International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Cryptographic Aspects of Real Hyperelliptic Curves

M. J. Jacobson
R. Scheidler
A. Stein
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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.
  title={Cryptographic Aspects of Real Hyperelliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / hyperelliptic curve cryptosystems, public-key cryptography},
  note={Tatra Mountains Mathematical Publication 14673 received 5 Mar 2010},
  author={M. J. Jacobson and R. Scheidler and A. Stein},