International Association
for Cryptologic Research

Recently, Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, there exists zeroizing attack in the GGH construction. We first describe an improved construction of multilinear maps from ideal lattices, by multiplying matrices on both sides of the level-1 encoding of non-zero element. The security of our construction depends upon new hardness assumption, which is seemingly closely related to hardness problems of lattices. Then, we describe an asymmetric construction to avoid any nontrivial encoding of zero. Using our constructions over polynomial ring instead of integer ring, we implement one-round multipartite Diffie-Hellman key exchange protocol to decrease the public parameter size.