Research on A Lattice-Based Fuzzy Signature and Bimodal Gaussian

Fuzzy signatures differ from standard signature schemes in that they use noisy strings as keys, thereby eliminating the need for user-specific auxiliary data. With the advent of quantum computing, lattice-based digital signatures are considered potential candidates for resisting quantum attacks. In this work, we revisited the lattice-based fuzzy signature scheme proposed by Zheng <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i>. and demonstrated how the scheme can be implemented more efficiently and securely. In our new signature scheme, our contributions are as follows: The utilization of bimodal Gaussian sampling reduces the number of aborting terminations while simultaneously decreasing the signature size. By eliminating the T matrix from the verification equation, we improve verification efficiency. Additionally, in response to the linear sketch proposed by the authors, we provide a proof of the collision resistance of the mapping <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i>, which further enhances the correctness of the scheme.