Efficient (Hierarchical) Inner-Product Encryption Tightly Reduced from the Decisional Linear Assumption

Tatsuaki OKAMOTO  Katsuyuki TAKASHIMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A    No.1    pp.42-52
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.42
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Public Key Based Protocols
functional encryption,  inner-product encryption,  attribute-hiding,  tight security reduction,  short ciphertexts/secret-keys,  

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This paper proposes an inner-product encryption (IPE) scheme, which achieves selectively fully-attribute-hiding security in the standard model almost tightly reduced from the decisional linear (DLIN) assumption, and whose ciphertext is almost the shortest among the existing (weakly/fully) attribute-hiding IPE schemes, i.e., it consists of n+4 elements of G and 1 element of GT for a prime-order symmetric bilinear group (G, GT), where n is the dimension of attribute/predicate vectors. We also present a variant of the proposed IPE scheme that enjoys shorter public and secret keys with preserving the security. A hierarchical IPE (HIPE) scheme can be realized that has short ciphertexts and selectively fully-attribute-hiding security almost tightly reduced from the DLIN assumption.