Name
Abstract | ||
|---|---|---|
In this work, we study functions that can be obtained by restricting a vectorial Boolean function
$$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$
to an affine hyperplane of dimension
$$n-1$$
and then projecting the output to an
$$n-1$$
-dimensional space. We show that a multiset of
$$2 \cdot (2^n-1)^2$$
EA-equivalence classes of such restrictions defines an EA-invariant for vectorial Boolean functions on
$$\mathbb {F}_{2}^n$$
. Further, for all of the known quadratic APN functions in dimension
$$n < 10$$
, we determine the restrictions that are also APN. Moreover, we construct 6368 new quadratic APN functions in dimension eight up to EA-equivalence by extending a quadratic APN function in dimension seven. A special focus of this work is on quadratic APN functions with maximum linearity. In particular, we characterize a quadratic APN function
$$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$
with linearity of
$$2^{n-1}$$
by a property of the ortho-derivative of its restriction to a linear hyperplane. Using the fact that all quadratic APN functions in dimension seven are classified, we are able to obtain a classification of all quadratic 8-bit APN functions with linearity
$$2^7$$
up to EA-equivalence. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s10623-022-01024-4 | Designs, Codes and Cryptography |
Keywords | DocType | Volume |
Almost perfect nonlinear, EA-equivalence, EA-invariant, Linearity, Restriction, Extension, 06E30, 94A60 | Journal | 90 |
Issue | ISSN | Citations |
4 | 0925-1022 | 0 |
PageRank | References | Authors |
0.34 | 13 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christof Beierle | 1 | 0 | 0.34 |
| Gregor Leander | 2 | 1287 | 77.03 |
| Léo Perrin | 3 | 0 | 0.34 |