Now showing items 1-12 of 12

• #### Binary Linear Codes With Few Weights From Two-to-One Functions ﻿

(Journal article; Peer reviewed, 2021)
In this paper, we apply two-to-one functions over b F 2n in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) (x 2t +x) e with ...
• #### Bounds on the nonlinearity of differentially uniform functions by means of their image set size, and on their distance to affine functions ﻿

(Journal article; Peer reviewed, 2021)
We revisit and take a closer look at a (not so well known) result of a 2017 paper, showing that the differential uniformity of any vectorial function is bounded from below by an expression depending on the size of its image ...
• #### The Connections Among Hamming Metric, b-Symbol Metric, and r-th Generalized Hamming Metric ﻿

(Journal article; Peer reviewed, 2023)
The r -th generalized Hamming metric and the b -symbol metric are two different generalizations of Hamming metric. The former is used on the wire-tap channel of Type II, and the latter is motivated by the limitations of ...
• #### Constructing APN functions through isotopic shifts ﻿

(Journal article; Peer reviewed, 2020)
Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method ...
• #### Covering Radius of Generalized Zetterberg Type Codes Over Finite Fields of Odd Characteristic ﻿

(Journal article; Peer reviewed, 2023)
Let Fq0 be a finite field of odd characteristic. For an integer s≥1 , let Cs(q0) be the generalized Zetterberg code of length qs0+1 over Fq0 . If s is even, then we prove that the covering radius of Cs(q0) is 3. Put q=qs0 ...
• #### The Differential Spectrum of the Power Mapping xpn−3 ﻿

(Journal article; Peer reviewed, 2022)
Let n be a positive integer and p a prime. The power mapping xpn−3 over Fpn has desirable differential properties, and its differential spectra for p=2,3 have been determined. In this paper, for any odd prime p , by ...
• #### A New Family of APN Quadrinomials ﻿

(Journal article; Peer reviewed, 2020)
The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified ...
• #### New Results on the -1 Conjecture on Cross-Correlation of m-Sequences Based on Complete Permutation Polynomials ﻿

(Journal article; Peer reviewed, 2023)
The cross-correlation between two maximum length sequences (m-sequences) of the same period has been studied since the end of 1960s. One open conjecture by Helleseth states that the cross- correlation between any two p-ary ...
• #### On the Distance Between APN Functions ﻿

(Journal article; Peer reviewed, 2020)
We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ...
• #### On Two Fundamental Problems on APN Power Functions ﻿

(Journal article; Peer reviewed, 2022)
The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open ...
• #### An Optimal Universal Construction for the Threshold Implementation of Bijective S-Boxes ﻿

(Journal article; Peer reviewed, 2023)
Threshold implementation is a method based on secret sharing to secure cryptographic ciphers (and in particular S-boxes) against differential power analysis side-channel attacks which was proposed by Nikova, Rechberger, ...
• #### Two New Families of Quadratic APN Functions ﻿

(Journal article; Peer reviewed, 2022)