| 词条 | 密码学中的代数 |
| 释义 | 图书信息出版社: 清华大学出版社; 第1版 (2010年12月1日) 外文书名: Algebraic of Cryptography 丛书名: 数学图书影印版系列 平装: 206页 正文语种: 英语 开本: 16 ISBN: 9787302242901 条形码: 9787302242901 尺寸: 22.8 x 17.8 x 1 cm 重量: 281 g 作者简介作者：（美国）科比次（Neal Koblitz） 内容简介《密码学中的代数》内容简介：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. 目录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 |
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