Analysis of impossible, integral and zero-correlation attacks on type-II generalized feistel networks using the matrix method

Abstract

While recent publications have shown strong relations between impossible differential and zero-correlation distinguishers as well as between zero-correlation and integral distinguishers, we analyze in this paper some relations between the underlying key-recovery attacks against Type-II Feistel networks. The results of this paper are build on the relation presented at ACNS 2014. In particular, using a matrix representation of the round function, we show that we can not only find impossible, integral and multidimensional zero-correlation distinguishers but also find the key-words involved in the underlined key-recovery attacks. Based on this representation, for matrix-method-derived strongly-related zero-correlation and impossible distinguishers, we show that the keywords involved in the zero-correlation attack is a subset of the key-words involved in the impossible differential attack. Other relations between the key-words involved in zero-correlation, impossible and integral attacks are also extracted. Also we show that in this context the data complexity of the multidimensional zero-correlation attack is larger than that of the other two attacks.