منابع مشابه
Binary Huff Curves
This paper describes the addition law for a new form for elliptic curves over fields of characteristic 2. Specifically, it presents explicit formulæ for adding two different points and for doubling points. The case of differential point addition (that is, point addition with a known difference) is also addressed. Finally, this paper presents unified point addition formulæ; i.e., point addition ...
متن کاملHashing into Generalized Huff Curves
Huff curves are well known for efficient arithmetics to their group law. In this paper, we propose two deterministic encodings from Fq to generalized Huff curves. When q ≡ 3 (mod 4), the first deterministic encoding based on Skalpa’s equality saves three field squarings and five multiplications compared with birational equivalence composed with Ulas’ encoding. It costs three multiplications les...
متن کاملArithmetic progressions on Huff curves
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, Edwards curves, and genus 2 curves. We find an infinite number...
متن کاملPairings on Generalized Huff Curves
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 کاملOn a new generalization of Huff curves
Recently two kinds of Huff curves were introduced as elliptic curves models and their arithmetic was studied. It was also shown that they are suitable for cryptographic use such as Montgomery curves or Koblitz curves (in Weierstrass form) and Edwards curves. In this work, we introduce the new generalized Huff curves ax(y − c) = by(x−d) with abcd(ac−bd) 6= 0, which contains the generalized Huff’...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2013
ISSN: 1935-7524
DOI: 10.1214/13-ejs862