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Title:
On the security of pairing-friendly abelian varieties over non-prime fields
Authors: Naomi Benger, Manuel Charlemagne, David Freeman
Abstract:Let A be an abelian variety defined over a non-prime finite field \F_{q} that has embedding degree k with respect to a subgroup of prime order r. In this paper we give explicit conditions on q, k, and r that imply that the minimal embedding field of A with respect to r is \F_{q^k}. When these conditions hold, the embedding degree k is a good measure of the security level of a pairing-based cryptosystem that uses A. We apply our theorem to supersingular elliptic curves and to supersingular genus 2 curves, in each case computing a maximum \rho-value for which the minimal embedding field must be \F_{q^k}. Our results are in most cases stronger (i.e., give larger allowable \rho-values) than previously known results for supersingular varieties, and our theorem holds for general abelian varieties, not only supersingular ones.
ePrint: https://eprint.iacr.org/2008/417
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