Fast pairings via biextensions and cubical arithmetic

ePrint Report: Fast pairings via biextensions and cubical arithmetic

Damien Robert

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 …

canonical eprint report fast line report robert structure