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In FES 2010, Suzaki and Minematsu strengthened the cryptanalysis security of $$\\texttt{GFS}$$<\/jats:tex-math>\n GFS<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> by searching for shuffles with the best diffusion property. In ASIACRYPT 2018, Shi\u00a0et al.\u00a0suggested a set of shuffles, which makes $$\\texttt{GFS}$$<\/jats:tex-math>\n GFS<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> a better resistance against Demirci\u2013Selcuk meet-in-the-middle cryptanalysis. Since these shuffles are different from the currently known good ones and also different from the shuffles used in $$\\texttt{TWINE}$$<\/jats:tex-math>\n TWINE<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$\\texttt{LBlock}$$<\/jats:tex-math>\n LBlock<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, our research focuses on a more comprehensive evaluation of $$\\texttt{GFS}$$<\/jats:tex-math>\n GFS<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with different shuffles, including diffusion property of shuffle, differential, linear, impossible differential, zero-correlation linear, integral and Demirci\u2013Selcuk 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 $$\\texttt{TWINE}$$<\/jats:tex-math>\n TWINE<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$\\texttt{LBlock}$$<\/jats:tex-math>\n LBlock<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are the best so far. We also find that the cryptanalysis resistances of $$\\texttt{GFS}$$<\/jats:tex-math>\n GFS<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are not necessarily consistent. It is this finding that makes the necessity of our more comprehensive evaluation self-evident.<\/jats:p>","DOI":"10.1186\/s42400-024-00220-0","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T02:02:13Z","timestamp":1730426533000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Revisiting the shuffle of generalized Feistel structure"],"prefix":"10.1186","volume":"7","author":[{"given":"Yincen","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuanyu","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianqian","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"key":"220_CR1","doi-asserted-by":"crossref","unstructured":"Anderson R, Biham E (1996) Two practical and provably secure block ciphers: bear and lion. 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