图书信息
图书目录
现代密码学与椭圆曲线：初学者指引（影印版）
暂无简介
作者：
Thomas R. Shemanske
定价：
135.00元
出版时间：
2025-02-07
ISBN：
978-7-04-063235-4
物料号：
63235-00
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：
代数几何学
重点项目：
暂无
版面字数：
438.00千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Preface
- Introduction
- Chapter 1. Three Motivating Problems
- §1.1. Fermat's Last Theorem
- §1.2. The Congruent Number Problem
- §1.3. Cryptography
- Chapter 2. Back to the Beginning
- §2.1. The Unit Circle: Real vs. Rational Points
- §2.2. Parametrizing the Rational Points on the Unit Circle
- §2.3. Finding all Pythagorean Triples
- §2.4. Looking for Underlying Structure: Geometry vs. Algebra
- §2.5. More about Points on Curves
- §2.6. Gathering Some Insight about Plane Curves
- §2.7. Additional Exercises
- Chapter 3. Some Elementary Number Theory
- §3.1. The Integers
- §3.2. Some Basic Properties of the Integers
- §3.3. Euclid's Algorithm
- §3.4. A First Pass at Modular Arithmetic
- §3.5. Elementary Cryptography: Caesar Cipher
- §3.6. Affine Ciphers and Linear Congruences
- §3.7. Systems of Congruences
- Chapter 4. A Second View of Modular Arithmetic: Zn and Un
- §4.1. Groups and Rings
- §4.2. Fractions and the Notion of an Equivalence Relation
- §4.3. Modular Arithmetic
- §4.4. A Few More Comments on the Euler Totient Function
- §4.5. An Application to Factoring
- Chapter 5. Public-Key Cryptography and RSA
- §5.1. A Brief Overview of Cryptographic Systems
- §5.2. RSA
- §5.3. Hash Functions
- §5.4. Breaking Cryptosystems and Practical RSA Security Considerations
- Chapter 6. A Little More Algebra
- §6.1. Towards a Classification of Groups
- §6.2. Cayley Tables
- §6.3. A Couple of Non-abelian Groups
- §6.4. Cyclic Groups and Direct Products
- §6.5. Fundamental Theorem of Finite Abelian Groups
- §6.6. Primitive Roots
- §6.7. Diffie-Hellman Key Exchange
- §6.8. ElGamal Encryption
- Chapter 7. Curves in Affine and Projective Space
- §7.1. Affine and Projective Space
- §7.2. Curves in the Affine and Projective Plane
- §7.3. Rational Points on Curves
- §7.4. The Group Law for Points on an Elliptic Curve
- §7.5. A Formula for the Group Law on an Elliptic Curve
- §7.6. The Number of Points on an Elliptic Curve
- Chapter 8. Applications of Elliptic Curves
- §8.1. Elliptic Curves and Factoring
- §8.2. Elliptic Curves and Cryptography
- §8.3. Remarks on a Post-Quantum Cryptographic World
- Appendix A. Deeper Results and Concluding Thoughts
- §A.1. The Congruent Number Problem and Tunnell's Solution
- §A.2. A Digression on Functions of a Complex Variable
- §A.3. Return to the Birch and Swinnerton-Dyer Conjecture
- §A.4. Elliptic Curves over C
- Appendix B. Answers to Selected Exercises
- §B.1. Chapter 2
- §B.2. Chapter 3
- §B.3. Chapter 4
- §B.4. Chapter 5
- §B.5. Chapter 6
- §B.6. Chapter 7
- Bibliography
- Index
