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 so-called complex multiplication method. Even if, for any reason, 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

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(2^N)
• 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(2^N) may be polynomial or normal.

Over GF(3^N)
• 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(3^N) may be polynomial or normal.

v3.0.0  (January 13, 2020)
• Modified the Setup dialog box.
• Added the Random Seed dialog box.
• Miscellaneous internal improvements.
• Updated the help file.

 Previous changes

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-300-lx64.7z   (763.7 kB, binary file)