International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 19 March 2015

Keita Xagawa
ePrint Report ePrint Report
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 $R^{\\mu}$, 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 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.

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