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 x∈Zpn for a prime p can be used to sign a message under an n-dimensional vector y∈Zpn and a range [ L, R] = { L, L+ 1, ⋯, R- 1, R} with L, R∈ Zp iff their inner product is within the range, i.e., ⟨x,y⟩∈[L,R](modp). 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.