Abelian varieties in pairing-based cryptography

12/30/2018

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by   Steve Thakur, et al.

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We study the problem of the embedding degree of an abelian variety over a finite field which is vital in pairing-based cryptography. In particular, we show that for a prescribed CM field L, prescribed integers m, n and a prime l≡ 1 mn, there exists an ordinary abelian variety over a finite field with endomorphism algebra L, embedding degree n with respect to l and the field extension generated by the l-torsion points of degree mn over the field of definition. We also provide algorithms for the construction of such abelian varieties.