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Title:
Key-Range Attribute-Based Signatures for Range of Inner Product and Its Applications
Authors: Masahito Ishizaka
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 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.
ePrint: https://eprint.iacr.org/2023/747
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