Formulae for Computation of Tate Pairing on Hyperelliptic Curve Using Hyperelliptic Nets

2014 ◽  
pp. 199-214 ◽  
Author(s):  
Christophe Tran
Keyword(s):  
Hyperelliptic Curve ◽  
Tate Pairing

Hardware acceleration of the Tate pairing on a genus 2 hyperelliptic curve

2007 ◽  
Vol 53 (2-3) ◽  
pp. 85-98 ◽  
Author(s):  
Robert Ronan ◽  
Colm ó hÉigeartaigh ◽  
Colin Murphy ◽  
Michael Scott ◽  
Tim Kerins
Keyword(s):  
Hyperelliptic Curve ◽  
Hardware Acceleration ◽  
Tate Pairing ◽  
Genus 2

Improved authentication and computation of medical data transmission in the secure IoT using hyperelliptic curve cryptography

2021 ◽  
Author(s):  
B. Prasanalakshmi ◽  
K. Murugan ◽  
Karthik Srinivasan ◽  
S. Shridevi ◽  
Shermin Shamsudheen ◽  
...  
Keyword(s):  
Data Transmission ◽  
Hyperelliptic Curve ◽  
Medical Data ◽  
Hyperelliptic Curve Cryptography

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

scholarly journals Faster computation of the Tate pairing

2011 ◽  
Vol 131 (5) ◽  
pp. 842-857 ◽  
Author(s):  
Christophe Arène ◽  
Tanja Lange ◽  
Michael Naehrig ◽  
Christophe Ritzenthaler
Keyword(s):  
Tate Pairing

On the Final Exponentiation in Tate Pairing Computations

2013 ◽  
Vol 59 (6) ◽  
pp. 4033-4041 ◽  
Author(s):  
Taechan Kim ◽  
Sungwook Kim ◽  
Jung Hee Cheon
Keyword(s):  
Tate Pairing

scholarly journals The Pairing Computation on Edwards Curves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfeng Wu ◽  
Liangze Li ◽  
Fan Zhang
Keyword(s):  
Geometric Interpretation ◽  
Tate Pairing ◽  
Quadric Surfaces ◽  
Edwards Curves ◽  
Explicit Formulae ◽  
Pairing Computation ◽  
Twisted Edwards Curves ◽  
Group Law

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.

Affine Variety Codes over a Hyperelliptic Curve

2021 ◽  
Vol 57 (1) ◽  
pp. 84-97
Author(s):  
N. Patanker ◽  
S. K. Singh
Keyword(s):  
Hyperelliptic Curve ◽  
Affine Variety ◽  
Affine Variety Codes

scholarly journals ON SELMER RANK PARITY OF TWISTS

2016 ◽  
Vol 102 (3) ◽  
pp. 316-330 ◽  
Author(s):  
MAJID HADIAN ◽  
MATTHEW WEIDNER
Keyword(s):  
Elliptic Curves ◽  
Abelian Variety ◽  
Number Field ◽  
Arbitrary Number ◽  
Hyperelliptic Curve ◽  
Abelian Varieties ◽  
Hyperelliptic Curves ◽  
Torsion Subgroup ◽  
Tate Conjecture ◽  
Quadratic Twists

In this paper we study the variation of the $p$-Selmer rank parities of $p$-twists of a principally polarized Abelian variety over an arbitrary number field $K$ and show, under certain assumptions, that this parity is periodic with an explicit period. Our result applies in particular to principally polarized Abelian varieties with full $K$-rational $p$-torsion subgroup, arbitrary elliptic curves, and Jacobians of hyperelliptic curves. Assuming the Shafarevich–Tate conjecture, our result allows one to classify the rank parities of all quadratic twists of an elliptic or hyperelliptic curve after a finite calculation.

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