On the use of conjugacy of substitutions in determining the key in Feistel networks

For Feistel networks with the key schedule being a sequence of subvectors of the key vector we consider a method for determining the key based on the conjugacy of substitutions. Conditions under which this method is more effective than the brute force one are investigated. Examples of application of the method to some Feistel networks of the indicated type are given. We discuss conditions on the key schedule in Feistel networks ensuring the practical impossibility of using both Isobe and Dinur–Dunkelman–Shamir methods and a method using the conjugacy of substitutions.