On one class of symmetric Boolean functions

Abstract

The properties of one class of symmetric Boolean funct which was denoted by  was discussed,a different method for proving that one subclass of  having maximum algebraic immunity was presented.A necessary condition was proposed for the functions of  with maximum algebraic immunity,of which a lower bound of the number was also given.Meanwhile,the algebraic degree of most functions of  was determined and linear structure and correlation immunity of  were also analyzed.The results show that the functions of  have no non-zero linear structure and only two functions of  have 1-correlation immunity.

Keywords

• symmetric Boolean functions
• algebraic immunity
• corre ion immunity
• nonlinearity