On CCZ-equivalence between the Bracken-Tan-Tan function and power functions
On CCZ-equivalence between the Bracken-Tan-Tan function and power functions
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DOI：
10.1016/j.ffa.2023.102340
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发表时间：
2024-01
期刊：
影响因子：
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通讯作者：
Chenmiao Shi;Jie Peng;H.-B. Kan;Lijing Zheng
中科院分区：
文献类型：
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作者：
Chenmiao Shi;Jie Peng;H.-B. Kan;Lijing Zheng
Permutations with differential and boomerang uniformity 4 over F 2 2 k offer good resistance to block ciphers against differential and boomerang attacks. There are five primarily constructed infinite classes of differentially 4-uniform permutations with the best known nonlinearity over F 2 2 k, namely the Gold functions, the Kasami functions, the Inverse functions, the Bracken-Leander functions and the Bracken-Tan-Tan functions. It has been shown by Boura et al. and by Mesnager et al. respectively, that the Gold functions and the Bracken-Tan-Tan functions also have boomerang uniformity 4. It is known that the Bracken-Tan-Tan functions are CCZ-inequivalent to the Inverse functions and the Bracken-Leander functions. In this paper, it is proved that the Bracken-Tan-Tan functions are also CCZ-inequivalent to the Gold functions and the Kasami functions. In particular, the Gold functions and the Bracken-Tan-Tan functions are two different classes of boomerang uniformity 4 permutations up to EA-equivalence.
