# More infinite classes of APN-like Power Functions

@article{Qu2022MoreIC, title={More infinite classes of APN-like Power Functions}, author={Longjiang Qu and Kangquan Li}, journal={ArXiv}, year={2022}, volume={abs/2209.13456} }

In the literature, there are many APN-like functions that generalize the APN properties or are similar to APN functions, e.g. locally-APN functions, 0-APN functions or those with boomerang uniformity 2. In this paper, we study the problem of constructing inﬁnite classes of APN-like but not APN power functions. For one thing, we ﬁnd two inﬁnite classes of locally-APN but not APN power functions over F 2 2 m with m even, i.e., F 1 ( x ) = x j (2 m − 1) with gcd( j, 2 m + 1) = 1 and F 2 ( x ) = x…

## 3 Citations

### New results of $0$-APN power functions over $\mathbb{F}_{2^n}$

- Mathematics, Computer Science
- 2022

Based on the multivariate method and resultant elimination, several new inﬁnite classes of 0-APN power functions over F 2 n are proposed and can explain some examples of exponents of Table 1 in [5].

### 2 7 O ct 2 02 2 Several classes of 0-APN power functions over F 2 n

- Mathematics, Computer Science
- 2022

Several new infinite classes of 0-APN power functions over F2n are proposed, CCZ-inequivalent to the known ones and can explain some exponents for 1 ≤ n ≤ 11 which are not yet “explained” in the tables of Budaghyan et al.

### Several new infinite classes of 0-APN power functions over $\mathbb{F}_{2^n}$

- Mathematics, Computer Science
- 2022

Several new inﬁnite classes of 0-APN power functions over F 2 n are presented by using the multivariate method and resultant elimination, and it is shown that these 0-APS power functions are CCZ-inequivalent to the known ones.

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