With the advancement of quantum computing, the utilization of quantum algorithms such as Shor’s algorithm enables the efficient resolution of problems that are intractable in classical computing paradigms, posing a significant threat to traditional signature schemes. Lattice-based cryptography is considered one of the most promising post-quantum cryptographic algorithms due to its computational advantages and potential resistance to quantum attacks. Proxy signature is an authorization mechanism that allows the original signer to delegate the signing power to a proxy. The security of existing proxy signature schemes is mostly based on classical hard problems, which cannot guarantee security under quantum attacks. Therefore, this paper combines lattice-based cryptography with proxy signatures to propose a new lattice-based proxy signature scheme (NLBPS). NLBPS constructs signatures using lattice-based trapdoor sampling algorithms and preimage sampling algorithms. Comparative analysis shows that the proposed scheme has relatively smaller key and signature sizes compared to some existing lattice-based proxy signature schemes, and it also offers a certain improvement in computational efficiency.

SymmetryFeb 9, 20252 citations

Pre‐image sample algorithm with irregular Gaussian distribution and construction of identity‐based signature

Jianhua Yan, Licheng Wang, Jing Li +3 more

Summary Lattice has become an attractive cryptographic tool due to its potential resistance to quantum attacks, worst‐case hardness, simple computation kind, and flexibility. The pre‐image sample algorithm is the most fundamental algorithm in lattice‐based cryptography for its comprehensive applications in various primitives. Currently, due to Micciancio and Peikert (MP) sample algorithm is the most efficient pre‐image sample algorithm. However, this algorithm also needs massive computations. On the one hand, it expenses the cube of the lattice dimension multiplications over reals to set matrices as Gaussian parameters. On the other hand, it needs complex discrete convolution computations. First, this paper proposes an efficient pre‐image sample algorithm with outputs obeying irregular Gaussian distribution. Two measures are adopted to prevent the leakage of the geometrical property of trapdoor caused by irregular Gaussian outputs. A variant of MP trapdoor is proposed, and a new trapdoor is randomly assembled from a big enough space in each sample. Although still using a matrix as the Guassian parameter, in the proposed algorithm, the computational cost to set Gaussian parameters is zero. Meanwhile, the computational overhead for every sample is far less than that of MP sample algorithm. Second, to demonstrate the security and efficiency of the proposed sample algorithm, a hierarchical identity‐based signature scheme is put forward. This scheme is proved existentially unforgeable against selective identity adaptively chosen‐message attacks. Furthermore, the theoretical analysis shows that the proposed identity‐based signature is more efficient than the existing schemes. Copyright © 2016 John Wiley & Sons, Ltd.

Concurrency and Computation Practice and ExperienceAug 27, 20163 citations