We address this efficiency issue by ``untwisting'' their twist and providing another twist. Our scheme supports inner-product predicates over $R^\mu$ where $R = \mathrm{GF}(q^n)$ instead of $\mathbb{Z}_q$. Our scheme has public parameters of size $O(\mu n^2 \lg^2{q})$ and ciphertexts of size $O(\mu n \lg^2{q})$. Since the cardinality of $\mathrm{GF}(q^n)$ is inherently exponential in $n$, we have no need to set $q$ as the exponential size for applications.
As side contributions, we extend our IPE scheme to a hierarchical IPE (HIPE) scheme and propose a fuzzy IBE scheme from IPE. Our HIPE scheme is more efficient than that developed by Abdalla, De Caro, and Mochetti (Latincrypt 2012). Our fuzzy IBE is secure under a much weaker assumption than that employed by Agrawal et al.~(PKC 2012), who constructed the first lattice-based fuzzy IBE scheme.
Category / Keywords: public-key cryptography / predicate encryption, (hierarchical) inner-product encryption, lattices, learning with errors, full-rank difference encoding, pseudo-commutativity. Original Publication (with major differences): IACR-PKC-2013 Date: received 16 Mar 2015 Contact author: xagawa keita at lab ntt co jp Available format(s): PDF | BibTeX Citation Note: This is the full version. Version: 20150319:073106 (All versions of this report) Short URL: ia.cr/2015/249