Two Classes of Quadratic Crooked Functions

2014 ◽  
Vol 513-517 ◽  
pp. 2734-2738 ◽  
Author(s):  
Xue Ying Duan ◽  
Yu Long Deng
Keyword(s):  
Quadratic Function ◽  
Apn Functions ◽  
Power Functions ◽  
Almost Perfect Nonlinear ◽  
Crooked Functions ◽  
The One

It is known that almost perfect nonlinear (APN) functions have many applications in cryptography, and a quadratic function is crooked if and only if it is APN. In this paper, we introduce two infinite classes of quadratic crooked multinomials on fields of order 22m. One class of APN functions constructed in [8] is a particular case of the one we construct in Theorem 1. Moreover, we prove that the two classes of crooked functions constructed in this paper are EA inequivalent to power functions and conjecture that CCZ inequivalence between them also holds.

scholarly journals Revisiting some results on APN and algebraic immune functions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Claude Carlet
Keyword(s):  
Boolean Functions ◽  
The Other ◽  
Immune Functions ◽  
Apn Functions ◽  
Power Functions ◽  
Differential Uniformity ◽  
Open Problems ◽  
Apn Function ◽  
Almost Perfect Nonlinear

<p style='text-indent:20px;'>We push a little further the study of two recent characterizations of almost perfect nonlinear (APN) functions. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to a new result about APN power functions and more general APN polynomials with coefficients in a subfield <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{2^k} $\end{document}</tex-math></inline-formula>, which eases the research of such functions. It also allows to construct automatically many differentially uniform functions from them (this avoids calculations for proving their differential uniformity as done in a recent paper, which are tedious and specific to each APN function). In a second part, we give simple proofs of two important results on Boolean functions, one of which deserves to be better known but needed clarification, while the other needed correction.</p>

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

scholarly journals Monomial Generalized Almost Perfect Nonlinear Functions

2020 ◽  
Vol 31 (03) ◽  
pp. 411-419
Author(s):  
Masamichi Kuroda
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Algebraic Degree ◽  
Apn Functions ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Basic Properties ◽  
Almost Perfect Nonlinear Functions

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In particular, on finite fields of even characteristic, GAPN functions coincide with APN functions. In this paper, we study monomial GAPN functions for odd characteristic. We give monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic. Moreover, we define a generalization of exceptional APN functions and give typical examples.

scholarly journals The n-Pythagorean Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1772
Author(s):  
Anna Bryniarska
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quadratic Function ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Power Functions ◽  
Pythagorean Fuzzy Sets ◽  
Conceptual Apparatus ◽  
Intuitionistic Fuzzy ◽  
Classic Theory

The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended shallow water wave model in (2+1)-dimensions

2020 ◽  
pp. 2150138
Author(s):  
Hajar F. Ismael ◽  
Aly Seadawy ◽  
Hasan Bulut
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Wave Model ◽  
Simple Method ◽  
Shallow Water Wave ◽  
Hirota Bilinear Form ◽  
The One ◽  
Physical Phenomena

In this paper, we consider the shallow water wave model in the (2+1)-dimensions. The Hirota simple method is applied to construct the new dynamics one-, two-, three-, [Formula: see text]-soliton solutions, complex multi-soliton, fusion, and breather solutions. By using the quadratic function, the one-lump, mixed kink-lump and periodic lump solutions to the model are obtained. The Hirota bilinear form variable of this model is derived at first via logarithmic variable transform. The physical phenomena to this model are explored. The obtained results verify the proposed model.

Three new classes of generalized almost perfect nonlinear power functions

2018 ◽  
Vol 53 ◽  
pp. 254-266 ◽  
Author(s):  
Zhengbang Zha ◽  
Lei Hu ◽  
Zhizheng Zhang
Keyword(s):  
Power Functions ◽  
Almost Perfect Nonlinear

scholarly journals Research on Urban Public Green Space Planning Based on Taxi Data: A Case Study on Three Districts of Shenzhen, China

2019 ◽  
Vol 11 (4) ◽  
pp. 1132 ◽  
Author(s):  
Quanyi Zheng ◽  
Xiaolong Zhao ◽  
Mengxiao Jin
Keyword(s):  
Green Space ◽  
Spatial Interaction ◽  
Quadratic Function ◽  
Unsupervised Classification ◽  
Spatial Layout ◽  
Trajectory Data ◽  
Activity Intensity ◽  
Access Mode ◽  
The One ◽  
Public Green Space

Urban public green space (UPGS) plays an important role in sustainable development. In China, the planning, classification, and management of green spaces are based on the Standard for Classification of Urban Green Space (SCUGS). However, limitations to the UPGS exist due to the over-emphasis on quantitative standards and insufficient consideration of the actual access mode of residents. Though the taxi trajectory data are widely selected to study public service facilities, its adoption in UPGSs research remains limited. Based on the case of UPGSs in the three districts of Shenzhen, we used the taxi (including cruise taxis and Didi cars, which are like Uber) trajectory data to investigate the spatial layout and the allocation of management resource of the UPGSs from the spatial interaction perspective. By rasterizing and visualizing the percentage of pick-up and drop-off points in the UPGSs’ buffer, the service scope of UPGSs was defined, which reflected the spatial distribution and activity intensity of the visitors. Then, an unsupervised classification method was introduced to reclassify the twenty two municipal parks in the three districts. Compared to the traditional planning method, the results show that the service scope of the same type of UPGS in the traditional classification is not the same as the one obtained by the study. Visitors to all UPGSs are distributed as a quadratic function and decay as the distance increases. In addition, the attenuation rates of the same type of UPGSs are similar. The findings of this study are expected to assist planners in improving the spatial layout of UPGSs and optimizing the allocation of UPGS management resources based on new classifications.

CONSTRUCTING NEW APN FUNCTIONS FROM KNOWN PN FUNCTIONS

2013 ◽  
Vol 24 (08) ◽  
pp. 1209-1219 ◽  
Author(s):  
ZHENGBANG ZHA ◽  
LEI HU
Keyword(s):  
Polynomial Functions ◽  
Apn Functions ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear

We present a method for constructing almost perfect nonlinear (APN) functions in odd characteristic by modifying some values of known perfect nonlinear functions. As a consequence, new APN polynomial functions such as ones over 𝔽13 which are CCZ-inequivalent to known APN functions are obtained.

Sign in / Sign up

Export Citation Format

Share Document