Compact Attribute-Based and Online-Offline Multi-input Inner Product Encryptions from Standard Static Assumptions (Short Paper)

Abstract

This paper presents an attribute-based encryption (ABE) construction for monotone span programs achieving the shortest known ciphertext size under well-studied static complexity assumptions. Our ABE construction is built in composite order bilinear group setting and involves only 2 group elements in the ciphertexts. For proving selective security of the proposed ABE scheme under the Subgroup Decision assumptions, 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 ABE 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 assumption.