## Abstract

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 and refining 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.

Original language | English |
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Title of host publication | Public-Key Cryptography – PKC 2019 - 22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings |

Editors | Kazue Sako, Dongdai Lin |

Publisher | Springer Verlag |

Pages | 127-158 |

Number of pages | 32 |

ISBN (Print) | 9783030172527 |

DOIs | |

Publication status | Published - 2019 |

Externally published | Yes |

Event | 22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2019 - Beijing, China Duration: 2019 Apr 14 → 2019 Apr 17 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11442 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2019 |
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Country | China |

City | Beijing |

Period | 19/4/14 → 19/4/17 |

## Keywords

- Arithmetic branching programs
- Arithmetic span programs
- Attribute-based signatures
- Bilinear groups
- Concrete efficiency
- Unbounded multi-use of attributes

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)