Quantum Computational Number Theory

Song Y. Yan

ISBN 10: 3319798464 / ISBN 13: 9783319798462

Published by Springer International Publishing, Springer International Publishing Mär 2018, 2018

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 264 pp. Englisch.

Seller Inventory # 9783319798462

Bibliographic Details

• Title: Quantum Computational Number Theory
• Publisher: Springer International Publishing, Springer International Publishing Mär 2018
• Publication Date: 2018
• Language: English
• ISBN 10: 3319798464
• ISBN 13: 9783319798462
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 15D millimeters 235 millimeters width by 155 millimeters height by 15 millimeters depth
• Weight: 406 grams

About this title

Synopsis

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.

Review

“Over the last two decades, the field of quantum computational number theory (QCNT) has grown, and this book summarizes the major developments in the area. ... I strongly recommend the book to all young computer science students and to mathematicians who love number theory so they can enjoy this new field.” (Manish Gupta, Computing Reviews, April, 2017)