| dc.creator |
Kirlar, Barış Bülent |
|
| dc.date |
2011-06-14T21:00:00Z |
|
| dc.date.accessioned |
2020-10-06T12:03:34Z |
|
| dc.date.available |
2020-10-06T12:03:34Z |
|
| dc.identifier |
fdc77251-3940-45ca-a6f3-83c3e17b7bc9 |
|
| dc.identifier |
10.1016/j.cam.2010.08.020 |
|
| dc.identifier |
https://avesis.sdu.edu.tr/publication/details/fdc77251-3940-45ca-a6f3-83c3e17b7bc9/oai |
|
| dc.identifier.uri |
http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/77112 |
|
| dc.description |
In this paper, we give a family of elliptic curves E in the form y(2) = x(3) - c over the prime field F-p with embedding degree k = 1. This was carried out by computing the explicit formula of the number of points #E(F-p) of the elliptic curve y(2) = x(3) - c. Using this computation, we show that the elliptic curve y(2) = x(3) - 1 over F-p for the primes p of the form 27A(2) + 1 has an embedding degree k = 1. Finally, we give examples of those primes p for which the security level of the pairing-based cryptographic protocols on the curve y(2) = x(3) - 1 over F-p is equivalent to 128-, 192-, or 256-bit AES keys. (C) 2010 Elsevier B.V. All rights reserved. |
|
| dc.language |
eng |
|
| dc.rights |
info:eu-repo/semantics/closedAccess |
|
| dc.title |
On the elliptic curves y(2)=x(3)-c with embedding degree one |
|
| dc.type |
info:eu-repo/semantics/article |
|