I have read the papers Wide Trail Strategy and Wide Trail Design Strategy for Binary MixColumns. These papers describe the need for a good linear transformation in a cipher, a provable mechanism to counter the differential and linear cryptanalysis, and also to determine the required rounds to mitigate these attacks. All these parameters are determined by determining the minimum number of active bundles after certain rounds. Now, my question is that for a cipher, if a single round transformation consists of Substitution-->> Permutation-->>Substitution; alternatively, a bundle/ byte(or some bits from one bundle and other bits from some another bundle) gets substituted multiple times in a recursive way. Can anyone tell that in such a scenario how to calculate the branch number/ active bundle weight? Any idea/ reference are mostly welcomed.


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