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Introduction to Cryptography with Coding Theory, 3rd Edition

Name: Introduction to Cryptography with Coding Theory, 3rd Edition
ISBN: 9780136758181

by Wade Trappe, Lawrence C. Washington

February 2020

Beginner

621 pages

19h 34m

English

Pearson

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Introduction to Cryptography with Coding Theory
Contents
Preface
Chapter 1 Overview of Cryptography and Its Applications
1.1 Secure Communications
1.1.1 Possible Attacks1.1.2 Symmetric and Public Key Algorithms1.1.3 Key Length
1.2 Cryptographic Applications
Chapter 2 Classical Cryptosystems
2.1 Shift Ciphers
2.2 Affine Ciphers
2.3 The Vigenère Cipher
2.3.1 Finding the Key Length2.3.2 Finding the Key: First Method2.3.3 Finding the Key: Second Method

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
Chapter 3 Basic Number Theory
3.1 Basic Notions
3.1.1 Divisibility3.1.2 Prime Numbers3.1.3 Greatest Common Divisor
3.2 The Extended Euclidean Algorithm
3.3 Congruences
3.3.1 Division3.3.2 Working with Fractions
3.4 The Chinese Remainder Theorem
3.5 Modular Exponentiation
3.6 Fermat’s Theorem and Euler’s Theorem
3.6.1 Three-Pass Protocol
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
3.11.1 Division3.11.2 GF(28)3.11.3 LFSR Sequences
3.12 Continued Fractions
3.13 Exercises
3.14 Computer Problems
Chapter 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
Chapter 5 Stream Ciphers
5.1 Pseudorandom Bit Generation
5.2 Linear Feedback Shift Register Sequences
5.3 RC4
5.4 Exercises
5.5 Computer Problems
Chapter 6 Block Ciphers
6.1 Block Ciphers
6.2 Hill Ciphers
6.3 Modes of Operation
6.3.1 Electronic Codebook (ECB)6.3.2 Cipher Block Chaining (CBC)6.3.3 Cipher Feedback (CFB)6.3.4 Output Feedback (OFB)6.3.5 Counter (CTR)
6.4 Multiple Encryption
6.5 Meet-in-the-Middle Attacks
6.6 Exercises
6.7 Computer Problems
Chapter 7 The Data Encryption Standard
7.1 Introduction
7.2 A Simplified DES-Type Algorithm
7.3 Differential Cryptanalysis
7.3.1 Differential Cryptanalysis for Three Rounds7.3.2 Differential Cryptanalysis for Four Rounds
7.4 DES
7.4.1 DES Is Not a Group
7.5 Breaking DES
7.6 Password Security
7.7 Exercises
7.8 Computer Problems
Chapter 8 The Advanced Encryption Standard: Rijndael
8.1 The Basic Algorithm
8.2 The Layers
8.2.1 The SubBytes Transformation8.2.2 The ShiftRows Transformation8.2.3 The MixColumns Transformation8.2.4 The RoundKey Addition8.2.5 The Key Schedule8.2.6 The Construction of the S-Box
8.3 Decryption
8.4 Design Considerations
8.5 Exercises
Chapter 9 The RSA Algorithm
9.1 The RSA Algorithm
9.2 Attacks on RSA
9.2.1 Low Exponent Attacks9.2.2 Short Plaintext9.2.3 Timing Attacks
9.3 Primality Testing
9.4 Factoring
9.4.1 x2≡y29.4.2 Using ar≡1
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
Chapter 10 Discrete Logarithms
10.1 Discrete Logarithms
10.2 Computing Discrete Logs
10.2.1 The Pohlig-Hellman Algorithm10.2.2 Baby Step, Giant Step10.2.3 The Index Calculus10.2.4 Computing Discrete Logs Mod 4
10.3 Bit Commitment
10.4 Diffie-Hellman Key Exchange
10.5 The ElGamal Public Key Cryptosystem
10.5.1 Security of ElGamal Ciphertexts
10.6 Exercises
10.7 Computer Problems
Chapter 11 Hash Functions
11.1 Hash Functions
11.2 Simple Hash Examples
11.3 The Merkle-Damgård Construction
11.4 SHA-2
Padding and PreprocessingThe Algorithm
11.5 SHA-3/Keccak
11.6 Exercises
Chapter 12 Hash Functions: Attacks and Applications
12.1 Birthday Attacks12.1.1 A Birthday Attack on Discrete Logarithms
12.2 Multicollisions
12.3 The Random Oracle Model
12.4 Using Hash Functions to Encrypt
12.5 Message Authentication Codes
12.5.1 HMAC12.5.2 CBC-MAC
12.6 Password Protocols
12.6.1 The Secure Remote Password protocol12.6.2 Lamport’s protocol
12.7 Blockchains
12.8 Exercises
12.9 Computer Problems
Chapter 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
Chapter 14 What Can Go Wrong
14.1 An Enigma “Feature”
14.2 Choosing Primes for RSA
14.3 WEP
14.3.1 CRC-32
14.4 Exercises
Chapter 15 Security Protocols
15.1 Intruders-in-the-Middle and Impostors
15.1.1 Intruder-in-the-Middle Attacks
15.2 Key Distribution
15.2.1 Key Pre-distribution15.2.2 Authenticated 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
Chapter 16 Digital Cash
16.1 Setting the Stage for Digital Economies
16.2 A Digital Cash System
16.2.1 Participants16.2.2 Initialization16.2.3 The Bank16.2.4 The Spender16.2.5 The Merchant16.2.6 Creating a Coin16.2.7 Spending the Coin16.2.8 The Merchant Deposits the Coin in the Bank16.2.9 Fraud Control16.2.10 Anonymity
16.3 Bitcoin Overview
16.3.1 Some More Details
16.4 Cryptocurrencies
16.5 Exercises
Chapter 17 Secret Sharing Schemes
17.1 Secret Splitting
17.2 Threshold Schemes
17.3 Exercises
17.4 Computer Problems
Chapter 18 Games
18.1 Flipping Coins over the Telephone
18.2 Poker over the Telephone
18.2.1 How to Cheat
18.3 Exercises
Chapter 19 Zero-Knowledge Techniques
19.1 The Basic Setup
19.2 The Feige-Fiat-Shamir Identification Scheme
19.3 Exercises
Chapter 20 Information Theory
20.1 Probability Review
20.2 Entropy
20.3 Huffman Codes
20.4 Perfect Secrecy
20.5 The Entropy of English
20.5.1 Unicity Distance
20.6 Exercises
Chapter 21 Elliptic Curves
21.1 The Addition Law
21.2 Elliptic Curves Mod p
21.2.1 Number of Points Mod p21.2.2 Discrete Logarithms on Elliptic Curves21.2.3 Representing Plaintext
21.3 Factoring with Elliptic Curves
21.3.1 Singular Curves
21.4 Elliptic Curves in Characteristic 2
21.5 Elliptic Curve Cryptosystems
21.5.1 An Elliptic Curve ElGamal Cryptosystem21.5.2 Elliptic Curve Diffie-Hellman Key Exchange21.5.3 ElGamal Digital Signatures
21.6 Exercises
21.7 Computer Problems
Chapter 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
22.5.1 BLS Signatures22.5.2 A Variation22.5.3 Identity-Based Signatures
22.6 Keyword Search
22.7 Exercises
Chapter 23 Lattice Methods
23.1 Lattices
23.2 Lattice Reduction
23.2.1 Two-Dimensional Lattices23.2.2 The LLL algorithm
23.3 An Attack on RSA
23.4 NTRU
23.4.1 An Attack on NTRU
23.5 Another Lattice-Based Cryptosystem
23.6 Post-Quantum Cryptography?
23.7 Exercises
Chapter 24 Error Correcting Codes
24.1 Introduction
24.2 Error Correcting Codes
24.3 Bounds on General Codes
24.3.1 Upper Bounds24.3.2 Lower Bounds
24.4 Linear Codes
24.4.1 Dual Codes
24.5 Hamming Codes
24.6 Golay Codes
Decoding G24
24.7 Cyclic Codes
24.8 BCH Codes
24.8.1 Decoding BCH Codes
24.9 Reed-Solomon Codes
24.10 The McEliece Cryptosystem
24.11 Other Topics
24.12 Exercises
24.13 Computer Problems
Chapter 25 Quantum Techniques in Cryptography
25.1 A Quantum Experiment
25.2 Quantum Key Distribution
25.3 Shor’s Algorithm
25.3.1 Factoring25.3.2 The Discrete Fourier Transform25.3.3 Shor’s Algorithm25.3.4 Final Words
25.4 Exercises
Appendix 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
Appendix 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
Appendix 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
Appendix 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
Appendix E Answers and Hints for Selected Odd-Numbered Exercises
Appendix F Suggestions for Further Reading
Bibliography
Index

Content preview from Introduction to Cryptography with Coding Theory, 3rd Edition

A.7 Examples for Chapter 9

Example 22

Suppose you need to find a large random prime of 50 digits. Here is one way. The function NextPrime[x] finds the next prime greater than $x$ . The function Random[Integer,{a,b}] gives a random integer between $a$ and $b$ . Combining these, we can find a prime:

In[1]:= NextPrime[Random[Integer, { $10 \hat{} 49$ , $10 \hat{} 50$ }]]

Out[1]= 73050570031667109175215303340488313456708913284291

If we repeat this procedure, we should get another prime:

In[2]:= NextPrime[Random[Integer, { $10 \hat{} 49$ , $10 \hat{} 50$ }]]

Out[2]= 97476407694931303255724326040586144145341054568331

Example 23

Suppose you want to change the text hellohowareyou to numbers:

In[3]:= txt2num1["hellohowareyou"]

Out[3]= 805121215081523011805251521

Note that we are now using ...

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