A Weil pairing on the $p$-torsion of ordinary elliptic curves over the dual numbers of $K$
| dc.creator | Belding, Juliana V. | |
| dc.date | 2007-03-30 | |
| dc.date.accessioned | 2026-07-07T07:55:05Z | |
| dc.date.available | 2026-07-07T07:55:05Z | |
| dc.description | For an elliptic curve $E$ over any field $K$, the Weil pairing $e_n$ is a bilinear map on $n$-torsion. For $K$ of characteristic $p>0$, the map $e_n$ is degenerate if and only if $n$ is divisible by $p$. In this paper, we consider $E$ over the dual numbers $K[ε]$ and define a non-degenerate ``Weil pairing on $p$-torsion" which shares many of the same properties of the Weil pairing. We also show that the discrete logarithm attacks on $p$-torsion subgroups of Semaev and Rück may be viewed as Weil-pairing-based attacks, just like the MOV attack. Finally, we describe an attack on the discrete logarithm problem on anomalous curves, analogous to that of Smart, using a lift of $E$ over the dual numbers of the finite field of $p$ elements. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703906 | |
| dc.identifier | http://arxiv.org/abs/math/0703906 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126851 | |
| dc.subject | Number Theory | |
| dc.title | A Weil pairing on the $p$-torsion of ordinary elliptic curves over the dual numbers of $K$ | |
| dc.type | text |