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On Prime-Order Elliptic Curves with Embedding Degrees 3, 4 and 6

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/2671
Date January 2007
CreatorsKarabina, Koray
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Format420953 bytes, application/pdf

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