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Title:
A CM construction for curves of genus 2 with p-rank 1
Authors: Laura Hitt O'Connor, Gary McGuire, Michael Naehrig, Marco Streng
Abstract:We construct Weil numbers corresponding to genus-2 curves with p-rank 1 over the finite field \F_{p^2} of p^2 elements. The corresponding curves can be constructed using explicit CM constructions. In one of our algorithms, the group of \F_{p^2}-valued points of the Jacobian has prime order, while another allows for a prescribed embedding degree with respect to a subgroup of prescribed order. The curves are defined over \F_{p^2} out of necessity: we show that curves of p-rank 1 over \F_p for large p cannot be efficiently constructed using explicit CM constructions.
ePrint: https://eprint.iacr.org/2008/491
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