Candidate Multilinear Maps from Ideal Lattices and Applications

We describe plausible lattice-based constructions with properties that approximate the soughtafter multilinear maps in hard-discrete-logarithm groups, and show that some applications of such multi-linear maps can be realized using our approximations. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function. This work was supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center (DoI/NBC) contract number D11PC20202. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government. ∗Research conducted while at the IBM Research, T.J. Watson funded by NSF Grant No.1017660.