Quantum Computational Number Theory | Buch

Cover: 9783319258218 | Quantum Computational Number Theory | Song Y. Yan | Buch | Englisch

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Beschreibung

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.

Zusammenfassung

Introduces the basic concepts and results in number theory and quantum computing

Discusses three major intractable number-theoretic problems related to the construction of modern public-key cryptography

Discusses known quantum algorithms for solving the intractable number-theoretic problems and for attacking the number-theoretic cryptographic schemes

Inhaltsverzeichnis

Introduction.- Classical and Quantum Computation.- Quantum Computing for Integer Factorization.- Quantum Computing for Discrete Logarithms.- Quantum Computing for Elliptic Curve Discrete Logarithms.- Miscellaneous Quantum Algorithms.

Details

Erscheinungsjahr:	2016
Genre:	Informatik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	ix 252 S. 40 farbige Illustr. 252 p. 40 illus. in color.
ISBN-13:	9783319258218
ISBN-10:	3319258214
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Yan, Song Y.
Auflage:	1st ed. 2015
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 20 mm
Von/Mit:	Song Y. Yan
Erscheinungsdatum:	06.01.2016
Gewicht:	0,565 kg