Name
Abstract | ||
|---|---|---|
Elliptic curves over a finite field <inline-formula><inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink=\"gcom_a_1083556_ilm0001.gif\"/</inline-formula> with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order ℓ. For <inline-formula><inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink=\"gcom_a_1083556_ilm0002.gif\"/</inline-formula>, these conditions give parameterizations of q in terms of ℓ and two integers m, n. We show several examples of families with infinitely many curves. Similar parameterizations for <inline-formula><inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink=\"gcom_a_1083556_ilm0003.gif\"/</inline-formula> need a fixed kth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1080/00207160.2015.1083556 | Int. J. Comput. Math. |
Keywords | Field | DocType |
elliptic curves, embedding degree, distortion maps, pairing-based Cryptography, Bateman-Horn's conjecture | Discrete mathematics,Supersingular elliptic curve,Twists of curves,Sato–Tate conjecture,Mathematical analysis,Hessian form of an elliptic curve,Edwards curve,Elliptic divisibility sequence,Counting points on elliptic curves,Mathematics,Schoof's algorithm | Journal |
Volume | Issue | ISSN |
93 | 12 | 0020-7160 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Josep M. Miret | 1 | 81 | 14.88 |
| D. Sadornil | 2 | 23 | 4.32 |
| J. G. Tena | 3 | 14 | 2.00 |