By analyzing the security of a certificateless signature scheme without bilinear pairing proposed by Wang Y, et al. (WANG Y, DU W. Security analysis and improvement of certificateless signature scheme without bilinear pairing. Journal of Computer Applications, 2013, 33(8): 2250-2252), the result that the scheme can not resist forgery attack was pointed out and an improved scheme was proposed. The improved scheme enhanced the relationship of parameters in signature algorithm to resist forgery attack. The results of security analysis show that the improved scheme is proved to be existentially unforgeable against adaptive chosen message and identity attacks in random oracle model. The improved scheme is more efficient than the existing schemes for avoiding bilinear pairings and inverse operation.

There are two inefficient steps in GEP-Cluster algorithm: one is screening and aggregation of clustering centers and the other is the calculation of distance between data objects and clustering centers. To solve the inefficiency, an auto-clustering algorithm based on Compute Unified Device Architecture (CUDA) and Gene Expression Programming (GEP), named as CGEP-Cluster, was proposed. Specifically, the screening, and aggregation of clustering center step was improved by Gene Read & Compute Machine (GRCM) method, and CUDA was used to parallel the calculation of distance between data objects and clustering centers. The experimental results show that compared with GEP-Cluster algorithm, CGEP-Cluster algorithm can speed up by almost eight times when the scale of data objects is large. CGEP-Cluster can be used to implement automatic clustering with the clustering number unknown and large data object scale.