Name
Abstract | ||
|---|---|---|
In this paper, we first propose a geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct Miller function. Then we present explicit formulae for the addition and doubling steps in Miller's algorithm to compute the Tate pairing on Jacobi quartic curves. Our formulae on Jacobi quartic curves are better than previously proposed ones for the general case of even embedding degree. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. Our pairing computation on Jacobi quartic curves are faster than the pairing computation on Weier-strass curves when j = 1728. The addition steps of our formulae are fewer than the addition steps on Weierstrass curves when j = 0. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/978-3-319-27998-5_20 | Lecture Notes in Computer Science |
Keywords | Field | DocType |
Elliptic curve,Jacobi quartic curve,Tate pairing,Miller function,Group law | Explicit formulae,Jacobi method,Pure mathematics,Pairing,Tate pairing,Quartic function,Quartic plane curve,Elliptic curve,Quartic surface,Mathematics | Conference |
Volume | ISSN | Citations |
9473 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 14 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fan Zhang | 1 | 54 | 16.27 |
| Liangze Li | 2 | 1 | 1.37 |
| Hongfeng Wu | 3 | 6 | 5.53 |