Protecting Information

Höfundar: Susan Loepp; William K. Wootters (Útgáfa: 1)
Protecting Information

Kaup valmöguleikar

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.

Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices.

Nánar um bókina

Útgefandi
Cambridge University Press
ISBN
9780511222849
Print ISBN
9780521827409
Format
Page Fidelity (PDF)
Útgáfa
1
Höfundar
Susan Loepp; William K. Wootters
Tungumál
English
Útgefið
2006-07-10
Prent takmörkun á líftíma
10
Prent takmörkun
5
Afritunar takmörkun
5

Kaflar

  • Half-title
  • Title
  • Copyright
  • Dedication
  • Contents
  • Preface
  • Acknowledgments
  • 1 Cryptography: An Overview
  • 1.1 Elementary Ciphers
  • 1.1.1 Substitution ciphers
  • 1.1.2 Vigenère ciphers
  • 1.1.3 One-time pad
  • 1.2 Enigma
  • 1.2.1 The Enigma cipher
  • Cracking Enigma
  • 1.3 A Review of Modular Arithmetic and Zn
  • 1.4 The Hill Cipher
  • 1.5 Attacks on the Hill Cipher
  • 1.6 Feistel Ciphers and DES
  • An r-Round Feistel Cipher with Block Size 64
  • DES
  • 1.7 A Word about AES
  • 1.8 Diffie–Hellman Public Key Exchange
  • Diffie–Hellman Public Key Exchange
  • 1.9 RSA
  • RSA
  • The Euclidean Algorithm
  • 1.10 Public Key Exchanges with a Group
  • 1.11 Public Key Exchange Using Elliptic Curves
  • 2 Quantum Mechanics
  • 2.1 Photon Polarization
  • 2.1.1 Linear polarization
  • 2.1.2 Review of complex numbers
  • 2.1.3 Circular and elliptical polarization
  • 2.2 General Quantum Variables
  • 2.3 Composite Systems
  • The composite system rule
  • 2.4 Measuring a Subsystem
  • Rule for measurements on subsystems
  • 2.5 Other Incomplete Measurements
  • 3 Quantum Cryptography
  • 3.1 The Bennett–Brassard Protocol
  • 3.2 The No-Cloning Theorem
  • 3.3 Quantum Teleportation
  • 4 An Introduction to Error-Correcting Codes
  • 4.1 A Few Binary Examples
  • 4.2 Preliminaries and More Examples
  • 4.3 Hamming Distance
  • 4.4 Linear Codes
  • 4.5 Generator Matrices
  • 4.6 Dual Codes
  • 4.7 Syndrome Decoding
  • 4.8 The Hat Problem
  • The Strategy
  • 5 Quantum Cryptography Revisited
  • 5.1 Error Correction for Quantum Key Distribution
  • 5.2 Introduction to Privacy Amplification
  • 5.2.1 Eve knows a fixed number of elements of the bit string
  • 5.2.2 Eve knows the parities of certain subsets of the bit string
  • 5.2.3 The general case
  • 6 Generalized Reed-Solomon Codes
  • 6.1 Definitions and Examples
  • 6.2 A Finite Field with Eight Elements
  • 6.3 General Theorems
  • 6.4 A Generator Matrix for a GRS Code
  • 6.5 The Dual of a GRS Code
  • 7 Quantum Computing
  • 7.1 Introduction
  • 7.2 Quantum Gates
  • 7.3 The Deutsch Algorithm
  • 7.4 A Universal Set of Quantum Gates
  • 7.5 Number Theory for Shor’s Algorithm
  • 7.6 Finding the Period of f (x)
  • 7.7 Estimating the Probability of Success
  • 7.8 Efficiency of Factoring
  • 7.9 Introduction to Quantum Error Correction
  • 7.9.1 An X-correcting code
  • 7.9.2 A Z-correcting code
  • 7.9.3 The Shor code
  • APPENDIX A
  • A.1 Fields
  • A.2 A Glossary of Linear Algebra Definitions and Theorems
  • A.3 Tables for the Alphabet
  • References
  • Index