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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