Despite widespread interest in cryptographic multilinear maps since
Boneh-Silverberg's 2003 paper, very few candidate maps have been
discovered. The first serious candidate was a scheme of
Garg-Gentry-Halevi (GGH), which is based on ideal lattices in cyclotomic
number rings. While the scheme was later shown to be broken, the only
other candidate schemes are hardened variants of GGH. We give a
relatively detailed description of the GGH multilinear map.