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编码理论与密码学中的Boole函数（影印版）

样章
作者：
O. A. Logachev ， A. A. Salnikov， V. V. Yashchenko
定价：
169.00元
版面字数：
562.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2026-01-05
ISBN：
978-7-04-066129-3
物料号：
66129-00
出版时间：
2026-03-27
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
分析
暂无
  • 前辅文
  • Foreword
  • Preface
  • Notation
  • Chapter 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
  • Chapter 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
  • Chapter 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
  • Chapter 4. Linear Codes over the Field F2
    • 4.1. Basic properties of linear block codes
    • 4.2. The decoding problem
    • 4.3. Cyclic codes
    • 4.4. Some classes of primitive cyclic codes
    • Comments to Chapter 4
  • Chapter 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
  • Chapter 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
  • Chapter 7. Correlation Immunity and Resiliency
    • 7.1. Main definitions and properties
    • 7.2. The 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
  • Chapter 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 k and order t
    • 8.6. Global avalanche characteristics of Boolean functions
    • Comments to Chapter 8
  • Chapter 9. Basics of Cryptanalysis
    • 9.1. The 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
  • Bibliography
  • Index

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