International Association
for Cryptologic Research

Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia presented an efficient attack on GGH map, which breaks two applications of multipartite key exchange (MPKE) and witness encryption (WE) based on the hardness of 3-exact cover problem by using GGH. We describe a new construction of multilinear map using random matrix, which supports the applications for public tools of encoding in the origin GGH, such as MPKE and WE. The security of our construction depends upon new hardness assumption. Furthermore, our construction removes the special structure of the ring element in the principal ideal lattice problem, and avoids potential attacks generated by algorithm of solving short principal ideal lattice generator.