The Interpolation Attack on Block Ciphers

In this paper we introduce a new method of attacks on block ciphers, the interpolation attack. This new method is useful for attacking ciphers using simple algebraic functions (in particular quadratic functions) as S-boxes. Also, ciphers of low non-linear order are vulnerable to attacks based on higher order diierentials. Recently, Knudsen and Nyberg presented a 6-round prototype cipher which is provably secure against ordinary diierential cryptanalysis. We show how to attack the cipher by using higher order diierentials and a variant of the cipher by the interpolation attack. It is possible to successfully cryptanalyse up to 32 rounds of the variant using about 2 32 chosen plaintexts with a running time less than 2 64. Using higher order diierentials, a new design concept for block ciphers by Kiefer is also shown to be insecure. Rij-men et al presented a design strategy for block ciphers and the cipher SHARK. We show that there exist ciphers constructed according to this design strategy which can be broken faster than claimed. In particular, we cryptanalyse 5 rounds of a variant of SHARK, which deviates only slightly from the proposed SHARK.