Paper 2024/517
Fast pairings via biextensions and cubical arithmetic
Abstract
Biextensions associated to line bundles on abelian varieties allows to reinterpret the usual Weil, Tate, Ate, optimal Ate, \ldots, pairings as monodromy pairings. We introduce a cubical arithmetic, derived from the canonical cubical torsor structure of these line bundles, to obtain an efficient arithmetic of these biextensions.
This unifies and extends Miller's standard algorithm to compute pairings along with other algorithms like elliptic nets and theta functions, and allows to adapt these algorithms to pairings on any model of abelian varieties with a polarisation
Note: Corrected some typos
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- pairingselliptic curvesdiscrete logarithm
- Contact author(s)
- damien robert @ inria fr
- History
- 2024-07-03: last of 4 revisions
- 2024-04-01: received
- See all versions
- Short URL
- https://ia.cr/2024/517
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/517, author = {Damien Robert}, title = {Fast pairings via biextensions and cubical arithmetic}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/517}, year = {2024}, url = {https://eprint.iacr.org/2024/517} }