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Science & Technology » Mathematics » Algebraic Geometry

Computational Number Theory

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Computational Number Theory

Authors :

Abhijit Das



Publisher :

Taylor and Francis Books Limited U.K.

Imprint :

CRC Press

Cover Price :

£ 57.99

CD Included :


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Computational Number Theory

Arithmetic of Integers
Basic Arithmetic Operations
Congruences and Modular Arithmetic
Linear Congruences
Polynomial Congruences
Quadratic Congruences
Multiplicative Orders
Continued Fractions
Prime Number Theorem and Riemann Hypothesis
Running Times of Arithmetic Algorithms

Arithmetic of Finite Fields
Existence and Uniqueness of Finite Fields
Representation of Finite Fields
Implementation of Finite Field Arithmetic
Some Properties of Finite Fields
Alternative Representations of Finite Fields
Computing Isomorphisms among Representations

Arithmetic of Polynomials
Polynomials over Finite Fields
Finding Roots of Polynomials over Finite Fields
Factoring Polynomials over Finite Fields
Properties of Polynomials with Integer Coefficients
Factoring Polynomials with Integer Coefficients

Arithmetic of Elliptic Curves
What Is an Elliptic Curve?
Elliptic-Curve Group
Elliptic Curves over Finite Fields
Some Theory of Algebraic Curves
Pairing on Elliptic Curves
Elliptic-Curve Point Counting

Primality Testing
Introduction to Primality Testing
Probabilistic Primality Testing
Deterministic Primality Testing
Primality Tests for Numbers of Special Forms

Integer Factorization
Trial Division
Pollardís Rho Method
Pollardís p - 1 Method
Dixonís Method
CFRAC Method
Quadratic Sieve Method
Cubic Sieve Method
Elliptic Curve Method
Number-Field Sieve Method

Discrete Logarithms
Square-Root Methods
Algorithms for Prime Fields
Algorithms for Fields of Characteristic Two
Algorithms for General Extension Fields
Algorithms for Elliptic Curves (ECDLP)

Large Sparse Linear Systems
Structured Gaussian Elimination
Lanczos Method
Wiedemann Method
Block Methods

Public-Key Cryptography
Public-Key Encryption
Key Agreement
Digital Signatures
Entity Authentication
Pairing-Based Cryptography

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