Paper 2023/747

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

Abstract

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 be 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., $⟨\mathbf{x},\mathbf{y}⟩\in [L,R](\mathrm{mod}p)$. 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.

Note: Some minor errors in the first version have been fixed.