Name
Abstract | ||
|---|---|---|
Recently there are lots of studies on the Tate pairing computation with different coordinate systems, such as twisted Edwards curves and Hessian curves coordinate systems. However, Jacobi intersections curves coordinate system, as another useful one, is overlooked in pairing-based cryptosystems. This paper proposes the explicit formulae for the doubling and addition steps in Miller's algorithm to compute the Tate pairing on twisted Jacobi intersections curves, as a larger class containing Jacobi intersections curves. Although these curves are not plane elliptic curves, our formulae are still very efficient and competitive with others. When the embedding degree is even, our doubling formulae are the fastest except for the formulae on Hessian/Selmer curves, and the parallel execution of our formulae are even more competitive with the Selmer curves case in the parallel manner. Besides, we give the detailed analysis of the fast variants of our formulae with other embedding degrees, such as the embedding degree 1, and the embedding degree dividing 4 and 6. At last, we analyze the relation between the Tate pairings on two isogenous elliptic curves, and show that the Tate pairing on twisted Jacobi intersections curves can be substituted for the Tate pairing on twisted Edwards curves completely. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/978-3-642-34704-7-16 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
Keywords | Field | DocType |
embedding degree,twisted edwards curve,tate pairing computation,jacobi intersection,tate pairing,selmer curves case,twisted edwards,jacobi intersections curve,tate pairings,twisted jacobi intersections curve | Coordinate system,Discrete mathematics,Explicit formulae,Embedding,Family of curves,Pairing,Tate pairing,Twisted Edwards curve,Elliptic curve,Mathematics | Conference |
Volume | Issue | ISSN |
7537 LNCS | null | 16113349 |
Citations | PageRank | References |
0 | 0.34 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xusheng Zhang | 1 | 39 | 13.00 |
| Shan Chen | 2 | 0 | 0.34 |
| Dongdai Lin | 3 | 762 | 98.54 |