Construction Of Odd Valued Rotationally Symmetric Boolean Functions With Optimal Algebraic Immunity

In the field of cryptography,nonlinear Boolean function plays an important role,which is mainly used in the research and design of cryptosystem.With the discovery and proposal of algebraic attack(AA)in 2003,algebraic immunity,as a new standard,is used to measure Boolean functions with good cryptographic properties.The research on Boolean functions has become a frontier topic in cryptography.Boolean functions with excellent nonlinear properties need to have many properties at the same time,such as balance,high non-linearity,high algebraic immunity,etc.there is a mutual restriction or equivalence relationship between the properties.The improvement of one property of Boolean function may lead to the reduction of another property.How to find the balance point between different properties is of great significance.Multiple choice logic function is an important symmetric Boolean function in cryptography,which has simple structure and optimal algebraic immunity.Rotationally symmetric Boolean function is a kind of function whose output value remains unchanged when the input value is circularly shifted.This paper proposes a scheme of constructing rotation symmetric Boolean functions with optimal immunity.(1)Based on the theory of integer splitting proposed a class of odd valued rotationally symmetric Boolean functions with optimal algebraic immunity is constructed by studying and modifying the support set of multiple choice logic functions.Through calculation and proof,this kind of functions has high nonlinearity and almost optimal fast algebraic immunity.(2)The algebraic degree of the first kind of function can be achieved under some variables,but its value is still less than or equal to other variables.By modifying the support set of the first kind of rotationally symmetric Boolean functions,a new class of odd balanced rotationally symmetric Boolean functions with better cryptographic properties is constructed,which has high nonlinearity,higher algebraic degree and almost optimal fast algebraic immunity.