有限域小波及其在密码学和译码中的应用（英文）
作 者： （美）法拉马兹 等编著
出版时间： 2012
内容简介
本书探讨了有限域小波与滤波器组理论，开创了“有限域小波变换理论”，此理论提出了一个定义在有限域上的一般的小波分解序列。《有限域小波及其在密码学和译码中的应用（影印版）》还介绍了此理论在纠错代码和数据安全性上的首次应用。本书可作为应用数学、密码学、差错控制编码领域研究者的参考书，对于从事密码项目开发的实际工作者也有很大的价值。
目录
Preface
Figures
Tables
Algorithms
Acronyms
1 Introduction and Some Algebra Preliminaries
1.1 Notations
1.1.1 Set Notation
1.1.2 Matrix Notation
1.1.3 Asymptotic Notation
1.1.4 General Notation
1.2 Abstract Algebraic Background
1.2.1 Group
1.2.2 Ring
1.2.3 Field
1.2.4 Irreducible and Primitive Polynomials
1.2.5 Construction of Extension Fields
1.2.6 Module
1.2.7 Algebra
1.3 Linear Algebra Background
1.3.1 Involution
1.3.2 Sesquilinear Form
1.3.3 Unitary Matrix
1.3.4 Paraunitary Matrix
I Finite-Field Wavelets
2 Background Review and Motivation
2.1 Wavelets for Discrete-Time Signals
2.2 Cyclic Wavelet Transforms
2.3 Review of Transforms over Finite Fields
2.3.1 Discrete Fourier Transform over Finite Fields
2.3.2 Base-Field Transforms over Finite Fields
2.3.3 Related Work on Finite-Field Wavelets
3 Finite-Field Wavelet Basis Functions
3.1 Finite-Field Discrete-Time Basis
3.1.1 Non-Degenerate Bilinear Form
3.1.2 Orthonormal Wavelet Basis over Finite Fields
3.1.3 Completeness of the Orthonormal Set
3.2 Construction of Mother Wavelet and Scaling Function
3.3 Summary
4 Theory of Paraunitary Filter Banks over Fields of Characteristic2
4.1 Background Review
4.1.1 Degree-1 Paraunitary Building Block over GF(2)
4.1.2 Degree-2 Paraunitary Building Blocks over GF(2)
4.1.3 Lapped Orthogonal Transforms over G F(2)
4.2 Unitary Matrices over GF(2r)
4.3 Paraunitary Matrices over Fields of Characteristic 2
4.3.1 Properties of 2 x 2 Paraunitary Matrices over GF (2r)
4.4 Factorization of Paraunitary Matrices over GF (2r)
4.4.1 Degree-1 Paraunitary Building Block over GF (2r)
4.4.2 Degree-2 Paraunitary Building Block over GF (2r)
4.4.3 Degree-2r Paraunitary Building Block over GF (2r)
4.4.4 Factorization of 2 x 2 Paraunitary Matrices over GF(2r)
4.4.5 Degree-Mr Paraunitary Building Block over GF (2r)
4.4.6 Factorization ofM x M Paraunitary Matrices over GF (2r)
4.5 Summary
II Multivariate Cryptography
5 Introduction
5.1 Historical Background and Motivation
5.2 RSA
5.3 Elliptic Curve Cryptography
5.4 Multivariate Cryptography
6 Wavelet Self-Synchronizing Stream Cipher
6.1 Background Review
6.1.1 Classification of Stream Ciphers
6.2 Wavelet Self-Synchronizing Stream Cipher (WSSC)
6.2.1 Modified Wavelet Transform
6.2.2 Basic Round of the WSSC
6.2.3 Multiple Rounds of the WSSC
6.2.4 Key Setup
6.3 Cryptanalysis of the WSSC
6.3.1 Interpolation Attack
6.3.2 Algebraic Attacks
6.3.3 Delta Attack
6.3.4 Time-Memory Tradeoff Attack
6.3.5 Divide-and-Conquer Attack
6.3.6 Correlation and Distinguishing Attacks
6.4 Performance Evaluation
6.5 Summary
7 Wavelet Block Cipher
7.1 Background Review
7.1.1 Feistel Cipher and Data Encryption Standard (DES)
7.1.2 Advanced Encryption Standard (AES)
7.2 Wavelet Block Cipher (WBC)
7.2.1 Linear Components of the WBC
7.2.2 Nonlinear Components of the WBC
7.3 Two-Round Wavelet Block Cipher
7.3.1 Key Setup
7.4 Cryptanalysis of the WBC
7.4.1 Differential and Linear Attacks
7.4.2 Divide-and-Conquer Attack
7.4.3 Interpolation Attack
7.4.4 Delta Attack
7.5 Performance Evaluation
7.6 Summary
8 Paraunitary Public-Key Cryptography
8.1 Background Review
8.1.1 Signature Based on Birational Permutations
8.1.2 Tame Transformation Methods
8.1.3 Tractable Rational Map Cryptosystem
8.1.4 C* Algorithm and its Variants
8.2 Paraunitary Asymmetric Cryptosystem (PAC)
8.2.1 Bijective Mappings
8.2.2 Polynomial Vector
8.2.3 Setup Algorithms
8.3 Probabilistic PAC
8.4 On the Computational Security of the PAC
8.5 A Practical Instance of the PAC
8.5.1 Constructing the Polynomial Vector
8.5.2 Complexity of the PAC
8.6 Cryptanalysis of the Instance of the PAC
8.6.1 Grobner Basis
8.6.2 Univariate Polynomial Representation of the PublicPolynomials
8.6.3 XL and FXL Algorithms
8.6.4 An Attack for Small r
8.7 Paraunitary Digital Signature Scheme (PDSS)
