Partial and Higher Order Differentials and Applications to the DES

Abstract

In 1994 Lai considered higher order derivatives of discrete functions and
introduced the concept of higher order differentials. We introduce the concept
of partial differentials and present attacks on ciphers presumably secure
against differential attacks, but vulnerable to attacks using higher order and
partial differentials. Also we examine the DES for partial and higher order
differentials and give a differential attack using partial differentials on DES
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.