Constructing Families of Pairing-Friendly Elliptic Curves
نویسنده
چکیده
We present a general method for constructing families of elliptic curves with prescribed embedding degree and prime order. We demonstrate this method by constructing curves of embedding degree k = 10, a value which has not previously appeared in the literature, and we show that our method applies to existing constructions for k = 3, 4, 6, and 12. We give evidence that our method is unlikely to produce infinite families of curves for embedding
منابع مشابه
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
We describe a new method for constructing Brezing-Wenglike pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new “record breaking” families of pairing-friendly curves with embedding degrees of k ∈ {16, 18, 36, 40}, and some interesting new constructions for the cases k ∈ {8, 32}.
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We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham [6]. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method...
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تاریخ انتشار 2005