Cryptanalysis of the New CLT Multilinear Maps, by Jung Hee Cheon, and Changmin Lee, and Hansol Ryu

Multilinear maps have many cryptographic applications. The first candidate construction of multilinear maps was proposed by Garg, Gentry, and Halevi (GGH13) in 2013, and soon afterwards, another candidate was suggested by Coron, Lepoint, and Tibouchi (CLT13) that works over the integers. However, both of these were found to be insecure in the face of a so-called zeroizing attack (HJ15, CHL+15). To improve on CLT13, Coron, Lepoint, and Tibouchi proposed another candidate of new multilinear maps over the integers (CLT15). In this paper, we describe an attack against CLT15. Our attack shares the essence of the cryptanalysis of CLT13 and exploits low level encodings of zero, as well as other public parameters. As in CHL+15, this leads to finding all the secret parameters of \kappa-multilinear maps in polynomial time of the security parameter.