International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Generators of Jacobians of Genus Two Curves

Authors:
Christian Robenhagen Ravnshoj
Download:
URL: http://eprint.iacr.org/2008/070
Search ePrint
Search Google
Abstract: We prove that in most cases relevant to cryptography, the Frobenius endomorphism on the Jacobian of a genus two curve is represented by a diagonal matrix with respect to an appropriate basis of the subgroup of l-torsion points. From this fact we get an explicit description of the Weil-pairing on the subgroup of l-torsion points. Finally, the explicit description of the Weil-pairing provides us with an efficient, probabilistic algorithm to find generators of the subgroup of l-torsion points on the Jacobian of a genus two curve.
BibTeX
@misc{eprint-2008-17747,
  title={Generators of Jacobians of Genus Two Curves},
  booktitle={IACR Eprint archive},
  keywords={Jacobians, hyperelliptic genus two curves, pairings, embedding degree},
  url={http://eprint.iacr.org/2008/070},
  note={ cr@imf.au.dk 13927 received 11 Feb 2008, last revised 18 Feb 2008},
  author={Christian Robenhagen Ravnshoj},
  year=2008
}