Algorithmic Number Theory: Efficient algorithms
Author: Eric Bach
Publisher: MIT Press
Published: 1996
Total Pages: 536
ISBN-13: 9780262024051
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Algorithmic Number Theory
Author: Florian Hess
Publisher: Springer Science & Business Media
Published: 2006-07-06
Total Pages: 609
ISBN-13: 3540360751
DOWNLOAD EBOOKThis 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
Author: J. P. Buhler
Publisher: Cambridge University Press
Published: 2008-10-20
Total Pages: 653
ISBN-13: 0521808545
DOWNLOAD EBOOKAn introduction to number theory for beginning graduate students with articles by the leading experts in the field.
Algorithmic Number Theory
Author: Duncan Buell
Publisher: Springer Science & Business Media
Published: 2004-06
Total Pages: 461
ISBN-13: 3540221565
DOWNLOAD EBOOKThis 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.
A Course in Computational Algebraic Number Theory
Author: Henri Cohen
Publisher: Springer Science & Business Media
Published: 2000-08-01
Total Pages: 580
ISBN-13: 9783540556404
DOWNLOAD EBOOKA 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.
Number-Theoretic Algorithms in Cryptography
Author: Oleg Nikolaevich Vasilenko
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 274
ISBN-13: 9780821840900
DOWNLOAD EBOOKAlgorithmic 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
Author: Wieb Bosma
Publisher: Springer
Published: 2006-12-30
Total Pages: 610
ISBN-13: 3540449949
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.
An Algorithmic Theory of Numbers, Graphs, and Convexity
Author: Laszlo Lovasz
Publisher: SIAM
Published: 1986-01-01
Total Pages: 96
ISBN-13: 9781611970203
DOWNLOAD EBOOKA study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization.
Algorithmic Number Theory
Author: Guillaume Hanrot
Publisher: Springer
Published: 2010-07-08
Total Pages: 407
ISBN-13: 3642145183
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
Algorithmic Number Theory
Author: Guillaume Hanrot
Publisher: Springer Science & Business Media
Published: 2010-07-07
Total Pages: 407
ISBN-13: 3642145175
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
