Cryptographic Aspects of Real Hyperelliptic Curves

M.  J.  Jacobson Jr.; R.  Scheidler; A.  Stein

Paper 2010/125 Original: eprint.iacr.org/2010/125 ↗

Cryptographic Aspects of Real Hyperelliptic Curves

M. J. Jacobson Jr.

R. Scheidler

A. Stein

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2010-03-06: last updated; 2010-03-06: published
Short URL: https://ia.cr/2010/125
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2010/125,
      author = {M.  J.  Jacobson Jr. and R.  Scheidler and A.  Stein},
      title = {Cryptographic Aspects of Real Hyperelliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/125},
      year = {2010},
      url = {https://eprint.iacr.org/2010/125}
}