Secure Threshold Multi Authority Attribute Based Encryption without a Central Authority

An attribute based encryption scheme (ABE) is a cryptographic primitive in which every user is identified by a set of attributes, and some function of these attributes is used to determine the ability to decrypt each ciphertext. Chase proposed the first multi authority ABE scheme in TCC 2007 as an answer to an open problem presented by Sahai and Waters in EUROCRYPT 2005. However, her scheme needs a fully trusted central authority which can decrypt every ciphertext in the system. This central authority would endanger the whole system if it’s corrupted. This paper presents a threshold multi authority fuzzy identity based encryption(MA-FIBE) scheme without a central authority for the first time. An encrypter can encrypt a message such that a user could only decrypt if he has at least dk of the given attributes about the message for at least t + 1, t ≤ n/2 honest authorities of all the n attribute authorities in the proposed scheme. This paper considers a stronger adversary model in the sense that the corrupted authorities are allowed to distribute incorrect secret keys to the users. The security proof is based on the secrecy of the underlying joint random secret sharing protocol and joint zero secret sharing protocol and the standard decisional bilinear Diffie-Hellman assumption. The proposed MA-FIBE could be extended to the threshold multi authority attribute based encryption (MA-ABE) scheme, and two secure MA-ABE schemes without a central authority are also presented in this paper. Moreover, some extensions about the proposed MA-ABE schemes, such as how to convert a large universe MA-ABE scheme into a proactive scheme, are also provided in this paper.