An Improved Fuzzy Vector Signature with Reusability

Fuzzy vector signature (FVS) is a new primitive where a fuzzy (biometric) data w is used to generate a verification key <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="sans-serif">VK</mi><mi>w</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and, later, a distinct fuzzy (biometric) data <inline-formula><math display="inline"><semantics><msup><mi>w</mi><mo>′</mo></msup></semantics></math></inline-formula> (as well as a message) is used to generate a signature <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msub><mi>σ</mi><msup><mi>w</mi><mo>′</mo></msup></msub><mo>)</mo></mrow></semantics></math></inline-formula>. The primary feature of FVS is that the signature <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msub><mi>σ</mi><msup><mi>w</mi><mo>′</mo></msup></msub><mo>)</mo></mrow></semantics></math></inline-formula> can be verified under the verification key <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="sans-serif">VK</mi><mi>w</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> only if w is close to <inline-formula><math display="inline"><semantics><msup><mi>w</mi><mo>′</mo></msup></semantics></math></inline-formula> in a certain predefined distance. Recently, Seo et al. proposed an FVS scheme that was constructed (loosely) using a subset-based sampling method to reduce the size of helper data. However, their construction fails to provide the reusability property that requires that no adversary gains the information on fuzzy (biometric) data even if multiple verification keys and relevant signatures of a single user, which are all generated with correlated fuzzy (biometric) data, are exposed to the adversary. In this paper, we propose an improved FVS scheme which is proven to be reusable with respect to arbitrary correlated fuzzy (biometric) inputs. Our efficiency improvement is achieved by strictly applying the subset-based sampling method used before to build a fuzzy extractor by Canetti et al. and by slightly modifying the structure of the verification key. Our FVS scheme can still tolerate sub-linear error rates of input sources and also reduce the signing cost of a user by about half of the original FVS scheme. Finally, we present authentication protocols based on fuzzy extractor and FVS scheme and give performance comparison between them in terms of computation and transmission costs.