Weil descent and cryptographic trilinear maps

It has recently been shown that cryptographic trilinear maps are sufficient for achieving indistinguishability obfuscation. In this paper we develop a method for constructing such maps on the Weil descent (restriction) of abelian varieties over finite fields, including the Jacobian varieties of hyperelliptic curves and elliptic curves. The security of these candidate cryptographic trilinear maps raises several interesting questions, including the computational complexity of a trapdoor discrete logarithm problem.