(Fine-Grained) Unbounded Inner-Product Functional Encryption from LWE

Abstract

Inner-product functional encryption (IPFE), introduced by Abdalla-Bourse-De Caro-Pointcheval (PKC'15), is a public-key primitive that allows to decrypt an encrypted vector x with a secret key associated to a vector y such that only their inner-product <x,y> is revealed. The initial definition and constructions all required the length of such vectors to be bounded at setup, and therefore, be fixed in the public parameters. In order to overcome this drawback, Dufour-Sans-Pointcheval (ACNS'19) and Tomida-Takashima (AC'18) introduced the notion of unbounded IPFE, where the length of vectors does not need to be fixed during the setup phase, and gave constructions from pairing-based assumptions. In this paper, we make progress and provide the first unbounded IPFE constructions that i) are based on the Learning With Errors (LWE) assumption and proven secure in the standard model, ii) achieve adaptive security, iii) provide fine-grained access control, i.e., are identity- and attribute-based, and iv) rely only on black-box access to cryptographic and lattice algorithms. Hence, our constructions are also plausibly post-quantum secure.