(2N) and GF(3N) are built using the so-called 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 64-bit (Ubuntu 18.04/x86-64 architecture)
Compiled with Free Pascal 3.0.4 and Lazarus 1.8.2
ECB screenshot

Properties of a curve created with ECB

  • over GF(P)
    • equation y2 = x3 + 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(2N)
    • equation y2 + xy = x3 + Ax2 + 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(2N) may be polynomial or normal.

  • over GF(3N)
    • equation y2 = x3 + Ax2 + 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(3N) may be polynomial or normal.


Examples of use

Here are three examples of use with the three Galois fields:



Changes
v2.0.5 (April 28, 2019)
  • Cosmetic changes.
 Previous changes



Download

The ECB software may be used free of charge but it might be a good idea to read the End-User License Agreement before downloading and using it.

  ecb-205-lx64.7z    761.0 kB   Executable  (binary file)