Construction Of Odd Variable Rotationally Symmetric Boolean Functions With Optimal Algebraic Immunity And Nonlinearity

In the encryption system,as an important function in cryptography,Boolean function plays an extremely key role in many encryption systems.Whether stream cipher or block cipher,there is a high demand for Boolean function.At the same time,the security of encryption system will also be directly affected by the cryptographic properties of Boolean function.The different properties of Boolean function can help encryption system resist different external attacks.Algebraic degree,algebraic degree,and immune degree.Rotationally symmetric Boolean function is a special function with excellent properties and simple structure based on multiple choice logic function,in which the algebraic immunity of multiple choice logic function is optimal and the structure is very simple.This paper mainly studies rotationally symmetric Boolean functions with high nonlinearity and optimal algebraic immunity.The main work is as follows:(1)Based on the basic principle of integer splitting,the support set of multiple choice logic functions is improved and reconstructed,and a class of odd variable rotationally symmetric Boolean functions is obtained.The research shows that the function not only achieves the optimal algebraic immunity,but also has high nonlinearity.It also has excellent properties such as balance and almost optimal fast algebraic immunity.(2)Although the algebraic degree of the new function obtained in(1)can also obtain the optimal value in a certain range,there are still many cases that are not optimal.In this case,the support set of multiple choice logic functions is further improved and reconstructed from two directions,so as to obtain two kinds of odd variable rotationally symmetric Boolean functions.Their algebraic immunity is optimal,and they have both balanced and almost optimal fast algebraic immunity.The algebraic degree of one kind of new function has been greatly improved,and the nonlinearity of the other kind of new function has been further improved.