scholarly journals TATE PAIRING COMPUTATION ON THE DIVISORS OF HYPERELLIPTIC CURVES OF GENUS 2

2008 ◽  
Vol 45 (4) ◽  
pp. 1057-1073 ◽  
Author(s):  
Eun-Jeong Lee ◽  
Yoon-Jin Lee
Keyword(s):  
Hyperelliptic Curves ◽  
Tate Pairing ◽  
Genus 2 ◽  
Pairing Computation

Faster pairing computation on genus 2 hyperelliptic curves

2011 ◽  
Vol 111 (10) ◽  
pp. 494-499 ◽  
Author(s):  
Chunming Tang ◽  
Maozhi Xu ◽  
Yanfeng Qi
Keyword(s):  
Hyperelliptic Curves ◽  
Genus 2 ◽  
Pairing Computation

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.

scholarly journals Cryptographic aspects of real hyperelliptic curves

2010 ◽  
Vol 47 (1) ◽  
pp. 31-65 ◽  
Author(s):  
Michael J. Jacobson ◽  
Renate Scheidler ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curve ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Hyperelliptic Curves ◽  
Cryptographic Protocols ◽  
Discrete Logarithm Problem ◽  
Explicit Formulas ◽  
Genus 2

Abstract In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2, and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.

An optimal Tate pairing computation using Jacobi quartic elliptic curves

2018 ◽  
Vol 35 (4) ◽  
pp. 1086-1103
Author(s):  
Srinath Doss ◽  
Roselyn Kaondera-Shava
Keyword(s):  
Elliptic Curves ◽  
Tate Pairing ◽  
Pairing Computation

scholarly journals Explicit formulas for real hyperelliptic curves of genus 2 in affine representation

2011 ◽  
Vol 5 (4) ◽  
pp. 623-666 ◽  
Author(s):  
Stefan Erickson ◽  
Michael Jacobson, Jr. ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curves ◽  
Explicit Formulas ◽  
Genus 2
Sign in / Sign up

Export Citation Format

Share Document