The analysis of software system evolution is highly significant in software research as the evolution runs throughout the lifecycle of a software system. Considering a software system as an algebraic engineering system, we propose a software system evolution analysis method based on algebraic topology. First, from a complex network perspective, we abstract a software system into the software structural topology diagram. Then, based on the algebraic topology principle, we abstract each node in the software structural topology diagram into an algebraic component represented by a 6-tuple. We propose three kinds of operation relationships between two algebraic components, so that the software system can be abstracted into an algebraic expression of components. In addition, we propose three forms of software system evolution, which help to analyze the structure and evolution of system software and facilitate its maintenance and reconfiguration.

ID-based constant-round group key agreement protocols are efficient in both computation and communication, but previous protocols did not provide valid message authentication. An improvement based on attack analysis is proposed in this paper. The improved method takes full advantage of the data transmitted at various stages of the protocol. By guaranteeing the freshness of authentication messages, the authenticity of the generator of authentication messages, and the completeness of the authenticator, the improved protocol can resist various passive and active attacks. The forward secrecy of the improved protocol is proved under a Katz-Yung (KY) model. Compared with existing methods, the improved protocol is more effective and applicable.