Abstract:

It was claimed that the construction and enumeration of symmetric correlation immune functions with order one was equivalent to the solutions in the binary field and their enumeration for a certain equation. It was also shown that the construction of symmetric correlation immune functions with order m was also related to the solutions in the binary field of the above equation. The equivalent equation was obtained. By solving the equivalent equation, the methods to construct symmetric correlation immune functions with higher order and to enumerate symmetric correlation immune functions with order one were presented. The lower bound of enumeration of symmetric correlation immune functions with order one was also given in two cases.

Key words: symmetric functions, symmetric correlation immune functions with order one, symmetric correlation immune functions with higher order；equivalent equation