Introduction to Cryptography with Coding Theory

About our author 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.

Overview of Cryptography and Its Applications

1.1 Secure Communications
1.2 Cryptographic Applications


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


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


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


Stream Ciphers

5.1 Pseudo-Random Bit Generation
5.2 LFSR Sequences
5.3 RC4
5.4 Exercises
5.5 Computer Problems


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


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


The Advanced Encryption Standard: Rijndael

8.1 The Basic Algorithm
8.2 The Layers
8.3 Decryption
8.4 Design Considerations
8.5 Exercises


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


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


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


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


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


What Can Go Wrong

14.1 An Enigma ‘Feature’
14.2 Choosing Primes for RSA
14.3 WEP
14.4 Exercises


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


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


Secret Sharing Schemes

17.1 Secret Splitting
17.2 Threshold Schemes
17.3 Exercises
17.4 Computer Problems


Games

18.1 Flipping Coins over the Telephone
18.2 Poker over the Telephone
18.3 Exercises


Zero-Knowledge Techniques

19.1 The Basic Setup
19.2 The Feige-Fiat-Shamir Identification Scheme
19.3 Exercises


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


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


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


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


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


Quantum Techniques in Cryptography

25.1 A Quantum Experiment
25.2 Quantum Key Distribution
25.3 Shor’s Algorithm
25.4 Exercises





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


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


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


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