Improved (Hierarchical) Inner-Product Encryption from Lattices

摘要

Inner-product encryption (IPE) provides fine-grained access control and has attractive applications. Agrawal, Freeman, and Vaikuntanathan (Asiacrypt 2011) proposed the first IPE scheme from lattices by twisting the identity-based encryption (IBE) scheme by Agrawal, Boneh, and Boyen (Eurocrypt 2010). Their IPE scheme supports inner-product predicates over R~μ, where the ring is R = 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(μn~2 lg~3 q) = O(μn~5) and ciphertexts of size O(μn lg~3 q) = O(μn~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 inner-product predicates over R~μ where R = GF(q~n) instead of Z_q. Our scheme has public parameters of size O(μn~2 lg~2 q) and ciphertexts of size O(μn lg~2 q). Since the cardinality of 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 (H1PE) 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.