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Jacobian Versus Infrastructure in Split Hyperelliptic Curves

  • Monireh Rezai Rad
  • Michael J. JacobsonJr.Email author
  • Renate Scheidler
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1133)

Abstract

Split (also known as real) hyperelliptic curves admit two main algebraic structures: the Jacobian and the infrastructure. In this paper, we describe exactly how the infrastructure and the Jacobian are related. We show that computations in the infrastructure using a new modified notion of distance and computations in a particular subgroup of the Jacobian heuristically have exactly the same cost for curves defined over sufficiently large finite fields. We also present a novel set of explicit formulas for genus three split hyperelliptic curves that improves on the current state-of-the-art.

Keywords

Split hyperelliptic curve Jacobian Balanced divisor Infrastructure Explicit formulas 

Supplementary material

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Monireh Rezai Rad
    • 1
  • Michael J. JacobsonJr.
    • 2
    Email author
  • Renate Scheidler
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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