scholarly journals Elliptic Curve over a Local Finite Ring Rn

2020 ◽  
Author(s):  
Abdelhakim Chillali ◽  
Lhoussain El Fadil
Keyword(s):  
Elliptic Curve ◽  
Local Ring ◽  
Finite Ring ◽  
Local Rings ◽  
Fourth Section ◽  
The Third ◽  
Research Perspectives ◽  
Weierstrass Equation

The goal of this chapter is to study some arithmetic proprieties of an elliptic curve defined by a Weierstrass equation on the local ring Rn=FqX/Xn, where n≥1 is an integer. It consists of, an introduction, four sections, and a conclusion. In the first section, we review some fundamental arithmetic proprieties of finite local rings Rn, which will be used in the remainder of the chapter. The second section is devoted to a study the above mentioned elliptic curve on these finite local rings for arbitrary characteristics. A restriction to some specific characteristic cases will then be considered in the third section. Using these studies, we give in the fourth section some cryptography applications, and we give in the conclusion some current research perspectives concerning the use of this kind of curves in cryptography. We can see in the conclusion of research in perspectives on these types of curves.

scholarly journals The n-insertive subgroups of units

2007 ◽  
Vol 75 (1) ◽  
pp. 23-26
Author(s):  
David Dolžn
Keyword(s):  
Local Ring ◽  
Jacobson Radical ◽  
Finite Ring ◽  
Local Rings ◽  
Arbitrary Integer ◽  
Group Of Units ◽  
Direct Sum ◽  
Group 1

Let R be a finite ring. Let us denote its group of units by G = G(R) and its Jacobson radical by J = J(R). Let n be an arbitrary integer. We prove that R is an n-insertive ring if and only if G is an n-insertive group and show that every n-insertive finite ring is a direct sum of local rings. We prove that if n is a unit, then the local ring R is n-insertive if and only if its Jacobson group 1 + J is n-insertive and find an example to show that this is not true if n is a non-unit.

scholarly journals Elliptic curve over a finite ring generated by 1 and an idempotent element $e$ with coefficients in the finite field $\mathbb{F}_{3^d}$

2021 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
A. Boulbot ◽  
Abdelhakim Chillali ◽  
A Mouhib
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Elliptic Curve ◽  
Polynomial Ring ◽  
Quotient Ring ◽  
Finite Ring ◽  
Idempotent Element ◽  
Characteristic 3 ◽  
Specific Equation ◽  
Weierstrass Equation

An elliptic curve over a ring $\mathcal{R}$ is a curve in the projective plane $\mathbb{P}^{2}(\mathcal{R})$ given by a specific equation of the form $f(X, Y, Z)=0$ named the Weierstrass equation, where $f(X, Y, Z)=Y^2Z+a_1XYZ+a_3YZ^2-X^3-a_2X^2Z-a_4XZ^2-a_6Z^3$ with coefficients $a_1, a_2, a_3, a_4, a_6$ in $\mathcal{R}$ and with an invertible discriminant in the ring $\mathcal{R}.$ %(see \cite[Chapter III, Section 1]{sil1}).  In this paper, we consider an elliptic curve over a finite ring of characteristic 3 given by the Weierstrass equation: $Y^2Z=X^3+aX^2Z+bZ^3$ where $a$ and $b$ are in the quotient ring $\mathcal{R}:=\mathbb{F}_{3^d}[X]/(X^2-X),$ where $d$ is a positive integer and $\mathbb{F}_{3^d}[X]$ is the polynomial ring with coefficients in the finite field $\mathbb{F}_{3^d}$ and such that $-a^3b$ is invertible in $\mathcal{R}$.

IMPLEMENTATION OF ELECTRONIC MONITORING OF SENTENCED PERSONS IN THE SLOVAK REPUBLIC

2020 ◽  
Vol 10 (5) ◽  
pp. 59-75
Author(s):  
JAROSLAV KLÁTIK ◽  
◽  
LIBOR KLIMEK
Keyword(s):  
Restorative Justice ◽  
Electronic Monitoring ◽  
Slovak Republic ◽  
Pilot Project ◽  
Legal Regulation ◽  
European Level ◽  
Criminal Proceedings ◽  
Council Of Europe ◽  
Fourth Section ◽  
The Third

The work deals with implementation of electronic monitoring of sentenced persons in the Slovak Republic. It is divided into eight sections. The first section introduces restorative justice as a prerequisite of electronic monitoring in criminal proceedings. While the second section points out at the absence of legal regulation of electronic monitoring of sentenced persons at European level, the third section points out at recommendations of the Council of Europe addressed to European States. The fourth section analyses relevant alternative punishments in Slovak criminal justice. The fifth section introduces early beginnings of implementation of concerned system - the pilot project “Electronic Personnel Monitoring System” of the Ministry of Justice of the Slovak Republic. While the sixth section is focused on Slovak national law regulating electronic monitoring of sentenced persons - the Act No. 78/2015 Coll. on Control of the Enforcement of Certain Decisions by Technical Instruments, the seventh section is focused on further amendments of Slovak national law - namely the Act No. 321/2018 Coll. and the Act No. 214/2019 Coll. The last eight section introduces costs of system implementation and its operation.

Logicism Reconsidered

2009 ◽  
Author(s):  
Agustín Rayo
Keyword(s):  
Fourth Section ◽  
Truth Values ◽  
The Third

This article is divided into four sections. The first two identify different logicist theses, and show that their truth-values can be established given minimal assumptions. The third section sets forth a notion of “content-recarving” as a possible constraint on logicist theses. The fourth section—which is largely independent from the rest of the article—is a discussion of “neologicism.”

Epistemic self-esteem of philosophers in the face of philosophical disagreement

Human Affairs ◽  
2020 ◽  
Vol 30 (3) ◽  
pp. 328-342
Author(s):  
László Bernáth ◽  
János Tőzsér
Keyword(s):  
Self Esteem ◽  
Moderate Level ◽  
Significant Extent ◽  
Fourth Section ◽  
Philosophical Beliefs ◽  
Low Level ◽  
The Third ◽  
Epistemic Peers ◽  
The Face ◽  
And Performance

AbstractOur paper consists of four parts. In the first part, we describe the challenge of the pervasive and permanent philosophical disagreement over philosophers’ epistemic self-esteem. In the second part, we investigate the attitude of philosophers who have high epistemic self-esteem even in the face of philosophical disagreement and who believe they have well-grounded philosophical knowledge. In the third section, we focus on the attitude of philosophers who maintain a moderate level of epistemic self-esteem because they do not attribute substantive philosophical knowledge to themselves but still believe that they have epistemic right to defend substantive philosophical beliefs. In the fourth section, we analyse the attitude of philosophers who have a low level of epistemic self-esteem in relation to substantive philosophical beliefs and make no attempt to defend those beliefs. We argue that when faced with philosophical disagreement philosophers either have to deny that the dissenting philosophers are their epistemic peers or have to admit that doing philosophy is less meaningful than it seemed before. In this second case, philosophical activity and performance should not contribute to the philosophers’ overall epistemic self-esteem to any significant extent.

The Concept of Political Equality: A Post-Dahl Analysis

1981 ◽  
Vol 29 (3) ◽  
pp. 392-406 ◽  
Author(s):  
Alan Ware
Keyword(s):  
Liberal Theory ◽  
Political Equality ◽  
Fourth Section ◽  
The Third ◽  
Introductory Section ◽  
Conservative Nature ◽  
Three Components

This article presents an analysis of the concept of political equality that is derived partly from the analysis of Robert Dahl. Following an introductory section, the conservative nature of Dahl's idea of political equality is outlined from four perspectives. With the last of these perspectives, a distinction between ‘populist’ and ‘liberal’ theories of democracy is introduced. In the third section it is argued that there are three components of political equality within a liberal theory, and the fourth section is devoted to an analysis of one of these—equality of treatment in the promotion of interests.

Journalistic objectivity and The Daily Show with Jon Stewart

2021 ◽  
Author(s):  
Ryan Harris Parker
Keyword(s):  
National Identities ◽  
Close Inspection ◽  
Fourth Section ◽  
The Daily Show ◽  
Daily Show ◽  
The Third ◽  
Holistic Understanding ◽  
The Press ◽  
The World ◽  
Definition Of

The press is a constitutive part of our society. It helps create national identities and formulates society's understanding of itself and its place in the world. Moreover, a free press is indispensable for ensuring the vibrancy of a democracy. For these reasons, a close inspection of news, and an evaluation of its performance, is crucial. We must look to the development of the mass press at the turn of the twentieth century to locate the beginnings of journalistic objectivity and the type of news we are familiar with today. The first section of this paper offers a review of accounts of this transformational period, placing opposing theories within the larger framework of the frictions between cultural studies and political economy, and underscores the need for a holistic understanding of the period. The second section chronicles the press's articulation of its new professional tenets, offers a definition of journalistic objectivity, and reveals its intrinsic limitations. The third section details how the modern press's ideal democratic mandate has been compromised, with the influence of the press being used instead to ensconce powerful interests. And the fourth section outlines the calls for a redefinition of journalism in light of the failures covered in the preceding section. Finally, The Daily Show with Jon Stewart is offered as an alternative journalistic form that transcends the dangerous dogma of traditional news outlets, allowing it to fulfill the democratic responsibility of the press by encouraging a critical and astute citizenry.

The Turkish Diaspora in Germany

1996 ◽  
Vol 5 (2) ◽  
pp. 275-301
Author(s):  
Wesley D. Chapin
Keyword(s):  
International Relations ◽  
Total Population ◽  
Turkish Population ◽  
Economic Effects ◽  
Political Issues ◽  
Fourth Section ◽  
German Politics ◽  
The Third ◽  
The Status ◽  
Prime Target

At the beginning of 1995, nearly two million Turkish nationals were living in Germany. While this represents only about 2.5% of the total population, the Turkish minority significantly influences German politics. As the single largest group of “foreigners” living in Germany, the Turkish population is a prime target of rightwing violence. Questions regarding Turkish rights to residency, work permits, and citizenship are controversial domestic political issues and their presence affects international relations between Germany and Turkey. This article examines the Turkish diaspora in Germany and its implications for Germany’s domestic and international politics. The first section identifies the status of the Turks living in Germany. The second traces the growth of the Turkish population in Germany. The third evaluates the domestic political and economic effects that the Turkish presence engenders, as well as prospects for assimilation. The fourth section identifies ways that international relations are influenced by the Turkish minority in Germany.

ELECTRONIC MONITORING OF SENTENCED PERSONS IN SLOVAK LEGAL PRACTICE

2020 ◽  
Vol 10 (6) ◽  
pp. 13-30
Author(s):  
JAROSLAV KLÁTIK ◽  
◽  
LIBOR KLIMEK
Keyword(s):  
Electronic Monitoring ◽  
Slovak Republic ◽  
Legal Practice ◽  
Fourth Section ◽  
Applicable Law ◽  
The Third ◽  
The Right To Privacy ◽  
Good Investment ◽  
Civil Proceedings ◽  
The Right

The work deals with practical issues of electronic monitoring of sentenced persons in the Slovak Republic. It is divided into seven sections. The first section deals with applicable law - the Act No. 78/2015 Coll. on Control of the Enforcement of Certain Decisions by Technical Instruments. The second section analyses types of the control of the enforcement of decisions and their use. The third section introduces the requirements for the control. The fourth section briefly introduces the application of the system in civil proceedings. The fifth section points out at the interference of the control with the right to privacy. The sixth section answers the question if the system was a good investment or a wasting of money. The last seventh section introduces recommendations for policymakers and legal practitioners.

Two-Dimensional Linear Groups Over Local Rings

1969 ◽  
Vol 21 ◽  
pp. 106-135 ◽  
Author(s):  
Norbert H. J. Lacroix
Keyword(s):  
Local Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Linear Groups ◽  
Local Rings ◽  
Two Dimensional ◽  
Normal Subgroups ◽  
Field Case

The problem of classifying the normal subgroups of the general linear group over a field was solved in the general case by Dieudonné (see 2 and 3). If we consider the problem over a ring, it is trivial to see that there will be more normal subgroups than in the field case. Klingenberg (4) has investigated the situation over a local ring and has shown that they are classified by certain congruence groups which are determined by the ideals in the ring.Klingenberg's solution roughly goes as follows. To a given ideal , attach certain congruence groups and . Next, assign a certain ideal (called the order) to a given subgroup G. The main result states that if G is normal with order a, then ≧ G ≧ , that is, G satisfies the so-called ladder relation at ; conversely, if G satisfies the ladder relation at , then G is normal and has order .

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