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密码学中的代数 英文版PDF|Epub|txt|kindle电子书版本网盘下载

密码学中的代数 英文版
  • （美）Neal Koblitz著 著
  • 出版社： 北京：清华大学出版社
  • ISBN：9787302242901
  • 出版时间：2010
  • 标注页数：206页
  • 文件大小：9MB
  • 文件页数：214页
  • 主题词：代数－应用－密码－理论－英文

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图书目录

Chapter 1．Cryptography1

1．Early History1

2．The Idea of Public Key Cryptography2

3．The RSA Cryptosystem5

4．Diffie-Hellman and the Digital Signature Algorithm8

5．Secret Sharing,Coin Flipping,and Time Spent on Homework10

6．Passwords,Signatures,and Ciphers12

7．Practical Cryptosystems and Useful Impractical Ones13

Exercises17

Chapter 2．Complexity of Computations18

1．The Big-O Notation18

Exercises21

2．Length of Numbers22

Exercises23

3．Time Estimates24

Exercises31

4．P,NP,and NP-Completeness34

Exercises41

5．Promise Problems44

6．Randomized Algorithms and Complexity Classes45

Exercises48

7．Some Other Complexity Classes48

Exercises52

Chapter 3．Algebra53

1．Fields53

Exercises55

2．Finite Fields55

Exercises61

3．The Euclidean Algorithm for Polynomials63

Exercises64

4．Polynomial Rings65

Exercises70

5．Gr？bner Bases70

Exercises78

Chapter 4．Hidden Monomial Cryptosystems80

1．The Imai-Matsumoto System80

Exercises86

2．Patarin's Little Dragon87

Exercises95

3．Systems That Might Be More Secure96

Exercises102

Chapter 5．Combinatorial-Algebraic Cryptosystems103

1．History103

2．Irrelevance of Brassard's Theorem104

Exercises105

3．Concrete Combinatorial-Algebraic Systems105

Exercises109

4．The Basic Computational Algebra Problem111

Exercises112

5．Cryptographic Version of Ideal Membership112

6．Linear Algebra Attacks113

7．Designing a Secure System114

Chapter 6．Elliptic and Hyperelliptic Cryptosystems117

1．Elliptic Curves117

Exercises129

2．Elliptic Curve Cryptosystems131

Exercises136

3．Elliptic Curve Analogues of Classical Number Theory Problems137

Exercises139

4．Cultural Background:Conjectures on Elliptic Curves and Surprising Relations with Other Problems139

5．Hyperelliptic Curves144

Exercises148

6．Hyperelliptic Cryptosystems148

Exercises154

Appendix．An Elementary Introduction to Hyperelliptic Curves&by Alfred J.Menezes,Yi-Hong Wu,and Robert J.Zuccherato155

1．Basic Definitions and Properties156

2．Polynomial and Rational Functions159

3．Zeros and Poles161

4．Divisors167

5．Representing Semi-Reduced Divisors169

6．Reduced Divisors171

7．Adding Reduced Divisors172

Exercises178

Answers to Exercises179

Bibliography193

Subject Index201

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