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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
verfasst von : Satoru Tanaka, Ken Nakamula
Erschienen in: Pairing-Based Cryptography – Pairing 2008
Verlag: Springer Berlin Heidelberg
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The problem of constructing pairing-friendly elliptic curves has received a lot of attention. To find a suitable field for the construction we propose a method to find a polynomial
u
(
x
), by the method of indeterminate coefficients, such that
Φ
k
(
u
(
x
)) factors. We also refine the algorithm by Brezing and Weng using a factor of
Φ
k
(
u
(
x
)). As a result, we produce new families of parameters using our algorithm for pairing-friendly elliptic curves with embedding degree 8, and we compute some explicit curves as numerical examples.