To remedy our rather poor understanding regarding NIPE schemes without bilinear maps, we provide two methods for constructing NIPE schemes: a direct construction from lattices and a generic construction from functional encryption schemes for inner products (LinFE). For our first direct construction, it highly departs from the traditional lattice-based constructions and we rely heavily on new tools concerning Gaussian measures over multi-dimensional lattices to prove security. For our second generic construction, using the recent constructions of LinFE schemes as building blocks, we obtain the first NIPE constructions based on the DDH and DCR assumptions. In particular, we obtain the first NIPE schemes without bilinear maps or lattices.
Category / Keywords: Non-zero inner product encryption, lattices, generic constructions, functional encryption for inner products Original Publication (with major differences): IACR-PKC-2019 Date: received 15 Jan 2019, last revised 15 Jan 2019 Contact author: shuichi katsumata000 at gmail com, shota yamada enc@gmail com, yamada-shota@aist go jp Available format(s): PDF | BibTeX Citation Version: 20190117:231457 (All versions of this report) Short URL: ia.cr/2019/036