Matrix Description on Propagation Characteristic of Boolean Function

With characteristic matrix of Boolean function, a necessary and sufficient condition is given on a Boolean function satisfying the propagation criterion on vector sGFn(2), which provides n3. On the basis of it, the necessary and sufficient conditions are given on a Boolean function satisfying Strict Avalanche Criterion (SAC) and on a balanced SAC function which achieves the maximum degree and no nonzero linear structure. Finally, two special filling vacancies in the proper order methods of construction are presented.