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The Resource Quantum Computational Number Theory

Quantum Computational Number Theory

Label
Quantum Computational Number Theory
Title
Quantum Computational Number Theory
Creator
Subject
Language
eng
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Quantum Computational Number Theory
Label
Quantum Computational Number Theory
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4206965
Publication
Copyright
Related Contributor
Related Location
Related Agents
Related Authorities
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Acknowledgments -- Contents -- 1 Introduction -- 1.1 What is Number Theory -- Problems for Section 1.1 -- 1.2 What is Computational Number Theory -- Problems for Section 1.2 -- 1.3 What is Quantum Computational Number Theory -- Problems for Section 1.3 -- 1.4 Chapter Notes and Further Reading -- References -- 2 Classical and Quantum Computation -- 2.1 Classical Computability Theory -- 2.1.1 Turing Machines -- 2.1.2 The Church-Turing Thesis -- 2.1.3 Decidability and Computability -- Problems for Section 2.1 -- 2.2 Classical Complexity Theory -- 2.2.1 Complexity Classes -- 2.2.2 The Cook-Karp Thesis -- Problems for Section 2.2 -- 2.3 Quantum Information and Computation -- Problems for Section 2.3 -- 2.4 Quantum Computability and Complexity -- Problems for Section 2.4 -- 2.5 Chapter Notes and Further Reading -- References -- 3 Quantum Algorithms for Integer Factorization -- 3.1 Classical Algorithms for Integer Factorization -- 3.1.1 Basic Concepts -- 3.1.2 Number Field Sieve Factoring -- 3.1.3 u-Factoring Method -- Problems for Section3.1 -- 3.2 Integer Factorization Based Cryptography -- Problems for Section3.2 -- 3.3 Shor's Algorithm for Integer Factorization -- 3.3.1 Quantum Order Finding Algorithm -- 3.3.2 Quantum Integer Factoring Algorithm -- 3.3.3 Quantum Algorithm for Breaking RSA -- Problems for Section3.3 -- 3.4 Variations of Quantum Factoring Algorithms -- Problems for Section3.4 -- 3.5 Chapter Notes and Further Reading -- References -- 4 Quantum Computing for Discrete Logarithms -- 4.1 Classical Algorithms for Discrete Logarithms -- 4.1.1 Basic Concepts -- 4.1.2 Shanks' Baby-Step Giant-Step Algorithm -- 4.1.3 Silver-Pohlig-Hellman Algorithm -- 4.1.4 u Method for DLP -- 4.1.5 Index Calculus Algorithm -- 4.1.6 Discrete Logarithm in Small Characteristic Fields Using FFS -- Problems for Section4.1
  • 4.2 Discrete Logarithm Based Cryptography -- 4.2.1 The Diffie-Hellman-Merkle Key-Exchange Protocol -- 4.2.2 ElGamal Cryptography -- 4.2.3 Massey-Omura Cryptography -- 4.2.4 DLP-Based Digital Signatures -- Problems for Section4.2 -- 4.3 Quantum Algorithms for Discrete Logarithms -- 4.3.1 Basic Ideas of Quantum Computing for DLP -- 4.3.2 Easy Case of Quantum DLP Algorithm -- 4.3.3 General Case of Quantum DLP Algorithm -- 4.3.4 Variations of Quantum DLP Algorithms -- Problems for Section4.3 -- 4.4 Chapter Notes and Further Reading -- References -- 5 Quantum Computing for Elliptic Curve Discrete Logarithms -- 5.1 Classical Algorithms for Elliptic Curve Discrete Logarithms -- 5.1.1 Basic Concepts -- 5.1.2 Pohlig-Hellman Algorithm for ECDLP -- 5.1.3 Baby-Step Giant-Step Algorithm for ECDLP -- 5.1.4 u Method for ECDLP -- 5.1.5 Xedni Calculus for ECDLP -- 5.1.6 Recent Progress in ECDLP -- Problems for Section5.1 -- 5.2 ECDLP-Based Cryptography -- 5.2.1 Basic Ideas in ECDLP-Based Cryptography -- 5.2.2 Precomputations of Elliptic Curve Cryptography -- 5.2.3 Elliptic Curve DHM -- 5.2.4 Elliptic Curve Massey-Omura -- 5.2.5 Elliptic Curve ElGamal -- 5.2.6 Menezes-Vanstone ECC -- 5.2.7 Elliptic Curve DSA -- Problems for Section5.2 -- 5.3 Quantum Algorithms for Elliptic Curve Discrete Logarithms -- 5.3.1 Basic Idea for Quantum Attacking on ECDLP/ECDLP-Based Cryptography -- 5.3.2 Eicher-Opoku's Quantum Algorithm for ECDLP -- 5.3.3 Proos-Zalka's Quantum Algorithm for ECDLP -- 5.3.4 Optimized Quantum Algorithm on ECDLP/ECC -- Problems for Section5.3 -- 5.4 Chapter Notes and Further Reading -- References -- 6 Miscellaneous Quantum Algorithms -- 6.1 Solving Pell's Equation -- Problems for Section6.1 -- 6.2 Verifying Number-Theoretic Conjectures -- 6.2.1 Verifying Riemann's Hypothesis -- 6.2.2 Verifying BSD Conjecture -- Problems for Section6.2
  • 6.3 More Quantum Algorithms -- 6.4 Chapter Notes and Further Reading -- References -- About the Author -- Index
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Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4384688'}
Extent
1 online resource (259 pages)
Form of item
online
Isbn
9783319258232
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

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