Revisiting the shuffle of generalized Feistel structure

Abstract

Abstract The Generalized Feistel Structure ( $$\texttt{GFS}$$ GFS ) is one of the most widely used frameworks in symmetric cipher design. In FES 2010, Suzaki and Minematsu strengthened the cryptanalysis security of $$\texttt{GFS}$$ GFS by searching for shuffles with the best diffusion property. In ASIACRYPT 2018, Shi et al. suggested a set of shuffles, which makes $$\texttt{GFS}$$ 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 $$\texttt{TWINE}$$ TWINE and $$\texttt{LBlock}$$ LBlock , our research focuses on a more comprehensive evaluation of $$\texttt{GFS}$$ 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 $$\texttt{TWINE}$$ TWINE and $$\texttt{LBlock}$$ LBlock are the best so far. We also find that the cryptanalysis resistances of $$\texttt{GFS}$$ GFS are not necessarily consistent. It is this finding that makes the necessity of our more comprehensive evaluation self-evident.

Keywords

• Block cipher design
• Generalized Feistel structure
• Security evaluation