This paper presents the first attribute-based signature (ABS) scheme in which the correspondence between signers and signatures is captured in an arithmetic model of computation. Specifically, we design a fully secure, i.e., adaptively unforgeable and perfectly signer-private ABS scheme for signing policies realizable by arithmetic branching programs (ABP), which are a quite expressive model of arithmetic computations. On a more positive note, the proposed scheme places no bound on the size and input length of the supported signing policy ABP's, and at the same time, supports the use of an input attribute for an arbitrary number of times inside a signing policy ABP, i.e., the so called unbounded multi-use of attributes. The size of our public parameters is constant with respect to the sizes of the signing attribute vectors and signing policies available in the system. The construction is built in (asymmetric) bilinear groups of prime order, and its unforgeability is derived in the standard model under (asymmetric version of) the well-studied decisional linear (DLIN) assumption coupled with the existence of standard collision resistant hash functions. Due to the use of the arithmetic model as opposed to the boolean one, our ABS scheme not only excels significantly over the existing state-of-the-art constructions in terms of concrete efficiency, but also achieves improved applicability in various practical scenarios. Our principal technical contributions are (a) extending the techniques of Okamoto and Takashima [PKC 2011, PKC 2013], which were originally developed in the context of boolean span programs, to the arithmetic setting; and (b) innovating new ideas to allow unbounded multi-use of attributes inside ABP's, which themselves are of unbounded size and input length.

This paper demonstrates how to achieve simulation-based strong attribute hiding against adaptive adversaries for predicate encryption (PE) schemes supporting expressive predicate families under standard computational assumptions in bilinear groups. Our main result is a simulation-based adaptively strongly partially-hiding PE (PHPE) scheme for predicates computing arithmetic branching programs (ABP) on public attributes, followed by an inner-product predicate on private attributes. This simultaneously generalizes attribute-based encryption (ABE) for boolean formulas and ABP's as well as strongly attribute-hiding PE schemes for inner products. The proposed scheme is proven secure for any a priori bounded number of ciphertexts and an unbounded (polynomial) number of decryption keys, which is the best possible in the simulation-based adaptive security framework. This directly implies that our construction also achieves indistinguishability-based strongly partially-hiding security against adversaries requesting an unbounded (polynomial) number of ciphertexts and decryption keys. The security of the proposed scheme is derived under (asymmetric version of) the well-studied decisional linear (DLIN) assumption. Our work resolves an open problem posed by Wee in TCC 2017, where his result was limited to the semi-adaptive setting. Moreover, our result advances the current state of the art in both the fields of simulation-based and indistinguishability-based strongly attribute-hiding PE schemes. Our main technical contribution lies in extending the strong attribute hiding methodology of Okamoto and Takashima [EUROCRYPT 2012, ASIACRYPT 2012] to the framework of simulation-based security and beyond inner products.