I will be happy to help you in your article about Ethereum: In addition, an elliptical curve.
Here is the sketch of your article:
Ethereum: In addition, an elliptical curve
When we dive deeper into the world of blockchain and cryptocurrencies, it is necessary to understand the basic technology that makes everything work. One of the key elements of Ethereum is the addition of an elliptical curve that plays an important role in its safety and scalability.
What is an elliptical curve?
Before we go, let’s take a short tour to the world of elliptical curves. The elliptical curve is a kind of mathematical curve that is used to represent points on a two -dimensional plane with coordinates (X, Y). These coordinates are defined by a few numbers (A, B), called “intersection y” and “intersection x”, respectively.
Elliptical curve operations
In the context of cryptography, elliptical curves ensure a safe way to perform such operations as adding, subtracting, multiplication and lecture. These operations are performed using built -in curve algorithms that ensure that the results are safe and resistant to manipulation.
ec multiplication
When it comes to multiplying the elliptical curve (EC), there are two main methods: adding a point and double the point. The point add -on consists in adding two points on the elliptical curve, while the doubles are used for faster calculations when many points need to be multiplied.
The point add -on is made using a specific formula, which takes into account the coordinates of two points added. This formula ensures that the result is in the elliptical curve, ensuring its safety.
EC add -on
In Ethereum, the EC add -on refers to the process of adding two points on an elliptical curve. To perform this operation, we must use a specific algorithm that includes:
- Spot additive: Add two points, P and Q, using the pattern
P + Qat the addition.
- Summoning point: If many points are multiplied together, we can use double points to reduce the number of calculations required.
Where does the second point come from?
In addition, EC is generated using a specific algorithm that provides it with an elliptical curve. The exact formula for generating a second point depends on the type of elliptical curve used (e.g. Sei-kun-mukai (SKM) or J-de Brion-Soule-Henry-Eelliot (J-Deh-He)).
In the case of SKM, the second point is generated as Q = p + y a, whereA is an element of the elliptical curve. In the case of J-Deh-He, the second point is generated as Q = P-X B, where ‘B` is another element of the elliptical curve.
In both cases, the algorithm ensures that the second point lies in the elliptical curve and warns a specific set of rules to ensure its safety.
Application
The EC Ethereum add -on is a key element of its cryptographic infrastructure. Understanding how the multiplication and addition of EC work, we can appreciate the complexity and sophistication of the Ethereum technology underlying. Although this article only scratched the surface of elliptical curves in Ethereum, I hope that it is a solid foundation for further exploration and learning.
Let me know if you have any questions or there is something else in which I can help!
