Introduction to Cryptography with Coding Theory

<div class="c-un-numbered-headers-and-contents-list__container"> <ol> <li><strong>Overview of Cryptography and Its Applications</strong> <ul> <li>1.1 Secure Communications</li> <li>1.2 Cryptographic Applications</li> </ul> </li> <li><strong>Classical Cryptosystems</strong> <ul> <li>2.1 Shift Ciphers</li> <li>2.2 Affine Ciphers</li> <li>2.3 The VigenÈre Cipher</li> <li>2.4 Substitution Ciphers</li> <li>2.5 Sherlock Holmes</li> <li>2.6 The Playfair and ADFGX Ciphers</li> <li>2.7 Enigma</li> <li>2.8 Exercises</li> <li>2.9 Computer Problems</li> </ul> </li> <li><strong>Basic Number Theory</strong> <ul> <li>3.1 Basic Notions</li> <li>3.2 The Extended Euclidean Algorithm</li> <li>3.3 Congruences</li> <li>3.4 The Chinese Remainder Theorem</li> <li>3.5 Modular Exponentiation</li> <li>3.6 Fermat and Euler</li> <li>3.7 Primitive Roots</li> <li>3.8 Inverting Matrices Mod n</li> <li>3.9 Square Roots Mod n</li> <li>3.10 Legendre and Jacobi Symbols</li> <li>3.11 Finite Fields</li> <li>3.12 Continued Fractions</li> <li>3.13 Exercises</li> <li>3.14 Computer Problems</li> </ul> </li> <li><strong>The One-Time Pad</strong> <ul> <li>4.1 Binary Numbers and ASCII</li> <li>4.2 One-Time Pads</li> <li>4.3 Multiple Use of a One-Time Pad</li> <li>4.4 Perfect Secrecy of the One-Time Pad</li> <li>4.5 Indistinguishability and Security</li> <li>4.6 Exercises</li> </ul> </li> <li><strong>Stream Ciphers</strong> <ul> <li>5.1 Pseudo-Random Bit Generation</li> <li>5.2 LFSR Sequences</li> <li>5.3 RC4</li> <li>5.4 Exercises</li> <li>5.5 Computer Problems</li> </ul> </li> <li><strong>Block Ciphers</strong> <ul> <li>6.1 Block Ciphers</li> <li>6.2 Hill Ciphers</li> <li>6.3 Modes of Operation</li> <li>6.4 Multiple Encryption</li> <li>6.5 Meet-in-the-Middle Attacks</li> <li>6.6 Exercises</li> <li>6.7 Computer Problems</li> </ul> </li> <li><strong>The Data Encryption Standard</strong> <ul> <li>7.1 Introduction</li> <li>7.2 A Simplified DES-Type Algorithm</li> <li>7.3 Differential Cryptanalysis</li> <li>7.4 DES</li> <li>7.5 Breaking DES</li> <li>7.6 Password Security</li> <li>7.7 Exercises</li> <li>7.8 Computer Problems</li> </ul> </li> <li><strong>The Advanced Encryption Standard: Rijndael</strong> <ul> <li>8.1 The Basic Algorithm</li> <li>8.2 The Layers</li> <li>8.3 Decryption</li> <li>8.4 Design Considerations</li> <li>8.5 Exercises</li> </ul> </li> <li><strong>The RSA Algorithm</strong> <ul> <li>9.1 The RSA Algorithm</li> <li>9.2 Attacks on RSA</li> <li>9.3 Primality Testing</li> <li>9.4 Factoring</li> <li>9.5 The RSA Challenge</li> <li>9.6 An Application to Treaty Verification</li> <li>9.7 The Public Key Concept</li> <li>9.8 Exercises</li> <li>9.9 Computer Problems</li> </ul> </li> <li><strong>Discrete Logarithms</strong> <ul> <li>10.1 Discrete Logarithms</li> <li>10.2 Computing Discrete Logs</li> <li>10.3 Bit Commitment</li> <li>10.4 Diffie-Hellman Key Exchange</li> <li>10.5 The ElGamal Public Key Cryptosystem</li> <li>10.6 Exercises</li> <li>10.7 Computer Problems</li> </ul> </li> <li><strong>Hash Functions</strong> <ul> <li>11.1 Hash Functions</li> <li>11.2 Simple Hash Examples</li> <li>11.3 The Merkle-Damg ̊ard Construction</li> <li>11.4 SHA-2</li> <li>11.5 SHA-3/Keccak</li> <li>11.6 Exercises</li> </ul> </li> <li><strong>Hash Functions: Attacks and Applications</strong> <ul> <li>12.1 Birthday Attacks</li> <li>12.2 Multicollisions</li> <li>12.3 The Random Oracle Model</li> <li>12.4 Using Hash Functions to Encrypt</li> <li>12.5 Message Authentication Codes</li> <li>12.6 Password Protocols</li> <li>12.7 Blockchains</li> <li>12.8 Exercises</li> <li>12.9 Computer Problems</li> </ul> </li> <li><strong>Digital Signatures</strong> <ul> <li>13.1 RSA Signatures</li> <li>13.2 The ElGamal Signature Scheme</li> <li>13.3 Hashing and Signing</li> <li>13.4 Birthday Attacks on Signatures</li> <li>13.5 The Digital Signature Algorithm</li> <li>13.6 Exercises</li> <li>13.7 Computer Problems</li> </ul> </li> <li><strong>What Can Go Wrong</strong> <ul> <li>14.1 An Enigma ‘Feature’</li> <li>14.2 Choosing Primes for RSA</li> <li>14.3 WEP</li> <li>14.4 Exercises</li> </ul> </li> <li><strong>Security Protocols</strong> <ul> <li>15.1 Intruders-in-the-Middle and Impostors</li> <li>15.2 Key Distribution</li> <li>15.3 Kerberos</li> <li>15.4 Public Key Infrastructures (PKI)</li> <li>15.5 X.509 Certificates</li> <li>15.6 Pretty Good Privacy</li> <li>15.7 SSL and TLS</li> <li>15.8 Secure Electronic Transaction</li> <li>15.9 Exercises</li> </ul> </li> <li><strong>Digital Cash</strong> <ul> <li>16.1 Setting the Stage for Digital Economies</li> <li>16.2 A Digital Cash System</li> <li>16.3 Bitcoin Overview</li> <li>16.4 Cryptocurrencies</li> <li>16.5 Exercises</li> </ul> </li> <li><strong>Secret Sharing Schemes</strong> <ul> <li>17.1 Secret Splitting</li> <li>17.2 Threshold Schemes</li> <li>17.3 Exercises</li> <li>17.4 Computer Problems</li> </ul> </li> <li><strong>Games</strong> <ul> <li>18.1 Flipping Coins over the Telephone</li> <li>18.2 Poker over the Telephone</li> <li>18.3 Exercises</li> </ul> </li> <li><strong>Zero-Knowledge Techniques</strong> <ul> <li>19.1 The Basic Setup</li> <li>19.2 The Feige-Fiat-Shamir Identification Scheme</li> <li>19.3 Exercises</li> </ul> </li> <li><strong>Information Theory</strong> <ul> <li>20.1 Probability Review</li> <li>20.2 Entropy</li> <li>20.3 Huffman Codes</li> <li>20.4 Perfect Secrecy</li> <li>20.5 The Entropy of English</li> <li>20.6 Exercises</li> </ul> </li> <li><strong>Elliptic Curves</strong> <ul> <li>21.1 The Addition Law</li> <li>21.2 Elliptic Curves Mod p</li> <li>21.3 Factoring with Elliptic Curves</li> <li>21.4 Elliptic Curves in Characteristic 2</li> <li>21.5 Elliptic Curve Cryptosystems</li> <li>21.6 Exercises</li> <li>21.7 Computer Problems</li> </ul> </li> <li><strong>Pairing-Based Cryptography</strong> <ul> <li>22.1 Bilinear Pairings</li> <li>22.2 The MOV Attack</li> <li>22.3 Tripartite Diffie-Hellman</li> <li>22.4 Identity-Based Encryption</li> <li>22.5 Signatures</li> <li>22.6 Keyword Search</li> <li>22.7 Exercises</li> </ul> </li> <li><strong>Lattice Methods</strong> <ul> <li>23.1 Lattices</li> <li>23.2 Lattice Reduction</li> <li>23.3 An Attack on RSA</li> <li>23.4 NTRU</li> <li>23.5 Another Lattice-Based Cryptosystem</li> <li>23.6 Post-Quantum Cryptography?</li> <li>23.7 Exercises</li> </ul> </li> <li><strong>Error Correcting Codes</strong> <ul> <li>24.1 Introduction</li> <li>24.2 Error Correcting Codes</li> <li>24.3 Bounds on General Codes</li> <li>24.4 Linear Codes</li> <li>24.5 Hamming Codes</li> <li>24.6 Golay Codes</li> <li>24.7 Cyclic Codes</li> <li>24.8 BCH Codes</li> <li>24.9 Reed-Solomon Codes</li> <li>24.10 The McEliece Cryptosystem</li> <li>24.11 Other Topics</li> <li>24.12 Exercises</li> <li>24.13 Computer Problems</li> </ul> </li> <li><strong>Quantum Techniques in Cryptography</strong> <ul> <li>25.1 A Quantum Experiment</li> <li>25.2 Quantum Key Distribution</li> <li>25.3 Shor’s Algorithm</li> <li>25.4 Exercises</li> </ul> </li> </ol> <ol type="A"> <li><strong>Mathematica® Examples</strong> <ul> <li>A.1 Getting Started with Mathematica</li> <li>A.2 Some Commands</li> <li>A.3 Examples for Chapter 2</li> <li>A.4 Examples for Chapter 3</li> <li>A.5 Examples for Chapter 5</li> <li>A.6 Examples for Chapter 6</li> <li>A.7 Examples for Chapter 9</li> <li>A.8 Examples for Chapter 10</li> <li>A.9 Examples for Chapter 12</li> <li>A.10 Examples for Chapter 17</li> <li>A.11 Examples for Chapter 18</li> <li>A.12 Examples for Chapter 21</li> </ul> </li> <li><strong>Maple® Examples</strong> <ul> <li>B.1 Getting Started with Maple</li> <li>B.2 Some Commands</li> <li>B.3 Examples for Chapter 2</li> <li>B.4 Examples for Chapter 3</li> <li>B.5 Examples for Chapter 5</li> <li>B.6 Examples for Chapter 6</li> <li>B.7 Examples for Chapter 9</li> <li>B.8 Examples for Chapter 10</li> <li>B.9 Examples for Chapter 12</li> <li>B.10 Examples for Chapter 17</li> <li>B.11 Examples for Chapter 18</li> <li>B.12 Examples for Chapter 21</li> </ul> </li> <li><strong>MATLAB® Examples</strong> <ul> <li>C.1 Getting Started with MATLAB</li> <li>C.2 Examples for Chapter 2</li> <li>C.3 Examples for Chapter 3</li> <li>C.4 Examples for Chapter 5</li> <li>C.5 Examples for Chapter 6</li> <li>C.6 Examples for Chapter 9</li> <li>C.7 Examples for Chapter 10</li> <li>C.8 Examples for Chapter 12</li> <li>C.9 Examples for Chapter 17</li> <li>C.10 Examples for Chapter 18</li> <li>C.11 Examples for Chapter 21</li> </ul> </li> <li><strong>Sage Examples</strong> <ul> <li>D.1 Computations for Chapter 2</li> <li>D.2 Computations for Chapter 3</li> <li>D.3 Computations for Chapter 5</li> <li>D.4 Computations for Chapter 6</li> <li>D.5 Computations for Chapter 9</li> <li>D.6 Computations for Chapter 10</li> <li>D.7 Computations for Chapter 12</li> <li>D.8 Computations for Chapter 17</li> <li>D.9 Computations for Chapter 18</li> <li>D.10 Computations for Chapter 21</li> </ul> </li> </ol> <h4 class="h5">E. Answers and Hints for Selected Odd-Numbered Exercises</h4> <h4 class="h5">F. Suggestions for Further Reading</h4> <h4 class="h5">Bibliography</h4> <h4 class="h5">Index</h4> </div>