《密碼學中的代數》是清華大學出版社在2012年12月1日出版的圖書，作者是（美國）科比次（Neal Koblitz）。本書主要講述了代數與密碼學的關係。
基本介紹
- 書名：密碼學中的代數
- 作者：（美國）科比次（Neal Koblitz）
- 原版名稱：Algebraic of Cryptography
- ISBN：9787302242901
- 頁數：206頁
- 出版社：清華大學出版社;
- 出版時間：2012年12月1日
- 裝幀：平裝
- 開本：16
- 叢書名： 數學圖書影印版系列
內容簡介,目錄,
內容簡介
《密碼學中的代數》內容簡介：This book is intended as a text for a course on cryptography with emphasis onalgebraic methods. It is written so as to be accessible to graduate or advancedundergraduate students, as well as to scientists in other fields. The first threechapters form a self-contained introduction to basic concepts and techniques. Heremy approach is intuitive and informal. For example, the treatment of computationalcomplexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspectsof the subject that are most important in cryptography.
目錄
Chapter 1. Cryptography
1. Early History
2. The Idea of Public Key Cryptography
3. The RSA Cryptosystem
4. Diffie-Hellman and the Digital Signature Algorithm
5. Secret Sharing, Coin Flipping, and Time Spent on Homework
6. Passwords, Signatures, and Ciphers
7. Practical Cryptosystems and Useful Impractical Ones
Exercises
Chapter 2. Complexity of Computations
1. The Big-O Notation
Exercises
2. Length of Numbers
Exercises
3. Time Estimates
Exercises
4. P, NP, and NP-Completeness
Exercises .
5. Promise Problems
6. Randomized Algorithms and Complexity Classes
Exercises
7. Some Other Complexity Classes
Exercises
Chapter 3. Algebra
1. Fields
Exercises
2. Finite Fields
Exercises
3. The Euclidean Algorithm for Polynomials
Exercises
4. Polynomial Rings
Exercises
5. Gr6bner Bases
Exercises
Chapter 4. Hidden Monomiai Cryptosystems .
1. The Imai-Matsumoto System
Exercises
2. Patarin's Little Dragon
Exercises
3. Systems That Might Be More Secure
Exercises
Chapter 5. Combinatorial-Algebraic Cryptosystems
1. History
2. Irrelevance of Brassard's Theorem
Exercises
3. Concrete Combinatorial-Algebraic Systems
Exercises
4. The Basic Computational Algebra Problem
Exercises
5. Cryptographic Version of Ideal Membership
6. Linear Algebra Attacks
7. Designing a Secure System
Chapter 6. Elliptic and Hyperelliptic Cryptosystems
1. Elliptic Curves
Exercises
2. Elliptic Curve Cryptosystems
Exercises
3. Elliptic Curve Analogues of Classical Number Theory Problems
Exercises
4. Cultural Background: Conjectures on Elliptic Curves
and Surprising Relations with Other Problems
5. Hyperelliptic Curves
Exercises
6. Hyperelliptic Cryptosystems
Exercises
Appendix. An Elementary Introduction to Hyperelliptic Curves
by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato
1. Basic Definitions and Properties
2. Polynomial and Rational Functions
3. Zeros and Poles
4. Divisors
5. Representing Semi-Reduced Divisors
6. Reduced Divisors
7. Adding Reduced Divisors
Exercises
Answers to Exercises
Bibliography
Subject Index
