Something cryptic…
Below you will find a listing of some of my research. This was previously found at http://fermat.ma.rhul.ac.uk/~paula/. Feel free to contact me at me@paulavalenca.org for any information.
S. D. Galbraith, J. McKee and P. Valenca, Ordinary abelian varieties having small embedding degree, eprint 2004/365.
To appear in proceedings of the `Mathematical Problems and Techniques in Cryptology' workshop, Barcelona, June 2005.Ordinary abelian varieties having small embedding degree (slides).
International Workshop on Pairings in Cryptography 12-15 June 2005, Dublin, Ireland,
`Mathematical Problems and Techniques in Cryptology' workshop, Barcelona, June 2005MNT families with co-factors 2 ≤ h ≤ 1024, embedding degree 3, 4 and 6. Before downloading and opening the files, please note that the full lists are quite big! Much smaller databases, with 2 ≤ h ≤ 16 are also available here. Data is made available in XML format but should be easily readable.
As a final comment, parameterisations that can be obtained from others via a transformation over the integers, will describe the same curves and are, as such, "equivalent". For example, q = 8l^2 + 6l + 3 and q = 8l^2 + 10l + 5. The lists, as they are presented here, are not filtered and most cases appear repeated in "equivalent" forms.
- embedding degree 3: cofactor up to 16 (4KB zipped, 26KB unzipped), cofactor up to 1024 (20MB zipped, 119MB unzipped)
- embedding degree 4: cofactor up to 16 (5KB zipped, 37KB unzipped), cofactor up to 1024 (28MB zipped, 178MB unzipped)
- embedding degree 6: cofactor up to 16 (4KB zipped, 25KB unzipped), cofactor up to 1024 (20MB zipped, 118MB unzipped)