04088nam a22002297a 4500 55973 55973 20191121122454.0 191121b ||||| |||| 00| 0 eng d 9781470437374 003.54 LOG 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. 00 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. Cryptography Coding theory Algebra, Boolean A A Salʹnikov ; V V I︠A︡shchenko BOOK 0 0 ddc 0 0 SNUL SNUL 2019-11-21 Maths Gifted Book 0.00 1 003.54 LOG G1569 2023-05-09 00:00:00 2023-05-02 2019-11-21 BOOK Maths Gifted Book