图书信息
图书目录
编码理论与密码学中的Boole函数（影印版）
暂无简介
作者：
O. A. Logachev ， A. A. Salnikov， V. V. Yashchenko
定价：
169.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-066129-3
物料号：
66129-00
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
重点项目：
暂无
版面字数：
562千字
开本：
16开
装帧形式：
精装
页数：
暂无
最新印次时间：
2026年01月
- 目录
- 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
- 1.1. Basic Algebra
- 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
- 2.1. Basic concepts and definitions
- 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
- 3.1. Group equivalence of mappings. Polya’s theorem
- 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
- 4.1. Basic properties of linear block codes
- 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
- 5.1. General properties of the Reed–Muller codes
- 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
- 6.1. Nonlinearity as a measure of cryptographic quality
- 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
- 7.1. Main definitions and properties
- 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
- 8.1. Almost perfect nonlinear and almost bent mappings
- 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
- 9.1. The Berlekamp–Massey algorithm. Linear complexity
- Bibliography
- Index
- 前辅文
