Fuzzy C-Means (FCM) clustering algorithm is sensitive to the initial clustering center and is easy to fall into local optimum. Therefore, a Firefly Fuzzy C-Means clustering Algorithm based on Levy flight (LFAFCM) was proposed. In LFAFCM, the random movement strategy of firefly algorithm was changed to balance the algorithm's local search and global search capabilities, the Levy flight mechanism was introduced during the firefly position update process to improve the global optimization ability, and the scale coefficient of each firefly was dynamically adjusted according to the number of iterations and the firefly position to limit the searchable range of Levy flight and speed up the convergence of the algorithm. The algorithm was validated by using five UCI datasets. The experimental results show that the algorithm avoids the local optimum and has a fast convergence speed.

To resist mobile attacks, a new dynamic threshold signature scheme based on Chinese Remainder Theorem (CRT) was proposed. Firstly, members exchanged their shadows to generate their private keys and the group public key. Secondly, a partial signature was generated by cooperation. Finally, the partial signature was used to synthesize the signature. The scheme does not expose the group private key in the signature process, so that the group private key can be reused. The members update their private keys periodically without changing the group public key to ensure that the signature is still valid before update. Besides, the scheme allows new members to join while keeping the old member's private keys and group private key unexposed. The scheme has forward security, which can resist mobile attacks effectively. Theoretical analysis and simulation results show that, compared with the proactive threshold scheme based on Lagrange interpolation, the updating time consumption of the proposed scheme is constant, therefore the scheme has time efficiency.