VladaSedlacek / efd

An export of the Explicit-Formulas Database.

Explicit-Formulas Database

A (modifed) export of the Explicit-Formulas Database (EFD) which contains the data files and three-operand-code files for the formulas.

Currently contains only the prime field curve models:

• Short Weierstrass
• Montgomery
• Edwards
• Twisted Edwards

This repository is used as a source of parse-able formulas in the pyecsca toolkit.

Differences to EFD data

In order to download the EFD data and compare it to this export do this in BASH:

mkdir efd-down
cd efd-down
wget -r -np -nv -nH --cut-dirs=1 http://www.hyperelliptic.org/EFD/
find . -name "*.html" -delete
rm -r oldefd g12o precomp.pdf g1p/auto-sage
for f in shortw montgom edwards twisted; do
  rsync -a g1p/auto-code/$f .;
  rsync -a g1p/data/$f .;
done;
rm -r g1p
cd ..

Then you can compare the efd-down directory with this repository using diff -r or some other tool.

The main differences are:

• Notation: The EFD data often does not explicitly mark multiplications by *, it just uses spaces, this is not nice when the data needs to be parsed and so this was fixed. Also changed the single equality sign used in the curve equation entry satisfying into a double equation sign so that it can be parsed as an expression.
• Output indices: Some EFD formulas like the differential addition one, use the 5 as the index of their output point (e.g. output coordinates are X5, Y5, Z5...). This is inconsistent with the notion that the output point coordinates are just after the last input point coordinates, as the differential add takes three input points and should have output on the fourth index. This is fixed in this export.
• Unified formulas: Formulas which claim to be unified are marked as so, using the unified tag in the coordinate system files.
• Infinity point: The infinity (or neutral) point was added to more coordinate systems.
• New formulas: Added the Short Weierstrass prime order complete formulas of Renes-Costello-Batina. Added negation formula for more coordinate systems as well as a scaling formula that was missing.
• Removed formulas: Removed some broken formulas, for example see the formulas at: shortw/projective-1/addition/add-1986-cc.op3 which contain lines such as: error: not sure how to handle P*(-t5).