Generating pairing-friendly elliptic curve parameters using sparse families
نویسندگان
چکیده
منابع مشابه
Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves
Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose ...
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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 کاملSpecial Polynomial Families for Generating More Suitable Pairing-Friendly Elliptic Curves
Constructing non-supersingular elliptic curves for pairing-based cryptosystems have attracted much attention in recent years. The best previous technique builds curves with ρ = lg(q) / lg(r) ≈ 1 (k = 12) and ρ = lg(q) / lg(r) ≈ 1.25 (k = 24). When k > 12, most of the previous works address the question by representing r(x) as a cyclotomic polynomial. In this paper, we propose a method to find m...
متن کاملA generating method of CM parameters of pairing-friendly abelian surfaces using Brezing-Weng family*
Brezing and Weng proposed a method to generate CM parameters of pairing-friendly elliptic curves using polynomial representations of a number field, and Freeman generalized the method for the case of abelian varieties. In this paper we derive explicit formulae to find a family of polynomials used in Brezing-Weng method especially in the case of abelian surfaces, and present some examples genera...
متن کاملConstruction of Pairing-Friendly Elliptic Curves
The aim of this paper is to construct pairing friendly elliptic curves. In this paper, we explain a method of finding the polynomials representing √−D and ζk over the field containing √−D and ζk and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing Q(ζk, √−D) for arbitrary k and D by CP method. By using the factorization of the cyclotomic polynomial combi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Cryptology
سال: 2018
ISSN: 1862-2976,1862-2984
DOI: 10.1515/jmc-2017-0024