Paper 2019/363

Efficient Attribute-Based Signatures for Unbounded Arithmetic Branching Programs

Pratish Datta, Tatsuaki Okamoto, and Katsuyuki Takashima


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.

Note: This is the full version of the paper.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Major revision. PKC 2019
attribute-based signaturesarithmetic branching programsarithmetic span programsconcrete efficiencyunbounded multi-use of attributesbilinear groups
Contact author(s)
pratish datta yg @ hco ntt co jp
2019-04-10: received
Short URL
Creative Commons Attribution


      author = {Pratish Datta and Tatsuaki Okamoto and Katsuyuki Takashima},
      title = {Efficient Attribute-Based Signatures for Unbounded Arithmetic Branching Programs},
      howpublished = {Cryptology ePrint Archive, Paper 2019/363},
      year = {2019},
      note = {\url{}},
      url = {}
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