Elliptic Curve Cryptography Masterclass From Scratch in Java

Learn fundamentals of public key cryptosystem which empowers bitcoin and blockchain. Hands on experience from scratch

Created bySefik Ilkin Serengil

Last updated 5/2023

English

What you'll learn

Learn the math behind elliptic curves
Understand the public key cryptography
Use elliptic curves for PKI from scratch
Apply key exchange, digital signature and symmetric encryption in real world
Figure out how bitcoin and blockchain works

Course content

9 sections • 20 lectures • 4h 1m total length

Introduction3:39
This is the introduction video. We will mention what this course covers and what this course offers.

Applying addition formulas in practice16:31
Previously, we have proven the addition and doubling formulas on an elliptic curve. Now, we would apply this formulas into the real world.
Double and Add Method11:51
We will mention how to calculate a specific point from a base point on an elliptic curve faster
Applying double and add method in practice11:04
Previously, we have mentioned the faster calculation procedure to accessing a sample point. Now, we would apply it.
Implement addition formulas for an elliptic curve over binary field

Modular Arithmetic and Modular Inverses7:32
We'll mention how to adapt modular arithmetic into elliptic curves, and what this adaption provide us.
Finding Multiplicative Inverse Faster: Extended Euclidean Algorithm8:23
There is a faster way to find modular inverse of a number for a mod value. We'll mention how to find it with extended euclidean algorithm.
Finite Fields21:50
Previously, key exchanging was handled on real numbers. What if parties round the shared keys differently? We will mention how to solve that problem in this lecture.
Applying Extended Euclidean Algorithm9:28
Previously, we've used the out-of-the-box modInverse function under Java BigDecimal class to find the modular inverse. We'd replace this function call to core extended euclidean algorithm.

Elliptic Curve Digital Signature Algorithm22:35
Elliptic curve cryptography can be used for digital signatures too!
Bitcoin5:03
The most common cryptocurrency bitcoin uses ECC to sign and verify signatures. In this lecture, we will mention bitcoin parameters.
Proof of ECDSA7:29
ECDSA verification operation will be proven in this lecture.
Role of Random Key in ECDSA17:57
In ECDSA, we've used a random key variable. This should be really random? What if this random key variable assigned to a constant value? In this lecture, we'll mention the role of random key in elliptic curve digital signature algorithm.
Attack Randomly Generated Elliptic Curve Based Signatures
Counting points on a finite field: order of group17:53
In ECDSA, a new modulo named order of group has to be involved in calculations. It means number of points on the finite field. In this lecture, we'll mention how to calculate order of group.

Requirements

Basic Calculus
Basic Java or Python

Description

Elliptic curve cryptography (ECC) is the most advanced cryptosystem nowadays in the modern cryptography world. It lies behind the most of encryption, key exchange and digital signature applications today. It guarantees same security with other public key algorithms such as RSA or Diffie Hellman whereas it can handle the security with smaller keys also in faster way. Today, even bitcoin and other blockchain based cryptocurrencies are based on ECC!

In this course, we will mention on both the math behind elliptic curve cryptography and gain hands on experience in Java. In other words, the course covers both theory and practice deeply. On the other hand, everything will be developed in java from scratch. Also, no out-of-the-box of feature of any language will be used. Elliptic curves in Weierstrass, Koblitz and Edwards form (or shortly Edwards Curves) will be covered. Then, we will focus on Elliptic Curve Diffie Hellman key (ECDH) exchange, Elliptic Curve ElGamal asymmetric encryption & decryption, digital signatures with elliptic curve digital signature algorithm (ECDSA).

Finally, you can have your own elliptic curve cryptography API when you enrolled the course, and no need to consume any other 3rd party dependency. No matter how deep java knowledge you have, being cryptography enthusiastic is enough to enroll this course.

Who this course is for:

Interested in crypto
Be an expert on public key cryptography
Enthusiastic about cryptographic engineering
Wonder what lies behind bitcoin and blockchain

Elliptic Curve Cryptography Masterclass From Scratch in Java

What you'll learn

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Course content

Introduction1 lecture • 4min

The Math Behind Elliptic Curves2 lectures • 26min

Generating public key on elliptic curves3 lectures • 39min

Why Elliptic Curves are Powerful1 lecture • 3min

Key Exchange2 lectures • 19min

Finite Fields4 lectures • 47min

Digital Signature5 lectures • 1hr 11min

Symmetric Encryption and Decryption1 lecture • 18min

Edwards Curves1 lecture • 15min

Requirements

Description

Who this course is for: