Cryptography and Communications
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Locally repairable codes with multiple repair sets based on packings of block size 4
Cryptography and Communications -
Cyclic codes over $$M_4 (\mathbb {F}_2+u\mathbb {F}_2)$$
Cryptography and Communications - Tập 14 - Trang 1021-1034 - 2022
Let p be a prime and
$$\mathbb {F}_q$$
be a finite field for
$$q=p^m$$
. In this paper, we consider the ring
$$R=M_4 (\mathbb {......
A construction of t-fold perfect splitting authentication codes with equal deception probabilities
Cryptography and Communications - Tập 7 - Trang 207-215 - 2014
Orthogonal multi-arrays were first formulated by Brickell in investigation of authentication codes. In this article, we will prove that t-fold perfect splitting authentication codes with equal deception probabilities can be characterized in terms of orthogonal multi-arrays. We will also investigate the existence of orthogonal multi-arrays, and show that the existence of orthogonal multi-arrays OMA......
Representing the inverse map as a composition of quadratics in a finite field of characteristic 2
Cryptography and Communications - - 2024
In 1953, Carlitz showed that all permutation polynomials over
$${\mathbb F}_q$$
, where
$$q>2$$
is a power of a prime, are generated by the special permutation polynomials
......
Welch bound equality sets with few distinct inner products from Delsarte-Goethals sets
Cryptography and Communications - Tập 15 - Trang 719-729 - 2023
Sets of signals that meet Welch bounds with equality or near equality are of value in communications and sensing applications, and the construction of such signal sets has been an active research area. Although Welch derived a family of bounds indexed by positive integers k, only the first Welch bound (i.e., for k = 1) has been considered in these constructions. Earlier, a frame-theoretic perspect......
On the higher-order nonlinearity of a Boolean bent function class (Constructed via Niho power functions)
Cryptography and Communications - Tập 14 - Trang 1055-1066 - 2022
The r th-order nonlinearity of a Boolean function plays a vital role in analyzing the security of stream and block ciphers. In this paper, we present a lower bound on the
$$\left (\frac{m}{2}\right )$$
th-order nonlinearity of a bent Boolean function class of the form
......
G-codes, self-dual G-codes and reversible G-codes over the ring ${\mathscr{B}}_{j,k}$
Cryptography and Communications - Tập 13 - Trang 601-616 - 2021
In this work, we study a new family of rings,
${\mathscr{B}}_{j,k}$
, whose base field is the finite field
${\mathbb {F}}_{p^{r}}$
. We study the structure of this family of rings and show that each......
Shifted plateaued functions and their differential properties
Cryptography and Communications - Tập 12 - Trang 1091-1105 - 2020
A bent4 function is a Boolean function with a flat spectrum with respect to a certain unitary transform
$\mathcal {T}$
. It was shown previously that a Boolean function f in an even number of variables is bent4 if and only if f + σ is bent, where σ is a certain quadratic function depending on
$\mathcal {T}$
. Hence bent4 functions are also called shifted bent functions. Similarly, a Boolean fu......
Affine linear cryptanalysis
Cryptography and Communications - Tập 11 - Trang 367-377 - 2018
In this paper a new variant of the linear cryptanalysis method for block ciphers is proposed. It is based on the existing method of multidimensional linear cryptanalysis, but offers the option of discarding a whole half-space of linear approximations that do not contribute to statistical nonrandomness of the multidimensional linear cryptanalysis, and keep only the information extracted from an aff......
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