《公钥密码学的数学基础 (英文版)》电子书下载

公钥密码学的数学基础 (英文版)txt,chm,pdf,epub,mobi下载
作者:Wang Xiaoyun/Xu Guangwu/Wang Mingqiang/Meng Xiaomeng
出版社: 科学出版社
出版年: 2016-4
页数: 240
定价: 98.00
装帧: 精装
ISBN: 9787030474308

内容简介 · · · · · ·

《公钥密码学的数学基础(英文版)》内容新颖,结构合理,注重严格的理论分析与启发性的数值实验相结合。适合从事数学、物理、天文和工程技术的科研工作者和研究生参考。

数论与代数结构这门课是数学学院信息安全专业的一门专业基础课。通过该课程的学习,让学生掌握密码学所需要的重要的数学基础理论,熟悉密码体制中常用的数学基本算法及其复杂性理论。

具体分为下面几个方面的内容：1.整除：整除的基本理论,辗转相除法；2.同余：同余、剩余类的基本理论,同余方程,Euler定理；3.原根：指标的基本理论,原根基本定理；4.群、环、域基本理论；5.群、环、域进一步的理论,扩域、有限域的理论；6.基本算法、及其复杂性理论；7.格理论。

作者简介 · · · · · ·

王小云,教授,1966年出生,1983年至1993年就读于山东大学数学系,先后获得学士、硕士和博士学位,博士生导师潘承洞教授。1993年毕业后留校任教。现为清华大学杨振宁讲座教授,中国密码学会副理事长。2005年国家杰出青年基金获得者,2006年被聘为清华大学“长江学者特聘教授”。主要研究方向是密码理论研究。在密码分析领域,给出了多个重要Hash函数算法MD5与SH：A-1等的碰撞攻击。

王明强,博士,1970年生,2004于山东大学数学系获得博士学位,导师展涛教授。现为山东大学副教授,中国密码学会会员。主要研究方向是数论、算术几何,在可证明安全密码体质研究及椭圆曲线密码快速实现方面取得多个重要研究成果。

孟宪萌,博士,1971年生,1989年起先后就读于吉林大学数学系和山东大学数学系获学士、硕士和博士学位,攻读硕士博士学位期问的导师为展涛教授。毕业...

目录 · · · · · ·

Preface to Mathematics Monograph Series
Foreword
Preface
Acknowledgments
CHAPTER 1 Divisibility of Integers
1.1 THE CONCEPT OF DIVISIBILITY
· · · · · ·()
Preface to Mathematics Monograph Series
Foreword
Preface
Acknowledgments
CHAPTER 1 Divisibility of Integers
1.1 THE CONCEPT OF DIVISIBILITY
1.2 THE GREATEST COMMON DIVISOR AND THE LEAST COMMON MULTIPLE
1.3 THE EUCLIDEAN ALGORITHM
1.4 SOLVING LINEAR DIOPHANTINE EQUATIONS
1.5 PRIME FACTORIZATION OF INTEGERS
CHAPTER 2 Congruences
2.1 CONGRUENCES
2.2 RESIDUE CLASSES AND SYSTEMS OF RESIDUES
2.3 EULER'S THEOREM
2.4 WILSON'S THEOREM
CHAPTER 3 Congruence Equations
3.1 BASIC CONCEPTS OF CONGRUENCES OF HIGH DEGREES
3.2 LINEAR CONGRUENCES
3.3 SYSTEMS OF LINEAR CONGRUENCE EQUATIONS AND THE CHINESE REMAINDER THEOREM
3.4 GENERAL CONGRUENCE EQUATIONS
3.5 QUADRATICRESIDUES
3.6 THE LEGENDRE SYMBOL AND THE JACOBI SYMBOL
CHAPTER 4 Exponents and Primitive Roots
4.1 EXPONENTS AND THEIR PROPERTIES
4.2 PRIMITIVE ROOTS AND THEIR PROPERTIES
4.3 INDICES,CONSTRUCTION OF REDUCED SYSTEM OF RESIDUES
4.4 NTH POWER RESIDUES
CHAPTER 5 Some Elementary Results for Prime Distribution
5.1 INTRODUCTION TO THE BASIC PROPERTIES OF PRIMES AND THE MAIN RESULTS OF PRIME NUMBER DISTRIBUTION
5.2 PROOF OF THE EULER PRODUCT FORMULA
5.3 PROOF OF AWEAKER VERSION OF THE PRIME NUMBER THEOREM
5.4 EQUIVALENT STATEMENTS OF THE PRIME NUMBER THEOREM
CHAPTER 6 Simple Continued Fractions
6.1 SIMPLE CONTINUED FRACTIONS AND THEIR BASIC PROPERTIES
6.2 SIMPLE CONTINUED FRACTION REPRESENTATIONS OF REAL NUMBERS
6.3 APPLICATION OF CONTINUED FRACTION IN CRYPTOGRAPHY—ATTACK TO RSA WITH SMALL DECRYPTION EXPONENTS
CHAPTER 7 Basic Concepts
7.1 MAPS
7.2 ALGEBRAIC OPERATIONS
7.3 HOMOMORPHISMS AND ISOMORPHISMS BETWEEN SETS WITH OPERATIONS
7.4 EQUIVALENCE RELATIONS AND PARTITIONS
CHAPTER 8 GroupTheory
8.1 DEFINITIONS
8.2 CYCLIC GROUPS
8.3 SUBGROUPS AND COSETS
8.4 FUNDAMENTAL HOMOMORPHISM THEOREM
8.5 CONCRETE EXAMPLES OF FINITE GROUPS
CHAPTER 9 Rings and Fields
9.1 DEFINITION OF A RING
9.2 INTEGRAL DOMAINS, FIELDS, AND DIVISION RINGS
9.3 SUBRINGS,IDEALS, AND RING HOMOMORPHISMS
9.4 CHINESE REMAINDER THEOREM
9.5 EUCLIDEAN RINGS
9.6 FINITE FIELDS
9.7 FIELD OF FRACTIONS
CHAPTER 10 Some Mathematical Problems in Public Key Cryptography
10.1 TIME ESTIMATION AND COMPLEXITY OF ALGORITHMS
10.2 INTEGER FACTORIZATION PROBLEM
10.3 PRIMALITY TESTS
10.4 THE RSA PROBLEM AND THE STRONG RSA PROBLEM
10.5 QUADRATIC RESIDUES
10.6 THE DISCRETE LOGARITHM PROBLEM
CHAPTER 11 Basics of Lattices
11.1 BASIC CONCEPTS
11.2 SHORTEST VECTOR PROBLEM
11.3 LATTICE BASIS REDUCTION ALGORITHM
11.4 APPLICATIONS OF LLL ALGORITHM
References
Further Reading
Index
· · · · · · ()

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