Signature Schemes with a Fuzzy Private Key

In this paper, we introduce a new concept of digital signature that we call fuzzy signature, which is a signature scheme that uses a noisy string such as biometric data as a private key, but does not require user-specific auxiliary data (which is also called a helper string in the context of fuzzy extractors), for generating a signature. Our technical contributions are three-fold: (1) We first give the formal definition of fuzzy signature, together with a formal definition of a “setting” that specifies some necessary information for fuzzy data. (2) We give a generic construction of a fuzzy signature scheme based on a signature scheme that has certain homomorphic properties regarding keys and satisfies a kind of related key attack security with respect to addition, and a new tool that we call linear sketch. (3) We specify two concrete settings for fuzzy data, and for each of the settings give a concrete instantiation of these building blocks for our generic construction, leading to two concrete fuzzy signature schemes. We also discuss how fuzzy signature schemes can be used to realize a biometric-based PKI that uses biometric data itself as a cryptographic key, which we call the public biometric infrastructure (PBI).