Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen

Cryptography (ECC) 6.1 Abelian Integrals, Fields, Groups 6.2 Curves, Cryptography 6.3 The Hasse Theorem, and an Example 6.4 More Examples 6.5 The Group Law on Elliptic Curves 6.6 Key Exchange with Elliptic Curves 6.7 Elliptic Curves mod n 6.8 Encoding Plain Text 6.9 Security of ECC 6.10 More Geometry of Cubic Curves 6.11 Cubic Curves and Arcs 6.12 Homogeneous Coordinates 6.13 Fermat's Last Theorem, Elliptic Curves, Gerhard Frey 6.14 A Modification of the Standard Version of Elliptic Curve Cryptography 6.15 Problems 6.16 Solutions Chapter 7: General and Mathematical Attacks in Cryptography 7.1 Cryptanalysis 7.2 Soft Attacks 7.3 Brute‐Force Attacks 7.4 Man‐in‐the‐Middle Attacks 7.5 Relay Attacks, Car Key Fobs 7.6 Known Plain Text Attacks 7.7 Known Cipher Text Attacks 7.8 Chosen Plain Text Attacks 7.9 Chosen Cipher Text Attacks, Digital Signatures 7.10 Replay Attacks 7.11 Birthday Attacks 7.12 Birthday Attack on Digital Signatures 7.13 Birthday Attack on the Discrete Log Problem 7.14 Attacks on RSA 7.15 Attacks on RSA using Low‐Exponents 7.16 Timing Attack 7.17 Differential Cryptanalysis 7.18 Attacks Utilizing Preprocessing 7.19 Cold Boot Attacks on Encryption Keys 7.20 Implementation Errors and Unforeseen States 7.21 Tracking. Bluetooth, WiFi, and Your Smart Phone 7.22 Keep Up with the Latest Attacks (If You Can) Notes Chapter 8: Practical Issues in Modern Cryptography and Communications 8.1 Introduction 8.2 Hot Issues 8.3 Authentication 8.4 User Anonymity 8.5 E‐commerce 8.6 E‐government 8.7 Key Lengths 8.8 Digital Rights 8.9 Wireless Networks 8.10 Communication Protocols Notes

      11  Part II: Mainly Information Theory Chapter 9: Information Theory and its Applications 9.1 Axioms, Physics, Computation 9.2 Entropy 9.3 Information Gained, Cryptography 9.4 Practical Applications of Information Theory 9.5 Information Theory and Physics 9.6 Axiomatics of Information Theory 9.7 Number Bases, Erdös and the Hand of God 9.8 Weighing Problems and Your MBA 9.9 Shannon Bits, the Big Picture Chapter 10: Random Variables and Entropy 10.1 Random Variables 10.2 Mathematics of Entropy 10.3 Calculating Entropy 10.4 Conditional Probability 10.5 Bernoulli Trials 10.6 Typical Sequences 10.7 Law of Large Numbers 10.8 Joint and Conditional Entropy 10.9 Applications of Entropy 10.10 Calculation of Mutual Information 10.11 Mutual Information and Channels 10.12 The Entropy of X + Y