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On equivalence between known polynomial APN functions and power APN functions
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2020-12-29 , DOI: 10.1016/j.ffa.2020.101762
Qianhong Wan , Longjiang Qu , Chao Li

Constructions and equivalence of APN functions play a significant role in the research of cryptographic functions. On finite fields of characteristic 2, 6 families of power APN functions and 14 families of polynomial APN functions have been constructed in the literature. However, the study on the equivalence among the aforementioned APN functions is rather limited to the equivalence in the power APN functions. Meanwhile, the theoretical analysis on the equivalence between the polynomial APN functions and the power APN functions, as well as the equivalence in the polynomial APN functions themselves, is far less studied. In this paper, we give the theoretical analysis on the inequivalence in 8 known families of polynomial APN functions and power APN functions.



中文翻译:

关于已知多项式APN函数和幂APN函数之间的等价关系

APN功能的构造和等效性在密码功能的研究中起着重要作用。在特征2的有限域上,文献中构造了6个幂级APN函数族和14个多项式APN函数族。然而,关于上述APN功能之间的等效性的研究相当限于功率APN功能中的等效性。同时,关于多项式APN函数和幂APN函数之间的等价关系以及多项式APN函数本身的等价关系的理论分析还很少研究。在本文中,我们对多项式APN函数和幂APN函数的8个已知族的不等式进行了理论分析。

更新日期:2020-12-29
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