Fang Feng

Fang Feng, Yuanyi Sun, Yue Yu

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning the perturbation parameter. However, the resulting uniform convergence rate is only of half-order, which is suboptimal. In this work, we demonstrate that the proposed IPVEM in fact achieves optimal and uniform error estimates, even in the presence of boundary layers. The theoretical results are substantiated through extensive numerical experiments, which confirm the validity of the error estimates and highlight the method's effectiveness for singularly perturbed problems.

Shangping Wang, Fang Feng

We propose a large universe attribute-based encryption (ABE ) scheme from lattices. It is inspired by Brent Waters' scheme which is a large universe attribute-based encryption using bilinear map. It is a very practical scheme but this scheme may not be security with the developing quantum computer. So we extend their good idea of large universe attribute-based encryption to lattices based cryptosystem. And our scheme is the first large universe ABE scheme from lattices. In a large universe ABE system any string can be used as attribute and attributes need not be determined at system setup. This is a desirable feature. And the master private key of our scheme is too short too a matrix. Moreover, our scheme is high efficient due to the ciphertext of our scheme is divided into three parts. Finally, under Learning with Errors assumption, we prove our scheme is secure under the select attribute attack.