A Provably Secure Lattice-Based Fuzzy Signature Scheme Using Linear Sketch

Fuzzy signatures (FS) are a kind of signature scheme that employs a noisy string (e.g., biometric data) as the secret key without requiring the user-specific auxiliary data. As the quantum computing era approaches, some research has been dedicated to developing quantum-resistant FS schemes, which can be classified into fuzzy extractor (FE) approach and linear sketch (LS) approach. However, the existing schemes utilizing FEs to obtain (variants of) fuzzy signatures require to produce the user-specific auxiliary information known as helper data to retrieve secret keys, leading to an additional computational cost. In light of the circumstance, we seek to construct a fuzzy signature scheme by employing a linear sketch, since this approach does not require the user-specific auxiliary data to derive secret keys. We modify the linear sketch which is an essential ingredient of the most practical fuzzy signature proposed by Katsumata et al. (CCS’ 21). Then we combine it with Lyubashevsky’s lattice-based signature scheme (EUROCRYPT’ 12) to construct our lattice-based fuzzy signature scheme. Moreover, to further demonstrate the security of our proposed scheme, we provide a rigorous security proof in the random oracle model. Finally, the comparison indicates that our proposed FS scheme not only avoids the use of FE but also shows a promising tendency in efficiency among the existing quantum-resistant FS schemes.