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Paper: CM construction of genus 2 curves with p-rank 1

Authors: Laura Hitt O'Connor Gary McGuire Michael Naehrig Marco Streng URL: http://eprint.iacr.org/2008/491 Search ePrint Search Google We present an algorithm for constructing cryptographic hyperelliptic curves of genus $2$ and $p$-rank $1$, using the CM method. We also present an algorithm for constructing such curves that, in addition, have a prescribed small embedding degree. We describe the algorithms in detail, and discuss other aspects of $p$-rank 1 curves too, including the reduction of the class polynomials modulo $p$.
BibTeX
@misc{eprint-2008-18138,
title={CM construction of genus 2 curves with p-rank 1},
booktitle={IACR Eprint archive},
keywords={foundations / hyperelliptic curve cryptography},
url={http://eprint.iacr.org/2008/491},
note={ gary.mcguire@ucd.ie 14203 received 20 Nov 2008, last revised 20 Nov 2008},
author={Laura Hitt O'Connor and Gary McGuire and Michael Naehrig and Marco Streng},
year=2008
}