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)


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.


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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