In 1994 Lai considered higher order derivatives of discrete functions and<br />introduced the concept of higher order differentials. We introduce the concept<br />of partial differentials and present attacks on ciphers presumably secure<br />against differential attacks, but vulnerable to attacks using higher order and<br />partial differentials. Also we examine the DES for partial and higher order<br />differentials and give a differential attack using partial differentials on DES<br />reduced to 6 rounds using only 46 chosen plaintexts with an expected running time of about the time of 3,500 encryptions. Finally it is shown how to find a minimum nonlinear order of a block cipher using higher order differentials.
Higher Order Differential Attack of Camellia(II)