Book Description
Volume 1.
Algorithmic Number Theory: Efficient algorithms
Author : Eric Bach
Publisher : MIT Press
Page : 536 pages
File Size : 11,94 MB
Release : 1996
Category : Computers
ISBN : 9780262024051
A Course in Computational Algebraic Number Theory
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 37,77 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662029456
Book Description
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Algorithmic Number Theory
Author : Joe P. Buhler
Publisher : Springer
Page : 0 pages
File Size : 12,86 MB
Release : 2003-06-29
Category : Computers
ISBN : 3540691138
Book Description
This book constitutes the refereed proceedings of the Third International Symposium on Algorithmic Number Theory, ANTS-III, held in Portland, Oregon, USA, in June 1998. The volume presents 46 revised full papers together with two invited surveys. The papers are organized in chapters on gcd algorithms, primality, factoring, sieving, analytic number theory, cryptography, linear algebra and lattices, series and sums, algebraic number fields, class groups and fields, curves, and function fields.
Algorithmic Algebraic Number Theory
Author : M. Pohst
Publisher : Cambridge University Press
Page : 520 pages
File Size : 36,73 MB
Release : 1997-09-25
Category : Mathematics
ISBN : 9780521596695
Book Description
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
Higher Arithmetic
Author : Harold M. Edwards
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 13,98 MB
Release : 2008
Category : Mathematics
ISBN : 9780821844397
Book Description
Among the topics featured in this textbook are: congruences; the fundamental theorem of arithmetic; exponentiation and orders; primality testing; the RSA cipher system; polynomials; modules of hypernumbers; signatures of equivalence classes; and the theory of binary quadratic forms. The book contains exercises with answers.
An Algorithmic Theory of Numbers, Graphs and Convexity
Author : Laszlo Lovasz
Publisher : SIAM
Page : 95 pages
File Size : 13,39 MB
Release : 1987-01-01
Category : Mathematics
ISBN : 0898712033
Book Description
Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.
Number Theory for Computing
Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 28,51 MB
Release : 2013-11-11
Category : Computers
ISBN : 366204773X
Book Description
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Computational Number Theory
Author : Abhijit Das
Publisher : CRC Press
Page : 614 pages
File Size : 50,91 MB
Release : 2016-04-19
Category : Computers
ISBN : 1482205823
Book Description
Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract
Quantum Computational Number Theory
Author : Song Y. Yan
Publisher : Springer
Page : 259 pages
File Size : 49,82 MB
Release : 2015-12-26
Category : Computers
ISBN : 3319258230
Book Description
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 develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.
Computational Algebra and Number Theory
Author : Wieb Bosma
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 10,23 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401711089
Book Description
Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.
