@inbook {IOPORT.05831621,
    author       = {Huang, Ming-Deh and Raskind, Wayne},
    title        = {A multilinear generalization of the Tate pairing.},
    year         = {2010},
    booktitle    = {Finite fields. Theory and applications. Proceedings of the 9th international conference on finite fields and applications, Dublin, Ireland, July 13--17, 2009},
    isbn         = {978-0-8218-4786-2},
    pages        = {255-263},
    publisher    = {Providence, RI: American Mathematical Society (AMS)},
    abstract     = {Summary: Efficiently computable multilinear maps are of considerable interest in cryptography. Though a variety of $n$-multilinear maps are known for $n>2$, an efficiently computable and cryptographically interesting one remains to be demonstrated. We consider a multilinear generalization of the Tate pairing that may serve as a candidate for such a map. Let $A$ be a principally polarized abelian variety of dimension $g$ over a finite field $\Bbb F$. We fix a prime number $\ell$ and denote by $V=A[\ell]$ the set of points $P$ of $A$ defined over $\overline{\Bbb F}$ such that $\ell P=0$. Let $\varphi$ be the geometric Frobenius and put $N=\varphi-1$. We demonstrate the existence of a $2g$-multilinear pairing that is an analogue of the Tate pairing when the action of $N$ is maximally nilpotent on $V$. That is, $N^{2g}=0$, but $N^{2g-1}\ne 0$. It remains to be seen whether the pairing can be efficiently computed.},
    identifier   = {05831621},
}