Paper 2015/249
Improved (Hierarchical) InnerProduct Encryption from Lattices
Keita Xagawa
Abstract
Innerproduct encryption (IPE) provides finegrained access control and has attractive applications. Agrawal, Freeman, and Vaikuntanathan~(Asiacrypt 2011) proposed the first IPE scheme from lattices by twisting the identitybased encryption (IBE) scheme by Agrawal, Boneh, and Boyen~(Eurocrypt 2010). Their IPE scheme supports innerproduct predicates over $R^{\mu}$, where the ring is $R = \mathbb{Z}_q$. Several applications require the ring $R$ to be exponentially large and, thus, they set $q = 2^{O(n)}$ to implement such applications. This choice results in the AFV IPE scheme with public parameters of size $O(\mu n^2 \lg^3{q}) = O(\mu n^5)$ and ciphertexts of size $O(\mu n \lg^3{q}) = O(\mu n^4)$, where $n$ is the security parameter. Hence, this makes the scheme impractical, as they noted. We address this efficiency issue by ``untwisting'' their twist and providing another twist. Our scheme supports innerproduct 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 latticebased fuzzy IBE scheme.
Note: This is the full version.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 A major revision of an IACR publication in PKC 2013
 Keywords
 predicate encryption(hierarchical) innerproduct encryptionlatticeslearning with errorsfullrank difference encodingpseudocommutativity.
 Contact author(s)
 xagawa keita @ lab ntt co jp
 History
 20150319: received
 Short URL
 https://ia.cr/2015/249
 License

CC BY
BibTeX
@misc{cryptoeprint:2015/249, author = {Keita Xagawa}, title = {Improved (Hierarchical) InnerProduct Encryption from Lattices}, howpublished = {Cryptology ePrint Archive, Paper 2015/249}, year = {2015}, note = {\url{https://eprint.iacr.org/2015/249}}, url = {https://eprint.iacr.org/2015/249} }