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Oleg A Logachev ; A A Salʹnikov ; V V I︠A︡shchenko

Boolean functions in coding theory and cryptography /Oleg A Logachev - Providence, R.I. : American Mathematical Society , ©2012. - xiv, 334 pages ; 26 cm. - Translations of mathematical monographs, v. 241. .

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.

ISBN: 9781470437374

Subjects--Topical Terms:
Cryptography

Index Terms--Genre/Form:
Coding theory--Algebra, Boolean

Dewey Class. No.: 003.54 LOG