Number Theoretic Algorithms

Number Theoretic Algorithms Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Number Theoretic Algorithms book. This book definitely worth reading, it is an incredibly well-written.

Number-Theoretic Algorithms in Cryptography

Oleg Nikolaevich Vasilenko
Number Theoretic Algorithms in Cryptography Book PDF

Author : Oleg Nikolaevich Vasilenko
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 48,5 Mb
Release : 2007
Category : Language Arts & Disciplines
ISBN : 0821840908

Get Book

Number-Theoretic Algorithms in Cryptography by Oleg Nikolaevich Vasilenko Pdf

Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one variable; applications of the theory of elliptic curves; algorithms for computation of discrete logarithms; algorithms for solving linear equations over finite fields; and, algorithms for performing arithmetic operations on large integers. The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Algorithmic Number Theory: Efficient algorithms

Eric Bach,Jeffrey Outlaw Shallit
Algorithmic Number Theory Efficient algorithms Book PDF

Author : Eric Bach,Jeffrey Outlaw Shallit
Publisher : MIT Press
Page : 536 pages
File Size : 51,9 Mb
Release : 1996
Category : Computers
ISBN : 0262024055

Get Book

Algorithmic Number Theory: Efficient algorithms by Eric Bach,Jeffrey Outlaw Shallit Pdf

Volume 1.

Number Theoretic Algorithms

N.B. Singh
Number Theoretic Algorithms Book PDF

Author : N.B. Singh
Publisher : N.B. Singh
Page : 41 pages
File Size : 42,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

Get Book

Number Theoretic Algorithms by N.B. Singh Pdf

"Number Theoretic Algorithms" presents a comprehensive exploration of algorithms specifically designed for number theory applications. Through clear explanations and illustrative examples, this book delves into various algorithmic techniques used to solve fundamental number theoretic problems. From prime number generation to factorization methods, and from modular arithmetic to advanced cryptographic protocols, readers will gain a deep understanding of the algorithms that underpin many important mathematical and cryptographic systems. This invaluable resource equips readers with the tools and insights needed to tackle a wide range of number theoretic challenges.

A Handbook of Algorithms in Number Theory

N.B. Singh
A Handbook of Algorithms in Number Theory Book PDF

Author : N.B. Singh
Publisher : N.B. Singh
Page : 44 pages
File Size : 44,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

Get Book

A Handbook of Algorithms in Number Theory by N.B. Singh Pdf

"A Handbook of Algorithms in Number Theory" is designed for absolute beginners, providing a comprehensive introduction to the fundamental concepts of number theory and their applications in computer science. This book explores a range of topics, from cryptographic hash functions and primality testing to random number generation and error detection. Through clear, step-by-step descriptions, readers will gain a solid understanding of how number theory underpins modern algorithms and cryptographic protocols, making complex ideas accessible and engaging for those new to the subject.

Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas,Henri Cohen
Numerical Algorithms for Number Theory Using Pari GP Book PDF

Author : Karim Belabas,Henri Cohen
Publisher : American Mathematical Soc.
Page : 429 pages
File Size : 41,9 Mb
Release : 2021-06-23
Category : Education
ISBN : 9781470463519

Get Book

Numerical Algorithms for Number Theory: Using Pari/GP by Karim Belabas,Henri Cohen Pdf

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

A Course in Computational Algebraic Number Theory

Henri Cohen
A Course in Computational Algebraic Number Theory Book PDF

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 47,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

Get Book

A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

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

Alf J. van der Poorten,Andreas Stein
Algorithmic Number Theory Book PDF

Author : Alf J. van der Poorten,Andreas Stein
Publisher : Springer
Page : 463 pages
File Size : 40,5 Mb
Release : 2008-05-07
Category : Computers
ISBN : 9783540794561

Get Book

Algorithmic Number Theory by Alf J. van der Poorten,Andreas Stein Pdf

This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.

Algorithmic Number Theory

Florian Hess
Algorithmic Number Theory Book PDF

Author : Florian Hess
Publisher : Springer Science & Business Media
Page : 609 pages
File Size : 46,7 Mb
Release : 2006-07-06
Category : Computers
ISBN : 9783540360759

Get Book

Algorithmic Number Theory by Florian Hess Pdf

This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006. The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.

Algorithmic Number Theory

Duncan Buell
Algorithmic Number Theory Book PDF

Author : Duncan Buell
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 40,7 Mb
Release : 2004-06
Category : Computers
ISBN : 9783540221562

Get Book

Algorithmic Number Theory by Duncan Buell Pdf

This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium, ANTS 2004, held in Burlington, VT, USA, in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions, elliptic curves, hyperelliptic curves, GCD algorithms, number field computations, complexity, primality testing, Weil and Tate pairings, cryptographic algorithms, function field sieve, algebraic function field mapping, quartic fields, cubic number fields, lattices, discrete logarithms, and public key cryptosystems.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 41,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662040539

Get Book

Number Theory for Computing by Song Y. Yan Pdf

Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.

Algorithmic Algebraic Number Theory

M. Pohst,H. Zassenhaus
Algorithmic Algebraic Number Theory Book PDF

Author : M. Pohst,H. Zassenhaus
Publisher : Cambridge University Press
Page : 520 pages
File Size : 53,9 Mb
Release : 1997-09-25
Category : Mathematics
ISBN : 0521596696

Get Book

Algorithmic Algebraic Number Theory by M. Pohst,H. Zassenhaus Pdf

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.

Quantum Computational Number Theory

Song Y. Yan
Quantum Computational Number Theory Book PDF

Author : Song Y. Yan
Publisher : Springer
Page : 252 pages
File Size : 47,7 Mb
Release : 2015-12-26
Category : Computers
ISBN : 9783319258232

Get Book

Quantum Computational Number Theory by Song Y. Yan Pdf

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.

Algorithmic Number Theory

J. P. Buhler,P. Stevenhagen
Algorithmic Number Theory Book PDF

Author : J. P. Buhler,P. Stevenhagen
Publisher : Cambridge University Press
Page : 653 pages
File Size : 53,8 Mb
Release : 2008-10-20
Category : Computers
ISBN : 9780521808545

Get Book

Algorithmic Number Theory by J. P. Buhler,P. Stevenhagen Pdf

An introduction to number theory for beginning graduate students with articles by the leading experts in the field.

Cryptanalysis of Number Theoretic Ciphers

Samuel S. Wagstaff, Jr.
Cryptanalysis of Number Theoretic Ciphers Book PDF

Author : Samuel S. Wagstaff, Jr.
Publisher : CRC Press
Page : 336 pages
File Size : 41,8 Mb
Release : 2019-08-22
Category : Mathematics
ISBN : 9781420057690

Get Book

Cryptanalysis of Number Theoretic Ciphers by Samuel S. Wagstaff, Jr. Pdf

At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

Analytic Methods in the Analysis and Design of Number-theoretic Algorithms

Eric Bach
Analytic Methods in the Analysis and Design of Number theoretic Algorithms Book PDF

Author : Eric Bach
Publisher : MIT Press (MA)
Page : 48 pages
File Size : 52,6 Mb
Release : 1985-01
Category : Computers
ISBN : 0262022192

Get Book

Analytic Methods in the Analysis and Design of Number-theoretic Algorithms by Eric Bach Pdf

This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic algorithms and to the construction of cryptographic protocols.Contents: Introduction; 1: Explicit Bounds for Primality Testing; Ankeny's Theorem and its Algorithmic Consequences; Background from Analytic Number Theory; Roots; Asymptotic Theorems; Zeta-function Estimates; Numerical Theorems; Computing Bounds for Specific Moduli; Comparisons with Empirical Results; 2: The Generation of Random Factorizations; Introduction; A Method That Almost Works; Doctoring the Odds; A Factor Generation Procedure; The Complete Algorithm; 2.5 Bounds for the Number of Prime Tests; A Single-precision Time Bound; The Use of Probabilistic Primality Tests.Eric Bach received his doctorate from the University of California at Berkeley. He is currently an Assistant Professor of Computer Science at the University of Wisconsin at Madison. Analytic Methods in the Analysis and Design of Number Theoretic Algorithms is a 1984 ACM Distinguished Dissertation.