Ming-Deh Huang has posted on arxiv the paper Trilinear maps for cryptography that proposes a cryptographic tri-linear map based on etale cohomology of abelian surfaces. Achieving multilinear maps is a major open problem, and already going from bilinear maps (pairings) to trilinear maps would have major implications in cryptography. It is too early for me to give any opinion on the security or correctness of this scheme.
Readers may be interested to watch this video of a lecture by Dan Boneh (from a few years ago) which is mostly about pairings but contains a segment around the middle that discusses multilinear maps (and trilinear maps in particular). Boneh even publicly commits to a US$ 1000 prize for a trilinear map. It will be interesting to see if Ming-Deg will be awarded this prize!
— Steven Galbraith