Elliptic Curve Cryptography Tutorial

[Nytro]

Table of Contents

1. 1 Arithmetic Primitives
   1. 1.1 Modular Arithmetic Primer
   2. 1.2 Addition and Subtraction
      1. 1.2.1 Example
   3. 1.3 Multiplication
      1. 1.3.1 Example
   4. 1.4 Division
      1. 1.4.1 Example
   5. 1.5 Exponentiation
      1. 1.5.1 Example
   6. 1.6 Square Root
2. 2 Elliptic Curve Cryptography
   1. 2.1 Introduction
   2. 2.2 Elliptic Curve Equation
   3. 2.3 Point representation
3. 3 Point Operations
   1. 3.1 Point Addition
   2. 3.2 Point Doubling
   3. 3.3 Scalar Point Multiplication
   4. 3.4 Checking if a point is on curve
4. 4 Doing useful ECC operations
   1. 4.1 Curve cryptosystem parameters
   2. 4.2 Generating a keypair
   3. 4.3 Encrypting using ECIES
      1. 4.3.1 Encryption
      2. 4.3.2 Decryption
   4. 4.4 Signing using ECDSA
      1. 4.4.1 Signing
      2. 4.4.2 Signature Verification
      3. 4.4.3 Why ECDSA works
   5. 4.5 Messing with ECDSA signatures
      1. 4.5.1 Excursion: Why the greatest morons of the universe work at Sony
5. 5 Advanced Topics
   1. 5.1 Point Compression
6. 6 Examples
   1. 6.1 Testing your integer arithmetic using Genius
   2. 6.2 Using Sage to play with elliptic curves
   3. 6.3 Extracting curve parameters from openssl
   4. 6.4 Playing with openssl ECDSA signatures
   5. 6.5 Visualizing a small curve
7. 7 FAQ
   1. 7.1 Cool! Now that I know how to use ECC, should I write my own crypto library?
   2. 7.2 Can I at least define my own curve then?
   3. 7.3 But I don't trust NIST/SECG. What alternatives do I have?
8. 8 Downloads
9. 9 Literature

 

 

Sursa: https://www.johannes-bauer.com/compsci/ecc/