9780134859064

A broad spectrum of cryptography topics, covered from a mathematical point of view.
Extensively revised and updated, the 3rd Edition of Introduction to Cryptography with Coding Theory mixes applied and theoretical aspects to build a solid foundation in cryptography and security. The authors' lively, conversational tone and practical focus inform a broad coverage of topics from a mathematical point of view, and reflect the most recent trends in the rapidly changing field of cryptography.

For courses in Cryptography, Network Security, and Computer Security.

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Wade Trappe is a Professor in the Electrical and Computer Engineering Department at Rutgers University, and Associate Director of the Wireless Information Network Laboratory (WINLAB). He has led several federally funded projects in the area of cybersecurity and communication systems. He was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2014 for contributions to information and communication security.

1. Overview of Cryptography and Its Applications

1.1 Secure Communications

1.2 Cryptographic Applications

2. Classical Cryptosystems

2.1 Shift Ciphers

2.2 Affine Ciphers

2.3 The Vigenère Cipher

2.4 Substitution Ciphers

2.5 Sherlock Holmes

2.6 The Playfair and ADFGX Ciphers

2.7 Enigma

2.8 Exercises

2.9 Computer Problems

3. Basic Number Theory

3.1 Basic Notions

3.2 The Extended Euclidean Algorithm

3.3 Congruences

3.4 The Chinese Remainder Theorem

3.5 Modular Exponentiation

3.6 Fermat and Euler

3.7 Primitive Roots

3.8 Inverting Matrices Mod n

3.9 Square Roots Mod n

3.10 Legendre and Jacobi Symbols

3.11 Finite Fields

3.12 Continued Fractions

3.13 Exercises

3.14 Computer Problems

4. The One-Time Pad

4.1 Binary Numbers and ASCII

4.2 One-Time Pads

4.3 Multiple Use of a One-Time Pad

4.4 Perfect Secrecy of the One-Time Pad

4.5 Indistinguishability and Security

4.6 Exercises

5. Stream Ciphers

5.1 Pseudo-Random Bit Generation

5.2 LFSR Sequences

5.3 RC4

5.4 Exercises

5.5 Computer Problems

6. Block Ciphers

6.1 Block Ciphers

6.2 Hill Ciphers

6.3 Modes of Operation

6.4 Multiple Encryption

6.5 Meet-in-the-Middle Attacks

6.6 Exercises

6.7 Computer Problems

7. The Data Encryption Standard

7.1 Introduction

7.2 A Simplified DES-Type Algorithm

7.3 Differential Cryptanalysis

7.4 DES

7.5 Breaking DES

7.6 Password Security

7.7 Exercises

7.8 Computer Problems

8. The Advanced Encryption Standard: Rijndael

8.1 The Basic Algorithm

8.2 The Layers

8.3 Decryption

8.4 Design Considerations

8.5 Exercises

9. The RSA Algorithm

9.1 The RSA Algorithm

9.2 Attacks on RSA

9.3 Primality Testing

9.4 Factoring

9.5 The RSA Challenge

9.6 An Application to Treaty Verification

9.7 The Public Key Concept

9.8 Exercises

9.9 Computer Problems

10. Discrete Logarithms

10.1 Discrete Logarithms

10.2 Computing Discrete Logs

10.3 Bit Commitment

10.4 Diffie-Hellman Key Exchange

10.5 The ElGamal Public Key Cryptosystem

10.6 Exercises

10.7 Computer Problems

11. Hash Functions

11.1 Hash Functions

11.2 Simple Hash Examples

11.3 The Merkle-Damg ̊ard Construction

11.4 SHA-2

11.5 SHA-3/Keccak

11.6 Exercises

12. Hash Functions: Attacks and Applications

12.1 Birthday Attacks

12.2 Multicollisions

12.3 The Random Oracle Model

12.4 Using Hash Functions to Encrypt

12.5 Message Authentication Codes

12.6 Password Protocols

12.7 Blockchains

12.8 Exercises

12.9 Computer Problems

13. Digital Signatures

13.1 RSA Signatures

13.2 The ElGamal Signature Scheme

13.3 Hashing and Signing

13.4 Birthday Attacks on Signatures

13.5 The Digital Signature Algorithm

13.6 Exercises

13.7 Computer Problems

14. What Can Go Wrong

14.1 An Enigma “Feature”

14.2 Choosing Primes for RSA

14.3 WEP

14.4 Exercises

15. Security Protocols

15.1 Intruders-in-the-Middle and Impostors

15.2 Key Distribution

15.3 Kerberos

15.4 Public Key Infrastructures (PKI)

15.5 X.509 Certificates

15.6 Pretty Good Privacy

15.7 SSL and TLS

15.8 Secure Electronic Transaction

15.9 Exercises

16. Digital Cash

16.1 Setting the Stage for Digital Economies

16.2 A Digital Cash System

16.3 Bitcoin Overview

16.4 Cryptocurrencies

16.5 Exercises

17. Secret Sharing Schemes

17.1 Secret Splitting

17.2 Threshold Schemes

17.3 Exercises

17.4 Computer Problems

18. Games

18.1 Flipping Coins over the Telephone

18.2 Poker over the Telephone

18.3 Exercises

19. Zero-Knowledge Techniques

19.1 The Basic Setup

19.2 The Feige-Fiat-Shamir Identification Scheme

19.3 Exercises

20. Information Theory

20.1 Probability Review

20.2 Entropy

20.3 Huffman Codes

20.4 Perfect Secrecy

20.5 The Entropy of English

20.6 Exercises

21. Elliptic Curves

21.1 The Addition Law

21.2 Elliptic Curves Mod p

21.3 Factoring with Elliptic Curves

21.4 Elliptic Curves in Characteristic 2

21.5 Elliptic Curve Cryptosystems

21.6 Exercises

21.7 Computer Problems

22. Pairing-Based Cryptography

22.1 Bilinear Pairings

22.2 The MOV Attack

22.3 Tripartite Diffie-Hellman

22.4 Identity-Based Encryption

22.5 Signatures

22.6 Keyword Search

22.7 Exercises

23. Lattice Methods

23.1 Lattices

23.2 Lattice Reduction

23.3 An Attack on RSA

23.4 NTRU

23.5 Another Lattice-Based Cryptosystem

23.6 Post-Quantum Cryptography?

23.7 Exercises

24. Error Correcting Codes

24.1 Introduction

24.2 Error Correcting Codes

24.3 Bounds on General Codes

24.4 Linear Codes

24.5 Hamming Codes

24.6 Golay Codes

24.7 Cyclic Codes

24.8 BCH Codes

24.9 Reed-Solomon Codes

24.10 The McEliece Cryptosystem

24.11 Other Topics

24.12 Exercises

24.13 Computer Problems

25. Quantum Techniques in Cryptography

25.1 A Quantum Experiment

25.2 Quantum Key Distribution

25.3 Shor’s Algorithm

25.4 Exercises

A. Mathematica ^® Examples

A.1 Getting Started with Mathematica

A.2 Some Commands

A.3 Examples for Chapter 2

A.4 Examples for Chapter 3

A.5 Examples for Chapter 5

A.6 Examples for Chapter 6

A.7 Examples for Chapter 9

A.8 Examples for Chapter 10

A.9 Examples for Chapter 12

A.10 Examples for Chapter 17

A.11 Examples for Chapter 18

A.12 Examples for Chapter 21

B. Maple ^® Examples

B.1 Getting Started with Maple

B.2 Some Commands

B.3 Examples for Chapter 2

B.4 Examples for Chapter 3

B.5 Examples for Chapter 5

B.6 Examples for Chapter 6

B.7 Examples for Chapter 9

B.8 Examples for Chapter 10

B.9 Examples for Chapter 12

B.10 Examples for Chapter 17

B.11 Examples for Chapter 18

B.12 Examples for Chapter 21

C. MATLAB ^® Examples

C.1 Getting Started with MATLAB

C.2 Examples for Chapter 2

C.3 Examples for Chapter 3

C.4 Examples for Chapter 5

C.5 Examples for Chapter 6

C.6 Examples for Chapter 9

C.7 Examples for Chapter 10

C.8 Examples for Chapter 12

C.9 Examples for Chapter 17

C.10 Examples for Chapter 18

C.11 Examples for Chapter 21

D. Sage Examples

D.1 Computations for Chapter 2

D.2 Computations for Chapter 3

D.3 Computations for Chapter 5

D.4 Computations for Chapter 6

D.5 Computations for Chapter 9

D.6 Computations for Chapter 10

D.7 Computations for Chapter 12

D.8 Computations for Chapter 17

D.9 Computations for Chapter 18

D.10 Computations for Chapter 21

E. Answers and Hints for Selected Odd-Numbered Exercises

F. Suggestions for Further Reading

Bibliography

Index

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