Cryptanalysis of the New Multilinear Map over the Integers

This article describes a polynomial attack on the new multilinear map over the integers presented by Coron, Lepoint and Tibouchi at Crypto 2015 (CLT15). This version is a fix of the first multilinear map over the integers presented by the same authors at Crypto 2013 (CLT13) and broken by Cheon et al. at Eurocrypt 2015. The attack essentially downgrades CLT15 to its original version CLT13, and leads to a full break of the multilinear map for virtually all applications. In addition to the main attack, we present an alternate probabilistic attack underpinned by a different technique, as well as an instant-time attack on the optimized variant of the scheme.