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Modern Cryptography and Elliptic Curves by Thomas R. Shemanske is a book available to read on EtoBox.

What is Modern Cryptography and Elliptic Curves about?

Cover 1 Title page 2 Contents 4 Preface 8 Introduction 10 Chapter 1. Three Motivating Problems 14 1.1. Fermat’s Last Theorem 16 1.2. The Congruent Number Problem 18 1.3. Cryptography 19 Chapter 2. Back to the Beginning 22 2.1. The Unit Circle: Real vs. Rational Points 23 2.2. Parametrizing the Rational Points on the Unit Circle 25 2.3. Finding all Pythagorean Triples 29 2.4. Looking for Underlying Structure: Geometry vs. Algebra 40 2.5. More about Points on Curves 47 2.6. Gathering Some Insight about Plane Curves 51 2.7. Additional Exercises 56 Chapter 3. Some Elementary Number Theory 58 3.1. The Integers 59 3.2. Some Basic Properties of the Integers 60 3.3. Euclid’s Algorithm 65 3.4. A First Pass at Modular Arithmetic 69 3.5. Elementary Cryptography: Caesar Cipher 76 3.6. Affine Ciphers and Linear Congruences 79 3.7. Systems of Congruences 83 Chapter 4. A Second View of Modular Arithmetic: \Z_{n} and U_{n} 86 4.1. Groups and Rings 86 4.2. Fractions and the Notion of an Equivalence Relation 90 4.3. Modular Arithmetic 92 4.4. A Few More Comments on the Euler Totient Function 106 4.5. An Application to Factoring 108 Chapter 5. Public-Key Cryptography and RSA 114 5.1. A Brief Overview

Author

Thomas R. Shemanske

Language

EN