Optimal combined distinguisher of stream cipher with multiple independent distinguishing characters

It is an open problem to combine many distinguishing characters to construct a distinguisher with more advantage. An optimal combined distinguisher based on multiple independent distinguishing characters was proposed. The computing method of distinguishing advantage of this combined distinguisher was presented and the conclusion was given that the data complexity decreased on the condition of same distinguishing advantage, and the distinguishing advantage increased on the condition of the same data complexity when more distinguishing characters were used in distinguishing attack. Let N denote the data complexity of distinguisher with only one character, then the data complexity of combined distinguisher with k-independent characters was about N/k for special case that all distinguishing advantages of k-independent characters were equal.