Bent functions have maximal minimum distance to the set of affine functions. In other words, they achieve the maximal minimum distance to all the coordinate functions of affine monomials. In this paper we introduce a new class of bent functions which we call hyper-bent functions. Functions within this class achieve the maximal minimum distance to all the coordinate functions of all bijective mo...

In order to design bent functions, evolutionary algorithm based on truth table, algebraic normal form or Walsh spectra are already known. Evolutionary algorithm based on trace function form is not known to authors’ knowledge. In this paper, we give an evolutionary algorithm based on the trace representation of boolean function. With the algorithm, we constructed many bent functions and made som...

UNLABELLED To find the faster and easier way than the existing intubating technique for double-lumen tube, we modified the angle of double-lumen tube according to an individual's upper airway anatomy and compared the time needed and the number of attempts for successful intubation between individually angle-modified and non-modified double-lumen tubes. Adult patients undergoing elective thoraci...

Treponema phagedenis Kazan 5 is a spirochete with multiple periplasmic flagella attached near each end of the cell cylinder. Dark-field microscopy revealed that most of the cell is right-handed (helix diameter, 0.23 micron; helix pitch, 1.74 microns), and the ends appear bent. These ends could move and gyrate while the central part of the cell remained stationary. The present study examines the...

Bent functions have connections into various areas of mathematics and computer science which makes them an interesting object to study. This thesis is meant as a comprehensive study summarizing many of the results published in the last 40 years. In the first chapter we will motivate the definition of bent functions before we discuss some basic properties in chapter 2. This is done with a specia...

Systematic authentication codes without secrecy were defined in [1]. In [2] two new systematic authentication codes based on the Gray map on a Galois ring are introduced with the purpose of optimally reducing the impersonation and substitution probabilities. The first code is another example of a previously constructed code using the Gray map on Galois rings and modules over these rings [3,4]. ...

The class of rotation symmetric functions is extremely rich in terms cryptographical significance. However, few constructions bent functions, which can correspond to idempotent have been presented the literature. In this paper, for any even integer $ n\geq{4} $, we first construct an n $-variable function by modifying truth table Rothaus's on vector space \mathbb{F}_2^n and then obtain a corres...