Abstract
We present a new method for constructing simple ordinary abelian surfaces with a small embedding degree. To a quartic CM field K, we associate a quadric surface H ⊂ ℙ3(ℚ) and use its parametrization to determine Weil numbers in K corresponding in the sense of Honda-Tate theory to such surfaces. In general, the resulting surfaces have parameter ρ ≈ 8. However, if there exist rational lines on H, they can be used to achieve ρ ≈ 4. We give examples of non-primitive quartic CM fields such that H has rulings by rational lines. Furthermore, we show how our method can be used to construct parametric families of pairing-friendly surfaces.
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Dryło, R. (2010). A New Method for Constructing Pairing-Friendly Abelian Surfaces. In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17455-1_19
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DOI: https://doi.org/10.1007/978-3-642-17455-1_19
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