Partial and Higher Order Differentials and Applications to the DES

Lars R. Knudsen

February 1995


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.

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