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

We study 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), which generalizes existing multi-authority attribute-based IPFE schemes by Agrawal et al. (TCC'21), by enabling approximate inner-product computation; and (2) multi-authority attribute-based evasive inner-product functional encryption (MA-evIPFE), a relaxed variant inspired by the evasive IPFE framework by Hsieh et al. (EUROCRYPT'24), shifting focus from ciphertext indistinguishability to a more relaxed pseudorandomness-based security notion. To support the above notions, we introduce two variants of lattice-based computational assumptions: evasive IPFE assumption and indistinguishability-based evasive IPFE assumption (IND-evIPFE). We present lattice-based constructions of both primitives for subset policies, building upon the framework of Waters et al.( TCC'22). 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 show our MA-AB(N)IPFE scheme can be transformed via modulus switching into a noiseless MA-IPFE scheme that supports exact inner-product functionality. 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.