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 ...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].展开更多
基金This work was supported by the Fundamental Research Funds for the Central Universities of China(2015QNA38)the Natural Science Foundation of China(Grant No.61972400).
文摘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].
