On prime-order elliptic curves with embedding
نویسندگان
چکیده
We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees k = 3, 4 or 6 (MNT curves) may be obtained. We give an explicit algorithm to generate such curves. We derive a heuristic lower bound for the number E(z) of MNT curves with k = 6 and discriminant D ≤ z, and compare this lower bound with experimental data.
منابع مشابه
Pairing-Friendly Elliptic Curves of Prime Order
Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k 6 6. More general methods produce curves over Fp where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the best published results achieve ρ ≡ log(p)/ log(r) ∼ 5/4. In this paper we make the first step towar...
متن کاملHeuristics on pairing-friendly elliptic curves
We present a heuristic asymptotic formula as x → ∞ for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree k ≥ 3, with fixed discriminant, with rho-value bounded by a fixed ρ0 such that 1 < ρ0 < 2, and with prime subgroup order at most x.
متن کاملJa n 20 06 Constructing Pairing - Friendly Elliptic Curves with Embedding Degree
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...
متن کاملConstructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
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...
متن کاملConstructing Families of Pairing-Friendly Elliptic Curves
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007