Ethereum: Why doesn’t basepoint G of Secp256K1 seem to be on the Elliptic Curve?

Understanding the elliptical efficiency curve from Ethereum

The elliptical curve is a mathematical representation that is used to secure digital transactions and to secure the integrity of blockchain data. In this article, we will deal with the special features of the basic point G (also as point 0) on the ECP256K1 elliptical curve in sixteen and decimal formats.

Elliptical Disposal Display

On the elliptical curve point P is defined by its coordinates (x, y) to:

X^2 + y^2 ≡ 1 (mod p)

However, X and Y are the coordinates of the point P on the curve. The point in Infinity (referred to as O) serves as an element of identity.

ECP256K1 elliptical curve

SECP256K1 is a cryptographic elliptical curve developed by Nist, which is compatible with existing cryptographic systems such as RSA and digital signatures of the elliptical curve. This specific curve uses a finished field with a 256 -bit (32 bytes) to save a private key.

BasePoint G on SECP256K1

The property G is an important element of the elliptical curve, which is the goal in the event of infinity. In the context of SECP256K1, the coordinates of the basic point G has:

GX = (79Be667E F9DCBBAC 55A06295 CE870B07 029BFCDB …

Sixteen representation

Hexadeic representation of these coordinates is what interests us.

`simply

GX = (79Be667E F9DCBBAC 55A06295 CE870B07 029BFCDB ...

This sixteen code consists of many numbers, each of which represents the value in a specific bit position. The first 64 -bit represent part of the “header” of coordinates, while the next 64 -bit contain additional information.

decimal presentation

For those who are not familiar with sixteen notation, you will find a short translation guide here:

• 79 represents the number 255 (2^8 – 1)

• Be" represents the hexadecimal value of0003

• 667Erepresented the decimal value '0x6c27fe'

• F9DCBBACrepresents the decimal value '0x5d4a96b

In combinations, these hexadeic values ​​represent a specific point of the ECP256K1 elliptical curve.

Why does BasePoint G not appear as an elliptical curve?

Despite its importance in cryptographic practice, the basic point G SECP256K1 is not usually shown as an elliptical curve. These are over a few reasons:

* Safety : Presentation of the basic point G as a single point would make it susceptible to various attacks, such as “base dot” or “dot to vulnerability to infinity”.

* complexity : An attempt to present a complex coordinate algebra with SECP256K1 can lead to arithmetic problems and reduce performance.

* Performance : In cryptographic applications, simplicity and performance are often priority before a detailed mathematical representation.

In summary, it can be said that hexadeic representations and the decimal of the basic point G on the SECP256K1 are interesting, but they do not directly correspond to the elliptical corner point. Fears of the complexity and security, which are so related to the presentation of the basic point G, make it impractical for cryptographic applications.