[Resource Topic] 2022/1451: Attribute-Based Signatures for Range of Inner Product and Its Applications

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

Authors: Masahito Ishizaka, Kazuhide Fukushima


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.

ePrint: https://eprint.iacr.org/2022/1451

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