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International Conference on Pairing-Based Cryptography

Pairing 2008: Pairing-Based Cryptography – Pairing 2008 pp 136–145Cite as

Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5209))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami Osawa, Hachioji city, Tokyo, 192-0397, Japan

    Satoru Tanaka & Ken Nakamula

Authors
  1. Satoru Tanaka
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  2. Ken Nakamula
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Steven D. Galbraith Kenneth G. Paterson

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© 2008 Springer-Verlag Berlin Heidelberg

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Tanaka, S., Nakamula, K. (2008). Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials. In: Galbraith, S.D., Paterson, K.G. (eds) Pairing-Based Cryptography – Pairing 2008. Pairing 2008. Lecture Notes in Computer Science, vol 5209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85538-5_10

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  • DOI: https://doi.org/10.1007/978-3-540-85538-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85503-3

  • Online ISBN: 978-3-540-85538-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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