The Generalized Feistel Structure ( \(\texttt{GFS}\) ) is one of the most widely used frameworks in symmetric cipher design. In FES 2010, Suzaki and Minematsu strengthened the cryptanalysis security of \(\texttt{GFS}\) by searching for shuffles with the best diffusion property. In ASIACRYPT 2018, Shi et al. suggested a set of shuffles, which makes \(\texttt{GFS}\) a better resistance against Demirci–Selcuk meet-in-the-middle cryptanalysis. Since these shuffles are different from the currently known good ones and also different from the shuffles used in \(\texttt{TWINE}\) and \(\texttt{LBlock}\) , our research focuses on a more comprehensive evaluation of \(\texttt{GFS}\) with different shuffles, including diffusion property of shuffle, differential, linear, impossible differential, zero-correlation linear, integral and Demirci–Selcuk meet-in-the-middle cryptanalysis, to find the best one. Such evaluations entail significant time consumption. Thus, we utilize Mixed Integral Linear Programming models and introduce an evaluate-and-filter strategy to achieve it efficiently. Our results verify that the shuffles discovered by Suzaki and Minematsu and those used in \(\texttt{TWINE}\) and \(\texttt{LBlock}\) are the best so far. We also find that the cryptanalysis resistances of \(\texttt{GFS}\) are not necessarily consistent. It is this finding that makes the necessity of our more comprehensive evaluation self-evident.
