Computational Number Theory

Written by an distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the bas

"Preface This book is a result of my teaching a Masters-level course with the same name for five years in the Indian Institute of Technology Kharagpur. The course was attended mostly by MTech and fina

This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develo

The process of securing communication and encoding all types of electronic and computer communication is known as cryptography. It is used to secure information from the third parties. The main concep

The only book to provide a unified view of the interplay between computational number theory and cryptographyComputational number theory and modern cryptography are two of the most important and funda

Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous su

A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiment

Describes 148 algorithms which are useful for serious number-theoretic computations, in particular for computations related to lattices, algebraic number theory, elliptic curves, primality testing and

Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Mont

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared t

This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in

Classical number theory and elliptic curves are examined in this textbook, which moves on from elementary topics such as primes, continued fractions, and quadratic forms, to elliptic curves and their

Duverney (Baggio Engineering School, France) introduces graduate and advanced undergraduate students, professional mathematicians, math teachers, and mathematically educated lay readers to number theo

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka’s paper is a continuation of his earlier paper published in the

This reference/text provides a detailed introduction to number theory and demonstrates how other areas of mathematics enter into the study of the properties of natural numbers.Offering helpful problem

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpos

Computational learning theory is a subject which has been advancing rapidly in the last few years. The authors concentrate on the probably approximately correct model of learning, and gradually develop the ideas of efficiency considerations. Finally, applications of the theory to artificial neural networks are considered. Many exercises are included throughout, and the list of references is extensive. This volume is relatively self contained as the necessary background material from logic, probability and complexity theory is included. It will therefore form an introduction to the theory of computational learning, suitable for a broad spectrum of graduate students from theoretical computer science and mathematics.

This volume represents an advance in our understanding of how to represent and reason about organizational phenomena. Although organizational theorists have long grappled with the complexities of adap