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Paper: The Brezing-Weng-Freeman Method for Certain Genus two Hyperelliptic Curves

Authors:
Takakazu Satoh
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URL: http://eprint.iacr.org/2009/103
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Abstract: We construct paring friendly curves of the form $Y^2 = X^5 + uX^3 + vX$ over large finite prime fields. The rho value of our family is always less than 4. Our method is based on the fact that, under a certain condition, the Jacobian $J$ of the curve splits to a square of an elliptic curve over the quadratic extension of the base field. However, the generated curves by our method are $F_p$-simple. A key ingredient is the construction of a pairing non-friendly elliptic curve by the modified Brezing-Weng-Freeman method so that $J$ is pairing friendly.
BibTeX
@misc{eprint-2009-18239,
  title={The Brezing-Weng-Freeman Method for Certain Genus two Hyperelliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / pairing based cryptography, pairing friendly curves, hyperelliptic curves},
  url={http://eprint.iacr.org/2009/103},
  note={(None) satohaar@mathpc-satoh.math.titech.ac.jp 14305 received 1 Mar 2009, last revised 1 Mar 2009},
  author={Takakazu Satoh},
  year=2009
}