Succinct Predicate and Online-Offline Multi-Input Inner Product Encryptions under Standard Static Assumptions

Abstract

This paper presents expressive predicate encryption (PE) systems, namely non-zero inner-product-predicate encryption (NIPPE) and attribute-based encryption (ABE) supporting monotone span programs achieving best known parameters among existing similar schemes under well-studied static complexity assumptions. Both the constructions are built in composite order bilinear group setting and involve only 2 group elements in the ciphertexts. More interestingly, our NIPPE scheme, which additionally features only 1 group element in the decryption keys, is the first to attain succinct ciphertexts and decryption keys simultaneously. For proving selective security of these constructions under the Subgroup Decision assumptions, which are the most standard static assumptions in composite order bilinear group setting, we apply the extended version of the elegant Déjà Q framework, which was originally proposed as a general technique for reducing the q-type complexity assumptions to their static counter parts. Our work thus demonstrates the power of this framework in overcoming the need of q-type assumptions, which are vulnerable to serious practical attacks, for deriving security of highly expressive PE systems with compact parameters. We further introduce the concept of online-offline multi-input functional encryption (OO-MIFE), which is a crucial advancement towards realizing this highly promising but computationally intensive cryptographic primitive in resource bounded and power constrained devices. We also instantiate our notion of OO-MIFE by constructing such a scheme for the multi-input analog of the inner product functionality, which has a wide range of application in practice. Our OO-MIFE scheme for multi-input inner products is built in asymmetric bilinear groups of prime order and is proven selectively secure under the well-studied k-Linear (k-LIN) assumption.