Introduction to cryptography : with coding theory
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書誌事項
Introduction to cryptography : with coding theory
Prentice Hall, c2002
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
For advanced undergraduate courses in cryptography and network security in departments of math and computer science. Assumes a minimal background in programming and a level of math sophistication equivalent to a course in linear algebra. *Assumes a math background of calculus and linear algebra. This background is needed more for 'math sophistication' than for actual content. *Flexible organization-Each chapter is modular and can be covered in any order. *Computer examples included in Appendix-Using Mathematica, Maple, MATLAB, these examples explain how to do computation and demonstrate important concepts. They can also be downloaded from the companion website. *Full chapter on error correcting codes-Allows professors to introduce the basic elements of coding theory.
目次
Preface.
1. Overview.
Secure Communications. Cryptographic Applications.
2. Classical Cryptosystems.
Shift Ciphers. Affine Ciphers. The Vingenere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. Linear Feedback Shift Register Sequences. Enigma. Exercises. Computer Problems.
3. Basic Number Theory.
Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Finite Fields. Exercises. Computer Problems.
4. The Data Encryption Standard.
Introduction. A Simplified DES-Type Algorithm. Differential Cryptoanalysis. DES. Modes of Operation. Breaking DES. Password Security. Exercises.
5. AES: Rijndael.
The Basic Algorithm. The Layers. Decryption. Design Considerations.
6. The RSA Algorithm.
The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems.
7. Discrete Logarithms.
Discrete Logarithms. Computing Discrete Logs. Bit Commitment. The ElGamal Public Key Cryptosystem. Exercise. Computer Problems.
8. Digital Signatures.
RSA Signatures. The ElGamal Signature Scheme. Hash Functions. Birthday Attacks. The Digital Signature Algorithm. Exercises. Computer Problems.
9. E-Commerce and Digital Cash.
Secure Electronic Transaction. Digital Cash. Exercises.
10. Secret Sharing Schemes.
Secret Splitting. Threshold Schemes. Exercises. Computer Problems.
11. Games.
Flipping Coins over the Telephone. Poker over the Telephone. Exercises.
12. Zero Knowledge Techniques.
The Basic Setup. Feige-Fiat-Shamir Identification Scheme. Exercises.
13. Key Establishment Protocols.
Key Agreement Protocols. Key Pre-distribution. Key Distribution. Public Key Infrastructures (PKI). Exercises.
14. Information Theory.
Probability Theory. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.
15. Elliptic Curves.
The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Exercises. Computer Systems.
16. Error Correcting Codes.
Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.
17. Quantum Cryptography.
A Quantum Experiment. Quantum Key Distribution. Shor's Algorithm. Exercises.
Appendix A: Mathematica.
Getting Started with Mathematica. Some Commands. Examples for Chapter 2. Examples for Chapter 3. Examples for Chapter 6. Examples for Chapter 8. Examples for Chapter 10. Examples for Chapter 11. Examples for Chapter 15.
Appendix B: Maple.
Getting Started with Maple. Some Commands. Examples for Chapter 2. Examples for Chapter 3. Examples for Chapter 6. Examples for Chapter 8. Examples for Chapter 10. Examples for Chapter 11. Examples for Chapter 15.
Appendix C: Matlab.
Getting Started with MATLAB. Examples for Chapter 2. Examples for Chapter 3. Examples for Chapter 6. Examples for Chapter 8. Examples for Chapter 10. Examples for Chapter 11. Examples for Chapter 15.
Appendix D: Further Reading.
Bibliography.
Index.
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