Elliptic Curve Cryptography in Rust

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Guido Giuntoli

6:01:24

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1. Course Description

1.1 Book Understanding Cryptography.html

1.2 GitHub Repository of the Elliptic Code Library.html

1. Course.mp4

03:51

2. Introduction

1.1 Book Understanding Cryptography.html

1. Infinite Groups Examples.mp4

05:28

2. Sets and Groups.mp4

08:04

3. Finite Groups Examples.mp4

07:39

4. Theorem Generate Groups under Multiplication.mp4

04:59

5. Corollary of using a prime group.mp4

01:18

6. Finite Groups Definition.mp4

05:54

7. Cyclic Groups and Generators.mp4

08:17

8. Three important Theorems.mp4

08:27

9. A Little Exercise.mp4

04:44

10. Searching for Generators in a Group.mp4

09:40

11. The Discrete Logarithm Problem.mp4

10:00

3. Elliptic Curves Cryptography (ECC)

1. Introduction to Elliptic Curves (EC).mp4

11:38

2. Visualizing EC Operations.mp4

04:52

3. Discrete Logarithm Problem in EC.mp4

04:21

4. Coding Elliptic Curve Basic Operation

1.1 GitHub Repository of the Elliptic Curve Library.html

1. Introduction.mp4

07:32

2. Basic Structures.mp4

13:29

3. Finite Fields Operations.mp4

24:28

4. EC Point Add.mp4

28:31

5. EC Point Add Unit Tests.mp4

16:18

6. EC Point Add for Reflected Points.mp4

05:42

7. EC Point Double.mp4

13:00

8. Double and Add Algorithm.mp4

05:28

9. Double and Add Implementation.mp4

12:08

10. Fix Doubling and Add + Code Refactoring.mp4

06:32

11. Secp256k1 Curve Example.mp4

13:16

12. Handling One More Case.mp4

01:12

13. Code the case where P1 = P2 = (x, y) and y = 0.html

5. Practical Application EC Digital Signature Algorithm

1. Introduction to Digital Signature Algorithms.mp4

08:06

2. ECDSA Algorithm and Proof.mp4

21:54

3. Code Reorganization.mp4

04:40

4. ECDSA Basic Code Structure.mp4

14:01

5. ECDSA Key Pair Generation.mp4

04:11

6. ECDSA Sign Method.mp4

24:38

7. ECDSA Verify Method.mp4

19:37

8. ECDSA Secp256k1.mp4

13:34

6. Summary

1. Course Summary.mp4

03:55

Description

with digital signature application

What You'll Learn?

The theory behind finite cyclic groups and the discrete logarithm problem
How elliptic curve works with finite fields at the bottom layer
How to code in Rust a complete elliptic curve library that can be used in multiple crypto-systems: digital signatures, encryption, zero-knowledge proofs, etc.
Implement in Rust a full digital signature algorithm (DSA) as a real life application

Who is this for?

The course is intended for curious users who want to pull aside from the current mass of programmers that learn easy things. This curse deeps into Cryptographic applications, a topic that only some have experience with. Even if you don't desire to work in that, the course will give you valuable knowledge and problem-solving skills when you see the abbreviations "EC" or "DSA".

What You Need to Know?

You don't need any special mathematical or programming knowledge. Having them will make it easier, but I recomend sitting with pencil and paper during the theory classes and try by itself the examples that we look at. In the programming part, I recommend you to create a Rust project locally in your machine and try them together with the videos. Also, with a GitHub account, you can upload a public repository for showing it to recruiters or firms to then find a job position.

More details

Description
This course teaches you how elliptic curve groups work together with finite fields and how to implement a Rust library from scratch to perform basic groups' operations. Additionally, you will learn how to use EC groups in digital signature algorithms and extend its usage to other crypto-systems. The course provides both: theoretical and practical examples on every topic that is discussed.

The course is divided into three main sections:

1. A theory section where I explain what finite cyclic groups are. In particular, we will see some theorems that will help us to understand, for example, why it is important to use a group with "prime order".

2. A practical implementation in Rust of the Elliptic Curve library using Finite Fields in the bottom layer. You can in this part additionally create your one GitHub repository and use it as a showcase to recruiters or firms.

3. A digital signature application of the elliptic curve library developed so far. This is the moment where you use everything together to build something that solves a real-world problem.

The intended audience consists of curious people who want to dive into cryptography, maybe for the first time, and those who want to increase their knowledge of them. I promise you that after finishing the course, you will not have any more fear when you see abbreviations such as "EC" and "DSA" and will be substantially more literate in cryptography and Rust.
Who this course is for:
The course is intended for curious users who want to pull aside from the current mass of programmers that learn easy things. This curse deeps into Cryptographic applications, a topic that only some have experience with. Even if you don't desire to work in that, the course will give you valuable knowledge and problem-solving skills when you see the abbreviations "EC" or "DSA".

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Cryptography

Rust

Guido Giuntoli

Instructor's Courses

I'm Guido, a software engineer passionate about new technologies and solving real-world problems. My main interests lie in cryptography, blockchain technology, entrepreneurship, and startups. I enjoy studying these subjects and engaging in discussions with others to explore different problems and potential solutions. With a focus on continuous learning and collaboration, I strive to broaden my knowledge and contribute to innovative advancements in the tech industry. Let's connect and embark on a journey of discovery together!

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