基本信息
- 原书名：Algebraic Aspects of Cryptography
- 原出版社： Springer
- 作者： Neal Koblitz
- 丛书名： 数学图书影印版系列
- 出版社：清华大学出版社
- ISBN：9787302242901
- 上架时间：2010-12-31
- 出版日期：2010 年12月
- 开本：16开
- 页码：206
- 版次：1-1
- 所属分类：数学 > 代数，数论及组合理论 > 综合
编辑推荐
this book is intended as a text for a course on cryptography with emphasis on algebraic methods. it is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields.
内容简介
书籍
数学书籍
This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography.
Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys-tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done.
数学书籍
This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography.
Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys-tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done.
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
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
媒体评论
This a textbook for a course (or self-instpaction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half -"hidden monomial"systems, combinatorial-algebraic systems, and hyperelliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security.
"...I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time' in a textbook, some of Patarin's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with their researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory."
P. Hajnal, Acta Scientiarum Mathematicarum 64. 1998
"...I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time' in a textbook, some of Patarin's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with their researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory."
P. Hajnal, Acta Scientiarum Mathematicarum 64. 1998
