Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2404

Search results for: prime field

2404 A Study of General Attacks on Elliptic Curve Discrete Logarithm Problem over Prime Field and Binary Field

Authors: Tun Myat Aung, Ni Ni Hla

Abstract:

This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: Discrete logarithm problem, general attacks, elliptic curves, strong curves, prime field, binary field, attack experiments.

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2403 (R, S)-Modules and (1, k)-Jointly Prime (R, S)-Submodules

Authors: Thawatchai Khumprapussorn

Abstract:

We introduced the notions of (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule as a generalization of prime ideal and jointly prime (R, S)-submodule, respectively. We provide a relationship between (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule. Characterizations of (1, k)-jointly prime (R, S)- submodules are also given.

Keywords: R, S)-module, (1, k)-prime ideal, (1, k)-jointly prime (R, S)-submodule.

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2402 Pythagorean-Platonic Lattice Method for Finding all Co-Prime Right Angle Triangles

Authors: Anthony Overmars, Sitalakshmi Venkatraman

Abstract:

This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography.

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2401 The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-ideals

Authors: Rattiya Boonruang, Aiyared Iampan

Abstract:

Using the idea of prime and semiprime bi-ideals of rings, the concept of prime and semiprime generalized bi-ideals of rings is introduced, which is an extension of the concept of prime and semiprime bi-ideals of rings and some interesting characterizations of prime and semiprime generalized bi-ideals are obtained. Also, we give the relationship between the Baer radical and prime and semiprime generalized bi-ideals of rings in the same way as of biideals of rings which was studied by Roux.

Keywords: ring, prime and semiprime (generalized) bi-ideal, Baer radical.

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2400 On Weakly Prime and Weakly Quasi-Prime Fuzzy Left Ideals in Ordered Semigroups

Authors: Jian Tang

Abstract:

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.

Keywords: Ordered semigroup, ordered fuzzy point, weakly prime fuzzy left ideal, weakly quasi-prime fuzzy left ideal.

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2399 Prime(Semiprime) Fuzzy h-ideal in Γ-hemiring

Authors: Sujit Kumar Sardar, Debabrata Mandal

Abstract:

The notions of prime(semiprime) fuzzy h-ideal(h-biideal, h-quasi-ideal) in Γ-hemiring are introduced and some of their characterizations are obtained by using "belongingness(∈)" and "quasi - coincidence(q)". Cartesian product of prime(semiprime) fuzzy h-ideals of Γ-hemirings are also investigated.

Keywords: Γ-hemiring, Fuzzy h-ideals, Prime fuzzy left h-ideal, Prime(semiprime) (∈, ∈ ∨q)-fuzzy left h-bi-ideal(h-ideal, h-quasiideal), Cartesian product

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2398 Prime Cordial Labeling on Graphs

Authors: S. Babitha, J. Baskar Babujee

Abstract:

A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and 0 if gcd(f(u), f(v)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper we exhibit some characterization results and new constructions on prime cordial graphs.

Keywords: Prime cordial, tree, Euler, bijective, function.

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2397 Preliminary Geophysical Assessment of Soil Contaminants around Wacot Rice Factory Argungu, North-Western Nigeria

Authors: A. I. Augie, Y. Alhassan, U. Z. Magawata

Abstract:

Geophysical investigation was carried out at wacot rice factory Argungu north-western Nigeria, using the 2D electrical resistivity method. The area falls between latitude 12˚44′23ʺN to 12˚44′50ʺN and longitude 4032′18′′E to 4032′39′′E covering a total area of about 1.85 km. Two profiles were carried out with Wenner configuration using resistivity meter (Ohmega). The data obtained from the study area were modeled using RES2DIVN software which gave an automatic interpretation of the apparent resistivity data. The inverse resistivity models of the profiles show the high resistivity values ranging from 208 Ωm to 651 Ωm. These high resistivity values in the overburden were due to dryness and compactness of the strata that lead to consolidation, which is an indication that the area is free from leachate contaminations. However, from the inverse model, there are regions of low resistivity values (1 Ωm to 18 Ωm), these zones were observed and identified as clayey and the most contaminated zones. The regions of low resistivity thereby indicated the leachate plume or the highly leachate concentrated zones due to similar resistivity values in both clayey and leachate. The regions of leachate are mainly from the factory into the surrounding area and its groundwater. The maximum leachate infiltration was found at depths 1 m to 15.9 m (P1) and 6 m to 15.9 m (P2) vertically, as well as distance along the profiles from 67 m to 75 m (P1), 155 m to 180 m (P1), and 115 m to 192 m (P2) laterally.

Keywords: Contaminant, leachate, soil, groundwater, 2D, electrical, resistivity, Argungu.

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2396 A Post Processing Method for Quantum Prime Factorization Algorithm based on Randomized Approach

Authors: Mir Shahriar Emami, Mohammad Reza Meybodi

Abstract:

Prime Factorization based on Quantum approach in two phases has been performed. The first phase has been achieved at Quantum computer and the second phase has been achieved at the classic computer (Post Processing). At the second phase the goal is to estimate the period r of equation xrN ≡ 1 and to find the prime factors of the composite integer N in classic computer. In this paper we present a method based on Randomized Approach for estimation the period r with a satisfactory probability and the composite integer N will be factorized therefore with the Randomized Approach even the gesture of the period is not exactly the real period at least we can find one of the prime factors of composite N. Finally we present some important points for designing an Emulator for Quantum Computer Simulation.

Keywords: Quantum Prime Factorization, RandomizedAlgorithms, Quantum Computer Simulation, Quantum Computation.

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2395 Estimation of Crustal Thickness within the Sokoto Basin North-Western Nigeria Using Bouguer Gravity Anomaly Data

Authors: T. T. Olugbenga, A. I. Augie

Abstract:

This research proposes an interpretation of the Bouguer’ gravity anomaly data of some parts of Sokoto basin for the estimation of crustal thickness. The study area is bounded between latitudes 1100′0″N and 1300′0″N, and longitudes 400′0″E and 600′0″E that covered Koko, Jega, B/Kebbi, Argungu, Lema, Bodinga, Tamgaza, Gunmi,Daki Takwas, Dange, Sokoto, Ilella, T/Mafara, Anka, Maru, Gusau, K/Namoda, and Sabon Birni within Sokoto, Kebbi and Zamfara state respectively. The established map of the study area was digitized in X, Y and Z format using excel software package and the digitized data were processed using Surfer version 13 software. The Moho and Conrad depths based on a relationship between Bouguer’ gravity anomaly determined crustal thickness were estimated as 35 to 37 km and 19 to 21 km, respectively. The crustal region has been categorized into: Crustal thinning zone that is the region with high gravity anomaly value due to its greater geothermal energy and also Crustal thickening zone which the region with low anomaly values due to its lower geothermal energy. Birnin kebbi, Jega, Sokoto were identified as the region of hydrocarbon potential with an estimate of 35 km thickness within the crustal region which is referred to as crustal thickening as a result of its low but sufficient geothermal energy to decompose organic matter within the region to form hydrocarbons.

Keywords: Bouguer gravity anomaly, crustal thickness, geothermal energy, hydrocarbons, Moho and Conrad Depths.

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2394 Occurrence of High Nocturnal Surface Ozone at a Tropical Urban Area

Authors: S. Dey, P. Sibanda, S. Gupta, A. Chakraborty

Abstract:

The occurrence of high nocturnal surface ozone over a tropical urban area (23̊ 32′16.99″ N and 87̊ 17′ 38.95″ E) is analyzed in this paper. Five incidences of nocturnal ozone maxima are recorded during the observational span of two years (June, 2013 to May, 2015). The maximum and minimum values of the surface ozone during these five occasions are 337.630 μg/m3 and 13.034 μg/m3 respectively. HYSPLIT backward trajectory analyses and wind rose diagrams support the horizontal transport of ozone from distant polluted places. Planetary boundary layer characteristics, concentration of precursor (NO2) and meteorology are found to play important role in the horizontal and vertical transport of surface ozone during nighttime.

Keywords: Nocturnal ozone, planetary boundary layer, horizontal transport, meteorology, urban area.

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2393 Analysis of Program PRIME at Brazil

Authors: Iracema Machado de Aragão Gomes, Íkaro Daniel Carvalho Barreto, Suzana Leitão Russo

Abstract:

Policies that support entrepreneurship are keys to the generation of new business. In Brazil, seed capital, installation of technology parks, programs and zero interest financing, economic subsidy as Program First Innovative Company (PRIME) are examples of incentive policies. For the implementation of PRIME, in particular the Brazilian Innovation Agency (FINEP) decentralized operationalization so that business incubators could select innovative projects. This paper analyzes the program PRIME Business Incubator Center of the State of Sergipe (CISE) after calculating the mean and standard deviation of the grades obtained by companies in the factors of innovation, market potential, financial return economic, market strategy and staff and application of the Mann-Whitney test.

Keywords: Entrepreneurship, innovation, technology parks, business incubators.

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2392 On Completely Semiprime, Semiprime and Prime Fuzzy Ideals in Ordered Semigroups

Authors: Jian Tang

Abstract:

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semigroups. Furthermore, we introduce the notion of semiprime fuzzy ideals of ordered semigroup S and establish the relations between completely semiprime fuzzy ideals and semiprime fuzzy ideals of S. Finally, we give a characterization of prime fuzzy ideals of an ordered semigroup S and show that a nonconstant fuzzy ideal f of an ordered semigroup S is prime if and only if f is twovalued, and max{f(a), f(b)} = inf f((aSb]), ∀a, b ∈ S.

Keywords: Ordered fuzzy point, fuzzy left (right) ideal of anordered semigroup, completely semiprime fuzzy ideal, semiprimefuzzy ideal, prime fuzzy ideal.

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2391 Performance Evaluation of One and Two Dimensional Prime Codes for Optical Code Division Multiple Access Systems

Authors: Gurjit Kaur, Neena Gupta

Abstract:

In this paper, we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension, i.e. time slots, whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research, we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for Optical Code Division Multiple Access (OCDMA) system on a single platform. Analysis shows that 2D prime code supports lesser number of active users than 1D codes, but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa.

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2390 Gender and Advertisements: A Content Analysis of Pakistani Prime Time Advertisements

Authors: Aaminah Hassan

Abstract:

Advertisements carry a great potential to influence our lives because they are crafted to meet particular ends. Stereotypical representation in advertisements is capable of forming unconscious attitudes among people towards any gender and their abilities. This study focuses on gender representation in Pakistani prime time advertisements. For this purpose, 13 advertisements were selected from three different categories of foods and beverages, cosmetics, cell phones and cellular networks from the prime time slots of one of the leading Pakistani entertainment channel, ‘Urdu 1’. Both quantitative and qualitative analyses are carried out for range of variables like gender, age, roles, activities, setting, appearance and voice overs. The results revealed that gender representation in advertisements is stereotypical. Moreover, in few instances, the portrayal of women is not only culturally inappropriate but is demeaning to the image of women as well. Their bodily charm is used to promote products. Comparing different entertainment channels for their prime time advertisements and broadening the scope of this research will yield greater implications for the researchers who want to carry out the similar research. It is hoped that the current study would help in the promotion of media literacy among the viewers and media authorities in Pakistan.

Keywords: Advertisements, content analysis, gender, prime time.

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2389 The Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields

Authors: Betül Gezer, Hacer Özden, Ahmet Tekcan, Osman Bizim

Abstract:

Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves.

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2388 Elliptic Divisibility Sequences over Finite Fields

Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.

Keywords: Elliptic divisibility sequences, singular elliptic divisibilitysequences, elliptic curves, singular curves.

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2387 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

Authors: Ahmet Tekcan

Abstract:

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

Keywords: Singular curve, elliptic curve, rational points.

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2386 Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime

Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul

Abstract:

In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.

Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.

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2385 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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2384 Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime

Authors: Gokhan Soydan, Musa Demirci, Nazli Yildiz Ikikardes, Ismail Naci Cangul

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.

Keywords: Elliptic curves over finite fields, rational points.

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2383 Zero Divisor Graph of a Poset with Respect to Primal Ideals

Authors: Hossein Pourali

Abstract:

In this paper, we extend the concepts of primal and weakly primal ideals for posets. Further, the diameter of the zero divisor graph of a poset with respect to a non-primal ideal is determined. The relation between primary and primal ideals in posets is also studied.

Keywords: Zero divisors graph, ideal, prime ideal, semiprime ideal, primal ideal, weakly primal ideal, associated prime ideal, primary ideal.

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2382 Water Depth and Optical Attenuation Characteristics of Natural Water Reservoirs nearby Kolkata City Assessed from Hyperion Hyperspectral and LISS-3 Multispectral Images

Authors: Barun Raychaudhuri

Abstract:

A methodology is proposed for estimating the optical attenuation and proportional depth variation of shallow inland water. The process is demonstrated with EO-1 Hyperion hyperspectral and IRS-P6 LISS-3 multispectral images of Kolkata city nearby area centered around 22º33′ N 88º26′ E. The attenuation coefficient of water was found to change with fine resolution of wavebands and in presence of suspended organic matter in water.

Keywords: Hyperion, hyperspectral, Kolkata, water depth.

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2381 The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields

Authors: Musa Demirci, Nazlı Yıldız İkikardeş, Gökhan Soydan, İsmail Naci Cangül

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.

Keywords: Elliptic curves over finite fields, rational points, quadratic residue.

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2380 The High Temperature Damage of DV – 2 Turbine Blade Made from Ni – Base Superalloy

Authors: Juraj Belan, Lenka Hurtalová, Eva Tillová, Alan Vaško, Milan Uhríčik

Abstract:

High pressure turbine (HPT) blades of DV – 2 jet engines are made from Ni – based superalloy. This alloy was originally manufactured in the Soviet Union and referred as ŽS6K. For improving alloy’s high temperature resistance are blades coated with Al – Si diffusion layer. A regular operation temperature of HPT blades vary from 705°C to 750°C depending on jet engine regime. An overcrossing working temperature range causes degradation of the protective coating as well as base material which microstructure is formed by the gamma matrix and strengthening phase gamma prime (forming small particles in the microstructure). Diffusion processes inside the material during exposition of the material to high temperatures causes mainly coarsening of the gamma prime particles, thus decreasing its strengthening effect. Degradation of the Al – Si coating caused its thickness growth. All the microstructure changes and coating layer thickness growth results in decreasing of the turbine blade operation lifetime.

Keywords: Alitize coating layer, gamma prime phase, high temperature degradation, Ni – base superalloy ŽS6K, turbine blade.

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2379 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

Authors: Ahmet Tekcan

Abstract:

Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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2378 Analysis of Electromagnetic Field Effects Using FEM for Transmission Lines Transposition

Authors: S. Tupsie, A. Isaramongkolrak, P. Pao-la-or

Abstract:

This paper presents the mathematical model of electric field and magnetic field in transmission system, which performs in second-order partial differential equation. This research has conducted analyzing the electromagnetic field radiating to atmosphere around the transmission line, when there is the transmission line transposition in case of long distance distribution. The six types of 500 kV transposed HV transmission line with double circuit will be considered. The computer simulation is applied finite element method that is developed by MATLAB program. The problem is considered to two dimensions, which is time harmonic system with the graphical performance of electric field and magnetic field. The impact from simulation of six types long distance distributing transposition will not effect changing of electric field and magnetic field which surround the transmission line.

Keywords: Transposition, Electromagnetic Field, Finite Element Method (FEM), Transmission Line, Computer Simulation

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2377 Electrical Field Around the Overhead Transmission Lines

Authors: S.S. Razavipour, M. Jahangiri, H. Sadeghipoor

Abstract:

In this paper, the computation of the electrical field distribution around AC high-voltage lines is demonstrated. The advantages and disadvantages of two different methods are described to evaluate the electrical field quantity. The first method is a seminumerical method using the laws of electrostatic techniques to simulate the two-dimensional electric field under the high-voltage overhead line. The second method which will be discussed is the finite element method (FEM) using specific boundary conditions to compute the two- dimensional electric field distributions in an efficient way.

Keywords: Electrical field, unloaded transmission lines, finite element method, electrostatic images technique.

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2376 The Relationship between the Energy of Gravitational Field and the Representative Pseudotensor

Authors: R. I. Khrapko

Abstract:

As is known, the role of the energy-momentum pseudotensors of the gravitational field is to extend the conservation law to the gravitational interaction by taking into account the energy and momentum of the gravitational field. We calculated the contribution of the Einstein pseudotensor to the total mass of a stationary material body and its gravitational field. It turned out that this contribution is positive, despite the fact that the mass-energy of a stationary gravitational field is negative. We concluded that the pseudotensor incorrectly describes the energy of the gravitational field. Nevertheless, this pseudotensor has been used in a large number of scientific works for 100 years. We explain this by the fact that the covariant component of the pseudotensor was regarded as the mass-energy. Besides, we prove the advantage of the covariant energy-momentum conservation law for matter in the Minkowski space-time.

Keywords: Conservation law, covariant integration, gravitation field, isolated system.

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2375 Software to Encrypt Messages Using Public-Key Cryptography

Authors: E. Inzunza-González, C. Cruz-Hernández, R. M. López-Gutiérrez, E. E. García-Guerrero, L. Cardoza- Avendaño, H. Serrano-Guerrero

Abstract:

In this paper the development of a software to encrypt messages with asymmetric cryptography is presented. In particular, is used the RSA (Rivest, Shamir and Adleman) algorithm to encrypt alphanumeric information. The software allows to generate different public keys from two prime numbers provided by the user, the user must then select a public-key to generate the corresponding private-key. To encrypt the information, the user must provide the public-key of the recipient as well as the message to be encrypted. The generated ciphertext can be sent through an insecure channel, so that would be very difficult to be interpreted by an intruder or attacker. At the end of the communication, the recipient can decrypt the original message if provide his/her public-key and his/her corresponding private-key.

Keywords: Asymmetric cryptography, Prime number, Publickey, Private-key, Software.

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