  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.
