Paper 2025/874

Decentralized Multi-Authority Attribute-Based Inner-Product Functional Encryption: Noisy and Evasive Constructions from Lattices

Abstract

We initiate the study of multi-authority attribute-based functional encryption for noisy inner-product functionality, and propose two new primitives: (1) multi-authority attribute-based (noisy) inner-product functional encryption (MA-AB(N)IPFE), and (2) multi-authority attribute-based evasive inner-product functional encryption (MA-ABevIPFE). The MA-AB(N)IPFE primitive generalizes the existing multi-authority attribute-based inner-product functional encryption schemes by Agrawal et al. [AGT21], by enabling approximate inner-product computation under decentralized attribute-based control. This newly proposed notion combines the approximate function evaluation of noisy inner-product functional encryption (IPFE) with the decentralized key-distribution structure of multi-authority attribute-based encryption. To better capture noisy functionalities within a flexible security framework, we formulate the MA-ABevIPFE primitive under a generic-model view, inspired by the evasive IPFE framework by Hsieh et al. [HLL24]. It shifts the focus from pairwise ciphertext indistinguishability to a more relaxed pseudorandomness-based game. To support the above notions, we introduce two variants of lattice-based computational assumptions: - The evasive IPFE assumption (evIPFE): it generalizes the assumption introduced in [HLL24] to the multi-authority setting and admits a reduction from the evasive LWE assumption proposed by Waters et al. [WWW22]; - The indistinguishability-based evasive IPFE assumption (IND-evIPFE): it is an indistinguishability-based variant of the evasive IPFE assumption designed to capture the stronger security guarantees required by our MA-AB(N)IPFE scheme. We present concrete lattice-based constructions for both primitives supporting subset policies, building upon the framework of [WWW22]. Our schemes are proven to be statically secure in the random oracle model under the standard LWE assumption and the newly introduced assumptions. Additionally, we demonstrate that our MA-AB(N)IPFE scheme can be transformed, via standard modulus switching, into a noiseless MA-ABIPFE scheme that supports exact inner-product functionality consistent with the MA-IPFE syntax in [AGT21,DP23]. This yields the first lattice-based construction of such a primitive. All our schemes support arbitrary polynomial-size attribute policies and are secure in the random oracle model under lattice assumptions with a sub-exponential modulus-to-noise ratio, making them practical candidates for noise-tolerant, fine-grained access control in multi-authority settings.