Redactable signature plays a significant role in real-life applications such as electronic health records, and has been studied extensively. Nevertheless, how to construct a redactable signature scheme with designated redactors is still unknown. In this paper, we affirmatively answer this problem by presenting a notion of ring trapdoor redactable signature (RTRS). RTRS is a variant of redactable signature where the redactors are specified. We first introduce the concept of ring trapdoor preimage sampleable functions (RPSFs), which inherits the merit of preimage sampleable functions and ring trapdoor functions, and then show an instantiation of RPSFs under the assumption of inhomogeneous small integer solution problem. We then present two concrete constructions of RTRS (a simplified version and a full version) from a family of RPSFs and a common signature scheme. It is proved that the unforgeability, privacy and restriction of proposed schemes relies on the security of underlying common signature schemes and ring one-way property of the RPSFs. Besides, we also prove that our schemes satisfy the indistinguishability.
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.
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