Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Differential Linear Connectivity Table of Vectorial Boolean
  Functions   Vectorial Boolean functions are crucial building blocks in symmetric ciphers.
Different known attacks on block ciphers have resulted in diverse cryptographic
criteria of vectorial Boolean functions,such as differential distribution table
and nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new
tool, called the Differential-Linear Connectivity Table (DLCT).This paper is a
follow-up work, which presents further theoretical characterization of the DLCT
of vectorial Boolean functions and also investigates this new criterion of
functions with certain forms. In this paper we introduce a generalized concept
of the additive autocorrelation, which is extended from Boolean functions to
the vectorial Boolean functions, and use it as a main tool to investigate the
DLCT property of vectorial Boolean functions. Firstly, by establishing a
connection between the DLCT and the additive autocorrelation, we characterize
properties of DLCT by means of the Walsh transform and the differential
distribution table, and present generic lower bounds on the differential-linear
uniformity (DLU) of vectorial Boolean functions. Furthermore, we investigate
the DLCT property of monomials, APN, plateaued and AB functions. Our study
reveals that the DLCT of these special functions are closely related to other
cryptographic criteria. Next, we prove that the DLU of vectorial Boolean
functions is invariant underthe EA equivalence but not invariant under the CCZ
equivalence, and that the DLCT spectrum is only invariant under affine
equivalence. In addition, under affine equivalence, we exhaust the DLCT spectra
and DLU of optimal S-boxes with $4$ bit by Magma. Finally, we investigate the
DLCT spectra and DLU of some polynomials over $F_{2^n}$, including the inverse,
Gold, Bracken-Leander power functions and all quadratic polynomials.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys