Well heights, Neron pairings and v-metrics on curves
نویسندگان
چکیده
منابع مشابه
Pairings on hyperelliptic curves
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptography. We also showcase the hyperelliptic pairings proposed to date, and develop a unifying framework. We discuss the techniques used to optimize the pairing computation on hyperelliptic curves, and present many direction...
متن کاملBilinear 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...
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This paper presents the Tate pairing computation on generalized Huff curves proposed by Wu and Feng in [22]. In fact, we extend the results of the Tate pairing computation on the standard Huff elliptic curves done previously by Joye, Tibouchi and Vergnaud in [14]. We show that the addition step of the Miller loop can be performed in 1M+(k+15)m+2c and the doubling one in 1M+1S+(k+12)m+5s+2c on t...
متن کاملSelf-pairings on hyperelliptic curves
A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate-Lichtenbaum pairing 〈D,φ(D)〉 on a curve more efficiently than the general case. The speedup is obtained by requiring a simpler final exponentiation. We also discuss how to use this pairing in cryp...
متن کاملCanonical Heights on Hyperelliptic Curves
We describe an algorithm to compute canonical heights of points on hyperelliptic curves over number fields, using Arakelov geometry. We include a worked example for illustration purposes.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1985
ISSN: 0035-7596
DOI: 10.1216/rmj-1985-15-2-417