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As a generalized integral property, division property was proposed by Todo at EUROCRYPT 2015. We propose a new security criterion of S-boxes against division property and prove that it is invariant under permutation-xor equivalence. Based on the criterion, the division properties of some important 4-bit S-boxes are showed. Then, we apply it to improve the resistance of ciphers against division-property-based integral attacks while keeping the same security level against other attacks.doi:10.1049/cje.2020.10.013 fatcat:l4qau22i3jaz5hnfclw76y6aae