由APN幂函数构造  F   2  2n    上的置换

doi:10.11959/j.issn.2096-109x.2017.00203

Abstract

Abstract:

APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over $F_{2^{2 n}}$ .By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics,methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over $F_{2^{2 n}}$ were constructed.According to the construction,the differential properties of permutations obtained by this method were discussed.

Key words: finite fields, permutation polynomials, APN, power functions

CLC Number:

TP393

Shi-zhu TIAN. Permutations from APN power functions over $F_{2^{2 n}}$ [J]. Chinese Journal of Network and Information Security, 2017, 3(10): 72-76.

Figures/Tables 3

References 16

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函数类型	2n	i	Δ	i	Δ
	4	1	6	—	—
	6	1	8	—	—
Kasami	8	1	10	3	10
	10	1	10	3	12
	12	1	12	5	12
Dobbertin	10	—	—	—	12

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Permutations from APN power functions over F 2 2n

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Permutations from APN power functions over $F_{2^{2 n}}$