New Instances of Quadratic APN Functions

被引：21
|
作者：
Beierle, Christof [1 ]
Leander, Gregor [1 ]
机构：
[1] Ruhr Univ Bochum, Fac Comp Sci, D-44801 Bochum, Germany
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2022年 / 68卷 / 01期
关键词：
Linearity; Boolean functions; Table lookup; Switches; Resistance; Ciphers; Writing; Almost perfect nonlinear; Walsh spectrum; linearity; self-equivalence; EA-equivalence; EQUIVALENCES; POWER;
D O I：
10.1109/TIT.2021.3120698
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In a recent work, Beierle, Brinkmann and Leander presented a recursive tree search for finding APN permutations with linear self-equivalences in small dimensions. In this paper, we describe how this search can be adapted to find many new instances of quadratic APN functions. In particular, we found 12,921 new quadratic APN functions in dimension eight, 35 new quadratic APN functions in dimension nine and five new quadratic APN functions in dimension ten up to CCZ-equivalence. Remarkably, two of the 35 new APN functions in dimension nine are APN permutations. Among the 8-bit APN functions, there are three extended Walsh spectra that do not correspond to any of the previously-known quadratic 8-bit APN functions and, surprisingly, there exist at least four CCZ-inequivalent 8-bit APN functions with linearity 2(7), i.e., the highest possible non-trivial linearity for quadratic functions in dimension eight.
引用
收藏
页码：670 / 678
页数：9
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