Bilinear pairings on elliptic curves have many cryptographic
applications such as identity based encryption,
one-round three-party key agreement protocols,
and short signature schemes.
The elliptic curves which are suitable for pairing-based cryptography
are called pairing friendly curves. The prime-order
pairing friendly curves with embedding degrees k=3,4
and 6 were characterized by Miyaji, Nakabayashi and Takano.
We study this characterization of MNT curves in details.
We present explicit algorithms
to obtain suitable curve
parameters and to construct the corresponding elliptic curves.
We also give a heuristic lower bound for the expected
number of isogeny classes of MNT curves. Moreover,
the related theoretical findings are compared
with our experimental results.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/2671 |
| Date | January 2007 |
| Creators | Karabina, Koray |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | 420953 bytes, application/pdf |
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