New construction method and enumeration of balanced correlation-immune function

Balance is the basic criteria for cryptography algorithm design, and is necessary means to avoid information leakage of cryptography. Correlation immunity has long been recognized as one of the critical indicators for cryptography to resist relevant attack. This paper studies correlation immune function based on column balanced matrix, and presents new method to construct balanced 1-st order correlation immune function. On the basis, the lower enumeration bound of balanced 1-st and m-th order correlation immune function is improved.