伪随机序列的设计及其密码学应用

1 Introduction

1.1 Stream Ciphers and Pseudorandom Sequences

1.2 Cryptographic Measures for Pseudorandom Sequences

1.2.1 Uniformly Distribution

1.2.2 Well-distribution and Correlation Measures

1.2.3 Binary Lattice

1.2.4 Linear Complexity

1.3 Exponential Sums

2 Elliptic Curve Generators

2.1 Elliptic Curves and Character Sums

2.2 Elliptic Curve Linear Congruential Generators

2.2.1 Uniformly Distribution in Parts of the Period

2.2.2 Linear Complexity

2.2.3 Non-linear Complexity

2.3 Binary Sequences from Elliptic Curves

1 Introduction

1.1 Stream Ciphers and Pseudorandom Sequences

1.2 Cryptographic Measures for Pseudorandom Sequences

1.2.1 Uniformly Distribution

1.2.2 Well-distribution and Correlation Measures

1.2.3 Binary Lattice

1.2.4 Linear Complexity

1.3 Exponential Sums

2 Elliptic Curve Generators

2.1 Elliptic Curves and Character Sums

2.2 Elliptic Curve Linear Congruential Generators

2.2.1 Uniformly Distribution in Parts of the Period

2.2.2 Linear Complexity

2.2.3 Non-linear Complexity

2.3 Binary Sequences from Elliptic Curves

2.3.1 Well-distribution and Correlation Measures

2.3.2 Extended Construction of Binary Sequences

2.4 Binary Lattice from Elliptic Curves

2.4.1 A Construction of Binary Lattices

2.4.2 A Construction of Binary Sequences Related to Binary

Lattices

2.5 Discrete-Log Sequences from Elliptic Curves

2.5.1 Elliptic Curve Legendre Sequences

2.5.2 Discrete-Log Binary Threshold Sequences

2.5.3 k-Ary Discrete-Log Sequences

2.5.4 Multi-Dimensional Discrete-Log Sequences

2.5.5 Linear Recursive Sequences over Elliptic Curves

2.6 Binary Sequences from Elliptic Curves and Their Twists

2.7 Binary Sequences from Elliptic Curves over Rings

3 Inversive Number Generators

3.1 Explicit Inversive Generators （I）

3.2 Explicit Inversive Generator （II）

3.2.1 Correlation Measure of Order Two

3.2.2 Correlation Measure of Higher Order

3.3 Inversive Binary Lattice

3.3.1 Construction of Inversive Binary Lattice

3.3.2 Well-distribution and Correlation Measures

3.3.3 Modified Measures

3.4 Modified Inversive Binary Sequences

4 Fermat quotients

4.1 Fermat Quotients Sequences

4.1.1 Distribution of Fermat Quotients

4.1.2 Linear Complexity Profile

4.2 Binary Threshold Sequences from Fermat Quotients

4.2.1 Well-distribution and Correlation Measures

4.2.2 Linear Complexity and Linear Complexity Profile

4.3 Legendre-Fermat Quotient Sequences

4.3.1 Well-distribution and Correlation Measures

4.3.2 Linear Complexity Profile

4.3.3 Linear Complexity

4.4 Euler Quotients

4.4.1 Least Period

4.4.2 Distribution for Dimension One

4.4.3 Distribution for Higher Dimensions

4.5 Polynomial Quotients

4.5.1 Small Degree

4.5.2 Monomials

Generalized Cyclotomic Sequences

5.1 Whiteman-Generalized Cyclotomic Sequences

5.2 Ding-Helleseth-Generalized Cyclotomic Sequences.

5.3 Generalized Cyclotomic Sequences of k-Symbols

5.3.1 Well-distribution and Correlation Measures

5.3.2 Linear Complexity Profile

5.3.3 Linear Complexity

5.4 Quaternary Sequences

5.5 Generalized Cyclotomic Sequences from Finite Fields

5.5.1 Well-distribution and Correlation Measures

5.5.2 Linear Complexity Profile

Pseudorandom Subsets

6.1 Pseudorandom Subsets from Elliptic Curves

6.2 Quasi-random Subsets from Elliptic Curves

6.3 Pseudorandom Subsets from Generalized Cyclotomic Classes

序列密码的安全性完全依赖于密钥序列的随机性，构造具有密码学特殊性质的序列是序列密码的关键技术。陈智雄编著的《伪随机序列的设计及其密码学应用》主要介绍作者在椭圆曲线序列生成器、有限域上逆函数序列生成器、费马商数序列生成器、广义割圆序列生成器等方面的相关研究成果，采用数论中的指数和理论、有限域理论讨论相应序列的分布性质、相关值性质、线性复杂度性质等密码学指标。

　　《伪随机序列的设计及其密码学应用》可作为高校数学专业、计算机专业研究生或高年级学生学习，也可供数论、信息安全、密码学专业人员参考。

陈智雄编著的《伪随机序列的设计及其密码学应用》主要介绍作者在椭圆曲线序列生成器、有限域上逆函数序列生成器、费马商数序列生成器、广义割圆序列生成器等方面的相关研究成果，采用数论中的指数和理论、有限域理论讨论相应序列的分布性质、相关值性质、线性复杂度性质等密码学指标。