Improved (Hierarchical) Inner-Product Encryption from Lattices

  • Keita Xagawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7778)


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 Rμ, where the ring is R = ℤq. Several applications require the ring R to be exponentially large and, thus, they set q = 2O(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 Rμ where R = GF(qn) instead of ℤq. 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 GF(qn) 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.


predicate encryption (hierarchical) inner-product encryption lattices learning with errors full-rank difference encoding pseudo-commutativity 


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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Keita Xagawa
    • 1
  1. 1.NTT Secure Platform LaboratoriesJapan

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