A Note on the Equivalent of Difference Distribution Table for Balanced (<i>n</i>, <i>n</i>)-Functions

Difference distribution table (DDT) plays an important role in studying the cryptographic properties of (n, n)-functions, (n, n)-functions with the same DDT are called DDT-equivalent. In this paper, we give one sufficient and necessary condition on DDT-equivalent according to autocorrelation distributions at first, and obtain some methods about new DDT-equivalent based on old DDT-equivalent. Finally, a construction algorithm on DDT-equivalent is present, we fully give DDT-equivalent for all balanced (3, 3)-functions.