Zeroizing without zeroes: Cryptanalyzing multilinear maps without encodings of zero, by Craig Gentry and Shai Halevi and Hemanta K. Maji and Amit Sahai

We extend the recent zeroizing attacks of Cheon et al. on multilinear maps to some settings where no encodings of zero below the maximal level are available. Some of the new attacks apply to the CLT scheme (resulting in total break) while others apply to the GGH scheme (resulting in a weak-DL attack).