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Some Elliptic Subcovers of Genus 3 Hyperelliptic Curves

  • Song TianEmail author
  • Wei Yu
  • Bao Li
  • Kunpeng Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9065)

Abstract

A morphism from an algebraic curve C to an elliptic curve is called an elliptic subcover of the curve C. Elliptic subcovers provide means of solving discrete logarithm problem in elliptic curves over extension fields. The GHS attack yields only degree 2 minimal elliptic subcovers of hyperelliptic curves of genus 3. In this paper, we study the properties of elliptic subcovers of genus 3 hyperelliptic curves. Using these properties, we find some minimal elliptic subcovers of degree 4, which can not be constructed by GHS attack.

Keywords

Elliptic Subcover Hyperelliptic Curve Discrete Logarithm Problem GHS Attack 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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