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Paper 2022/1451

Attribute-Based Signatures for Range of Inner Product and Its Applications

Abstract

In attribute-based signatures (ABS) for inner products, the digital signature analogue of attribute-based encryption for inner products (Katz et al., EuroCrypt'08), a signing-key (resp. signature) is labeled with an $n$-dimensional vector $\mathbf{x}\in\mathbf{Z}_p^n$ (resp. $\mathbf{y}\in\mathbf{Z}_p^n$) for a prime $p$, and the signing succeeds iff their inner product is zero, i.e., $ \langle \mathbf{x}, \mathbf{y} \rangle=0 \pmod p$. We generalize it to ABS for range of inner product (ARIP), requiring the inner product to be within an arbitrarily-chosen range $[L,R]$. As security notions, we define adaptive unforgeablity and perfect signer-privacy. The latter means that any signature reveals no more information about $\mathbf{x}$ than $\langle \mathbf{x}, \mathbf{y} \rangle \in[L,R]$. We propose two efficient schemes, secure under some Diffie-Hellman type assumptions in the standard model, based on non-interactive proof and linearly homomorphic signatures. The 2nd (resp. 1st) scheme is independent of the parameter $n$ in secret-key size (resp. signature size and verification cost). We show that ARIP has many applications, e.g., ABS for range evaluation of polynomials/weighted averages, fuzzy identity-based signatures, time-specific signatures, ABS for range of Hamming/Euclidean distance and ABS for hyperellipsoid predicates.