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 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

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