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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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
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