Efficient Inner Product Functional Encryption with Full-Hiding Security

Junichi TOMIDA  Masayuki ABE  Tatsuaki OKAMOTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A    No.1    pp.33-40
Publication Date: 2020/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019CIP0003
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
functional encryption,  inner product,  function privacy,  pairing,  

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Inner product functional encryption (IPFE) is a subclass of functional encryption (FE), whose function class is limited to inner product. We construct an efficient private-key IPFE scheme with full-hiding security, where confidentiality is assured for not only encrypted data but also functions associated with secret keys. Recently, Datta et al. presented such a scheme in PKC 2016 and this is the only scheme that achieves full-hiding security. Our scheme has an advantage over their scheme for the two aspects. More efficient: keys and ciphertexts of our scheme are almost half the size of those of their scheme. Weaker assumption: our scheme is secure under the k-linear (k-Lin) assumption, while their scheme is secure under a stronger assumption, namely, the symmetric external Diffie-Hellman (SXDH) assumption. It is well-known that the k-Lin assumption is equivalent to the SXDH assumption when k=1 and becomes weak as k increases.