Multilinear maps via secret ring

Garg, Gentry and Halevi (GGH13) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia recently presented an efficient attack on the GGH13 map, which breaks the multipartite key exchange (MPKE) and witness encryption (WE) based on GGH13. In this work, we describe a new variant of GGH13 using secret ring, which preserves the origin functionality of GGH13. The security of our variant depends upon the following new hardness problem. Given the determinant of the circular matrix of some element in a secret ring, the problem is to find this secret ring and reconstruct this element