A new construction method of balanced correlation-immune functions

As an important index of cryptosystems against correlation attacks, correlation-immune functions are widely used in the design of the cryptosystems. This paper researches construction and enumeration of balanced correlation-immune functions by column-balanced matrices. Using method of exhaustion and statistics, we give a new construction method of balanced 1-order correlation immune functions by constructing column-balanced matrixes. Based on new method, the enumeration lower bounds of balanced 1-order correlation-immune functions and balanced m-order correlation-immune functions are improved.