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Paper 2007/110

Construction of Pairing-Friendly Elliptic Curves

Woo Sug Kang

Abstract

We explain a method of finding the polynomials representing $\sqrt{-D}$ and $\zeta_k$ over the field containing $\sqrt{-D}$ and $\zeta_k$ and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing ${\mathbb Q} (\zeta_k, \sqrt{-D})$ for arbitrary $k$ and $D$ by CP method. By using the factorization of the cyclotomic polynomial combined some polynomial, we extend the construction over cyclotomic fields to the construction over some extensions of the cyclotomic fields containing ${\mathbb Q} (\zeta_k, \sqrt{-D})$. We explain the limitation of finding more families of pairing friendly elliptic curves with embedding degree 10. For all computation, we use the PARI-GP \cite{GP}.

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Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curvesembedding degreepairing based cryptography
Contact author(s)
wsgkang @ korea ac kr
History
2007-05-18: last of 5 revisions
2007-03-26: received
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Short URL
https://ia.cr/2007/110
License
Creative Commons Attribution
CC BY
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