Fuzzy Identity Based Signature

We introduce a new cryptographic primitive which is the signature analogue of fuzzy identity based encryption(IBE). We call it fuzzy identity based signature(IBS). It possesses similar error-tolerance property as fuzzy IBE that allows a user with the private key for identity ω to decrypt a ciphertext encrypted for identity ω′ if and only if ω and ω′ are within a certain distance judged by some metric. A fuzzy IBS is useful whenever we need to allow the user to issue signature on behalf of the group that has certain attributes. Fuzzy IBS can also be applied to biometric identity based signature. To our best knowledge, this primitive was never considered in the identity based signature before. We give the definition and security model of the new primitive and present the first practical implementation based on Sahai-Waters construction[6] and the two level hierarchical signature of Boyen and Waters[9]. We prove that our scheme is existentially unforgeable against adaptively chosen message attack without random oracles.