## CryptoDB

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

Authors: Takakazu Satoh URL: http://eprint.iacr.org/2009/103 Search ePrint Search Google 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
}