International Association
for Cryptologic Research

In attribute-based signatures (ABS) for range of inner product (ARIP), recently proposed by Ishizaka and Fukushima at ICISC 2022, a secret-key labeled with an $n$-dimensional vector $\mathbf{x}\in\mathbb{Z}_p^n$ for a prime $p$ can used to sign a message under an $n$-dimensional vector $\mathbf{y}\in\mathbb{Z}_p^n$ and a range $[L,R]=\{L, L+1, \cdots, R-1, R\}$ with $L,R\in\mathbb{Z}_p$ iff their inner product is within the range, i.e., $\langle \mathbf{x}, \mathbf{y} \rangle \in [L,R]\pmod p$. We consider its key-range version, named key-range ARIP (KARIP), where the range $[L,R]$ is associated with a secret-key but not with a signature. We propose three generic KARIP constructions based on linearly homomorphic signatures and non-interactive witness-indistinguishable proof, which lead to concrete KARIP instantiations secure under standard assumptions with different features in terms of efficiency. We also show that KARIP has various applications, e.g., key-range ABS for range evaluation of polynomials/weighted averages/Hamming distance/Euclidean distance, key-range time-specific signatures, and key-range ABS for hyperellipsoid predicates.