Weil descent and cryptographic trilinear maps
This addresses the need for cryptographic trilinear maps to achieve indistinguishability obfuscation, but it appears incremental as it builds on existing methods for constructing such maps.
The paper tackles constructing cryptographic trilinear maps using Weil descent on abelian varieties over finite fields, including Jacobian varieties of hyperelliptic and elliptic curves, and raises security questions about trapdoor discrete logarithm problems.
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.