Further study on indecomposable cryptographic functions

1 Introduction Boolean functions have important applications in stream ciphers and block ciphers.Over the last decades,the constructions of cryptographic Boolean functions have paid a lot of attention[1,2].Direct sum is a well-known secondary construction of cryptographic functions[3].By using the direct sum,a lot of functions with high nonlinearities can be obtained[4,5].However,the direct sum of two functions are decomposable functions,which have numerous null secondorder derivatives(which represents a potential weakness with respect to the higher order differential attack)[6].(In)decomposable functions were also studied in[7]by Zheng and Zhang under the name(non)separable functions.They provided some sufficient conditions that the functions are indecomposable[7].