منابع مشابه
Bilinear pairings on elliptic curves
We give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. For the first time in the literature, the three different definitions of the Weil pairing are stated correctly and proved to be equivalent using Weil reciprocity. Pairings with shorter loops, such as the ate, atei, R-ate and optimal pairings, together with their twisted variants, are present...
متن کاملComputing bilinear pairings on elliptic curves with automorphisms
In this paper, we present a novel method for constructing a super-optimal pairing with great efficiency, which we call the omega pairing. The computation of the omega pairing requires the simple final exponentiation and short loop length in Miller’s algorithm which leads to a significant improvement over the previously known techniques on certain pairing-friendly curves. Experimental results sh...
متن کاملComputing the Bilinear Pairings on Elliptic Curves with Automorphisms
In this paper, a super-optimal pairing based on the Weil pairing is proposed with great efficiency. It is the first approach to reduce the Miller iteration loop when computing the variants of the Weil pairing. The super-optimal pairing based on the Weil pairing is computed rather fast, while it is slightly slower than the previous fastest pairing on the corresponding elliptic curves.
متن کاملCompression of Tate Pairings on Elliptic Curves
In this paper, utilizing maps between cyclic groups contained in a finite field, two efficient methods for compressing a Tate pairing defined on a supersingular elliptic curve with prime characteristic p and MOV degree 3 are presented. They compress a pairing value from a string of length of 6logp bits to ones of 3logp and 2logp bits, respectively, and an implementation for both the compressed ...
متن کاملSpeeding up the Bilinear Pairings Computation on Curves with Automorphisms
In this paper we present a new algorithm for computing the bilinear pairings on a family of non-supersingular elliptic curves with non-trivial automorphisms. We obtain a short iteration loop in Miller’s algorithm using non-trivial efficient automorphisms. The proposed algorithm is as efficient as the algorithm in [12].
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ژورنال
عنوان ژورنال: L’Enseignement Mathématique
سال: 2015
ISSN: 0013-8584
DOI: 10.4171/lem/61-1/2-9