Aiming at the universality of individual interaction and the heterogeneity of individual social influence in opinion spreading, an opinion formation model of social network was proposed on the basis of Hegselmann-Krause model. By introducing the concepts of intimacy between individuals, interpersonal similarity and interaction strength, the individual interactive set was extended, the influence weight was reasonably quantified, and more realistic view of interaction rule was built. Through a series of simulation experiments, the effects of main parameters in the model on opinion evolution were analyzed. The simulation results indicate that group views can converge to the same and form consensus under different confidence thresholds. And the larger the confidence threshold is, the shorter the convergence time is. When confidence threshold is 0.2, convergence time is only 10. Meanwhile, extending the interactive set and increasing the strength of interpersonal similarity will promote consensus formation. Besides, when the clustering coefficient and the average degree of scale-free network are higher, the group views are more likely to produce convergence effect. The results are helpful to understand the dynamic process of opinion formation, and can guide social managers to make decisions and analysis.

Algebraic immunity is one of the most significant cryptographic properties for Boolean functions. In order to resist algebraic attack, high algebraic immunity is necessary for those Boolean functions used in stream ciphers. This paper constructed more than one even-variable rotation symmetric Boolean functions with optimum algebraic immunity by giving an even n. Based on majority function, some orbits of different hamming weights were chosen, then the values of functions on these orbits were changed. Given a sufficient condition of Boolean functions with optimum algebraic immunity, the new constructed Boolean functions were proved to satisfy the condition. Therefore, it shows the algebraic immunity of the functions is optimum. Thus, algebraic attacks can be resisted effectively.