A signature scheme with a fuzzy private key

Abstract

In this paper, we introduce a new concept 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 auxiliary data (which is also called 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 with certain homomorphic properties regarding keys and signatures, and a new tool that we call linear sketch. (3) We specify a certain setting for fuzzy data, and then give concrete instantiations of these building blocks for our generic construction, leading to our proposed fuzzy signature scheme. 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).