New results of 0-APN power functions over \mathbbF_2ⁿ

2022/10/05 by Wang Yan-ping, Wang, Yan-Ping, Zhengbang Zha +1
Computer Science · Medicine · #Coding theory and cryptography #Cryptographic Implementations and Security #Peptidase Inhibition and Analysis

paper · pdf · doi:10.48550/arxiv.2210.02207

Abstract

Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite classes of 0-APN power functions over \mathbbF_2ⁿ. Furthermore, two infinite classes of 0-APN power functions x^d over \mathbbF_2ⁿ are characterized completely where (2^k-1)d≡ 2^m-1~(\rm mod 2ⁿ-1) or (2^k+1)d≡ 2^m+1~(\rm mod 2ⁿ-1) for some positive integers n, m, k. These infinite classes of 0-APN power functions can explain some examples of exponents of Table 1 in \citeBKRS2020.

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