The Resource Boolean functions in coding theory and cryptography, O.A. Logachev, A.A. Salnikov, V.V. Yashchenko ; translated by Svetla Nikova

Boolean functions in coding theory and cryptography, O.A. Logachev, A.A. Salnikov, V.V. Yashchenko ; translated by Svetla Nikova

Label
Boolean functions in coding theory and cryptography
Title
Boolean functions in coding theory and cryptography
Statement of responsibility
O.A. Logachev, A.A. Salnikov, V.V. Yashchenko ; translated by Svetla Nikova
Creator
Contributor
Subject
Language
  • eng
  • rus
  • eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Logachev, Oleg A
Index
index present
LC call number
QA268
LC item number
.L6413 2011
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Salʹnikov, A. A.
  • I︠A︡shchenko, V. V
Series statement
Translations of mathematical monographs
Series volume
v. 241
http://library.link/vocab/subjectName
  • Coding theory
  • Cryptography
  • Algebra, Boolean
  • Algebra, Boolean
  • Coding theory
  • Cryptography
  • Information and communication, circuits
  • Information and communication, circuits
  • Information and communication, circuits
Label
Boolean functions in coding theory and cryptography, O.A. Logachev, A.A. Salnikov, V.V. Yashchenko ; translated by Svetla Nikova
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1 Arithmetics of Finite Fields and Polynomials -- 1.1. Basic Algebra -- 1.2. Construction of finite fields -- 1.3. Polynomials over finite fields -- Comments to Chapter 1 -- ch. 2 Boolean Functions -- 2.1. Basic concepts and definitions -- 2.2. Numerical and metric characteristics -- 2.3. Autocorrelation and crosscorrelation -- 2.4. Group algebra of Boolean functions -- 2.5. Cryptographic properties of Boolean functions and mappings -- 2.6. Covering sequences of Boolean functions -- Comments to Chapter 2 -- ch. 3 Classifications of Boolean Functions -- 3.1. Group equivalence of mappings. Polya's theorem -- 3.2. Classification of Boolean functions of five variables -- 3.3. Classification of quadratic Boolean functions -- 3.4. Classification of homogeneous cubic forms of 8 variables -- 3.5. RM-equivalence of Boolean functions -- Comments to Chapter 3 -- ch. 4 Linear Codes over the Field F2 -- 4.1. Basic properties of linear block codes -- 4.2. decoding problem -- 4.3. Cyclic codes -- 4.4. Some classes of primitive cyclic codes -- Comments to Chapter 4 -- ch. 5 Reed-Muller Codes -- 5.1. General properties of the Reed-Muller codes -- 5.2. Reed's decoding algorithm -- 5.3. First order Reed-Muller codes and connections with other codes -- 5.4. Reed-Muller codes of second order and related codes -- 5.5. Classification of Boolean functions and Reed-Muller codes of the 3rd order -- Comments to Chapter 5 -- ch. 6 Nonlinearity -- 6.1. Nonlinearity as a measure of cryptographic quality -- 6.2. Maximum-nonlinear bent functions and their properties -- 6.3. Some classes of maximum-nonlinear bent functions -- 6.4. Partially maximum-nonlinear (partially bent) functions and their properties -- 6.5. Plateaued functions and partially defined mn-bent functions -- 6.6. Hyperbent functions -- 6.7. Biorthogonal bases -- Comments to Chapter 6 -- ch. 7 Correlation Immunity and Resiliency -- 7.1. Main definitions and properties -- 7.2. inheritance of properties under restrictions of Boolean functions -- 7.3. General methods for constructing correlation-immune functions and resilient mappings -- 7.4. Nonlinearity of correlation-immune and resilient functions -- 7.5. Construction of resilient Boolean functions with good cryptographic properties -- 7.6. Covering sequences of correlation-immune and resilient functions -- 7.7. Quadratic resilient Boolean functions of maximum order -- Comments to Chapter 7 -- ch. 8 Codes, Boolean Mappings, and Their Cryptographic Properties -- 8.1. Almost perfect nonlinear and almost bent mappings -- 8.2. Coding-theoretic approach to the study of APN and AB mappings -- 8.3. Cyclic codes and Boolean mappings -- 8.4. Avalanche criteria and propagation criteria -- 8.5. Construction of Boolean functions satisfying the propagation criterion of degree m and order t -- 8.6. Global avalanche characteristics of Boolean functions -- Comments to Chapter 8 -- ch. 9 Basics of Cryptanalysis -- 9.1. Berlekamp-Massey algorithm. Linear complexity -- 9.2. Principles of the statistical method for cryptanalysis of block ciphers -- 9.3. Principles of the correlation cryptanalysis method -- 9.4. Principles of the linear cryptanalysis method -- 9.5. Principles of the difference (differential) cryptanalysis method -- Comments to Chapter 9
Dimensions
26 cm.
Extent
xiv, 334 pages
Isbn
9780821846803
Isbn Type
(alk. paper)
Lccn
2011035308
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
  • (OCoLC)754105051
  • (OCoLC)ocn754105051
Label
Boolean functions in coding theory and cryptography, O.A. Logachev, A.A. Salnikov, V.V. Yashchenko ; translated by Svetla Nikova
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1 Arithmetics of Finite Fields and Polynomials -- 1.1. Basic Algebra -- 1.2. Construction of finite fields -- 1.3. Polynomials over finite fields -- Comments to Chapter 1 -- ch. 2 Boolean Functions -- 2.1. Basic concepts and definitions -- 2.2. Numerical and metric characteristics -- 2.3. Autocorrelation and crosscorrelation -- 2.4. Group algebra of Boolean functions -- 2.5. Cryptographic properties of Boolean functions and mappings -- 2.6. Covering sequences of Boolean functions -- Comments to Chapter 2 -- ch. 3 Classifications of Boolean Functions -- 3.1. Group equivalence of mappings. Polya's theorem -- 3.2. Classification of Boolean functions of five variables -- 3.3. Classification of quadratic Boolean functions -- 3.4. Classification of homogeneous cubic forms of 8 variables -- 3.5. RM-equivalence of Boolean functions -- Comments to Chapter 3 -- ch. 4 Linear Codes over the Field F2 -- 4.1. Basic properties of linear block codes -- 4.2. decoding problem -- 4.3. Cyclic codes -- 4.4. Some classes of primitive cyclic codes -- Comments to Chapter 4 -- ch. 5 Reed-Muller Codes -- 5.1. General properties of the Reed-Muller codes -- 5.2. Reed's decoding algorithm -- 5.3. First order Reed-Muller codes and connections with other codes -- 5.4. Reed-Muller codes of second order and related codes -- 5.5. Classification of Boolean functions and Reed-Muller codes of the 3rd order -- Comments to Chapter 5 -- ch. 6 Nonlinearity -- 6.1. Nonlinearity as a measure of cryptographic quality -- 6.2. Maximum-nonlinear bent functions and their properties -- 6.3. Some classes of maximum-nonlinear bent functions -- 6.4. Partially maximum-nonlinear (partially bent) functions and their properties -- 6.5. Plateaued functions and partially defined mn-bent functions -- 6.6. Hyperbent functions -- 6.7. Biorthogonal bases -- Comments to Chapter 6 -- ch. 7 Correlation Immunity and Resiliency -- 7.1. Main definitions and properties -- 7.2. inheritance of properties under restrictions of Boolean functions -- 7.3. General methods for constructing correlation-immune functions and resilient mappings -- 7.4. Nonlinearity of correlation-immune and resilient functions -- 7.5. Construction of resilient Boolean functions with good cryptographic properties -- 7.6. Covering sequences of correlation-immune and resilient functions -- 7.7. Quadratic resilient Boolean functions of maximum order -- Comments to Chapter 7 -- ch. 8 Codes, Boolean Mappings, and Their Cryptographic Properties -- 8.1. Almost perfect nonlinear and almost bent mappings -- 8.2. Coding-theoretic approach to the study of APN and AB mappings -- 8.3. Cyclic codes and Boolean mappings -- 8.4. Avalanche criteria and propagation criteria -- 8.5. Construction of Boolean functions satisfying the propagation criterion of degree m and order t -- 8.6. Global avalanche characteristics of Boolean functions -- Comments to Chapter 8 -- ch. 9 Basics of Cryptanalysis -- 9.1. Berlekamp-Massey algorithm. Linear complexity -- 9.2. Principles of the statistical method for cryptanalysis of block ciphers -- 9.3. Principles of the correlation cryptanalysis method -- 9.4. Principles of the linear cryptanalysis method -- 9.5. Principles of the difference (differential) cryptanalysis method -- Comments to Chapter 9
Dimensions
26 cm.
Extent
xiv, 334 pages
Isbn
9780821846803
Isbn Type
(alk. paper)
Lccn
2011035308
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
System control number
  • (OCoLC)754105051
  • (OCoLC)ocn754105051

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