Cryptology ePrint Archive: Report 2009/126

Threshold Attribute-Based Signatures and Their Application to Anonymous Credential Systems

Siamak F Shahandashti and Reihaneh Safavi-Naini

Abstract: Inspired by the recent developments in attribute-based encryption, in this paper we propose threshold attribute-based signatures (t-ABS). In a t-ABS, signers are associated with a set of attributes and verification of a signed document against a verification attribute set succeeds if the signer has a threshold number of (at least t) attributes in common with the verification attribute set. A t-ABS scheme enables a signature holder to prove possession of signatures by revealing only the relevant (to the verification attribute set) attributes of the signer, hence providing signer-attribute privacy for the signature holder. We define t-ABS schemes, formalize their security and propose two t-ABS schemes: a basic scheme that is selectively unforgeable and a second one that is existentially unforgeable, both provable in the standard model, assuming hardness of the computational Diffie-Hellman problem. We show that our basic t-ABS scheme can be augmented with two extra protocols that are used for efficiently issuing and verifying t-ABS signatures on committed values. We call the augmented scheme a threshold attribute based c-signature scheme (t-ABCS). We show how a t-ABCS scheme can be used to realize a secure {threshold attribute-based anonymous credential system (t-ABACS) providing signer-attribute privacy. We propose a security model for t-ABACS and give a concrete scheme using t-ABCS scheme. Using the simulation paradigm, we prove that the credential system is secure if the t-ABCS scheme is secure.

Category / Keywords: public-key cryptography / Attribute-Based Cryptography, Anonymous Credential Systems, Identity-based Cryptography, User Privacy, Fuzzy Identity-based Signature

Publication Info: An abridged version of this paper is to appear in AfricaCrypt 2009. This is the full version.

Date: received 17 Mar 2009, last revised 1 Apr 2009

Contact author: siamax at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20090402:042124 (All versions of this report)

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