• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Factoring Integers The problem of … resolving composite numbers
Factoring Integers The problem of … resolving composite numbers

... Factoring Integers The problem of … resolving composite numbers into their prime factors is one of the most important and useful in all arithmetic …the dignity of science seems to demand that every aid to the solution of such an elegant and celebrated problem be zealously cultivated K.F. Gauss, Disq ...
07-057-Ch02-Sec2.1 pp6.qxd
07-057-Ch02-Sec2.1 pp6.qxd

chapter:1 number system
chapter:1 number system

Routing
Routing

... • The Dijkstra’s algorithm is totally distributed ◦ It can also be implemented in parallel and ◦ Does not require synchronization • In the algorithm ◦ Dj can be thought of as estimate of shortest path length between 1 and j during the course of algorithm • The algorithm is one of the earliest exampl ...
NS 2.4 Prime Factorization Part 1 (PowerPoint)
NS 2.4 Prime Factorization Part 1 (PowerPoint)

EASY DECISION-DIFFIE-HELLMAN GROUPS 1. Introduction It is
EASY DECISION-DIFFIE-HELLMAN GROUPS 1. Introduction It is

A New Range-Reduction Algorithm
A New Range-Reduction Algorithm

GENERALIZED CAYLEY`S Ω-PROCESS 1. Introduction We assume
GENERALIZED CAYLEY`S Ω-PROCESS 1. Introduction We assume

x - ClassZone
x - ClassZone

Building Portfolios for the Protein Structure Prediction
Building Portfolios for the Protein Structure Prediction

Factors and Prime Factorization
Factors and Prime Factorization

CTZ3MEM SUMMATIVE ASSESSMENT – I, 2014 MATHEMATICS
CTZ3MEM SUMMATIVE ASSESSMENT – I, 2014 MATHEMATICS

3 Factorisation into irreducibles
3 Factorisation into irreducibles

4.5 distributed mutual exclusion
4.5 distributed mutual exclusion

... In software, a logical ring is constructed in which each process is assigned a position in the ring, as shown in the previous Fig. The ring positions may be allocated in numerical order of network addresses or some other means. It does not matter what the ordering is. All that matters is that each p ...
Study of Finite Field over Elliptic Curve: Arithmetic Means
Study of Finite Field over Elliptic Curve: Arithmetic Means

Iterative and recursive versions of the Euclidean algorithm
Iterative and recursive versions of the Euclidean algorithm

... numbers a and b is Euclidean algorithm. The algorithm does not require integer factorization. It is one of the oldest algorithms named after by Euclid who described it in his Elements in 300 BC. ...
4.4 Greatest Common Factor.notebook
4.4 Greatest Common Factor.notebook

print Chapter 5 notes
print Chapter 5 notes

pdf file
pdf file

... FACT: [Exponentiation on the non-negative elements of a model of PA] The graph of the exponential function 2y = z on N is definable by an L-formula, and P A proves the basic properties of exponentiation. Thus any model of P A is endowed with an exponential function exp. This provides a key connectio ...
security engineering - University of Sydney
security engineering - University of Sydney

... The strength of Diffie-Hellman is based upon two issues: – given p, g, ga, it is difficult to calculate a (the discrete logarithm problem) – given p, g, ga, gb it is difficult to calculate gab (the Diffie-Hellman problem) – we know that DL → DH but it is not known if DH → DL ...
Document
Document

Real algebraic numbers and polynomial systems
Real algebraic numbers and polynomial systems

The task is available in PDF-format here
The task is available in PDF-format here

Lower Bounds for the Relative Greedy Algorithm for Approximating
Lower Bounds for the Relative Greedy Algorithm for Approximating

PH Kropholler Olympia Talelli
PH Kropholler Olympia Talelli

< 1 ... 113 114 115 116 117 118 119 120 121 ... 231 >

Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report