Compression Art: Understanding of the coordinates of the public key
In the reign of encryption, the compression of the public key is an intelligent technique used to reduce the size of the great public keys, the preservation and the essential properties. One aspect of this compression process is related to the coordinate system used in public key systems, in particular Ethereum. In this article, we will deepen the world of the compressed public keys and explore because a uniform or strange coordinated corresponds to the positive or negative sign.
According to Andreas Møller’s book on the public tablets/non -tablets, “Chapter 4 – Section – formed by Keys”, non -compressed public keys have a prefix of 04, followed by a sequence of bytes representing the cryptographic hash of the public key. When this public key is compressed, it usually takes on the form of a digital signature of the elliptical curve (Ecdsa) or a similar algorithm. As part of the compression process, the coordinated y of the compressed public key is often influenced.
The reason behind this apparently arbitrary choice consists in mathematics at the basis of elliptical curves and encryption. In a system based on the elliptical curve, such as Ethereum, every point on the curve corresponds to a unique couple of coordinate (X, Y). These points are represented by couples (x, y), where y is generally calculated caog (x).
When we consider the compressed public keys, the compression algorithm often reduces the size of coordinates, maintaining the integrity and safety of the key. However, coordinate Y, which represents the point on the curve corresponding to a certain public key, can experience changes during the compression process.
The reason for this change of behavior is rooted in the way the compression algorithm works. When compressing a public key based on the elliptical curve, the algorithm usually uses a simple transformation that maps the original (x, y) coordinates in a new series of coordinate '(x', y '). In many cases, this transformation involves the reduction of the coordination Y by a constant factor or the application of a non -linear function.
The specific implementation of the compression algorithms may vary according to the encryption scheme and the cryptographic bookcase. However, in general, a uniform or strange Y coordinated Y corresponds respectively to a positive or negative sign, due to the intrinsic mathematical properties of the elliptical curves. This is due to the fact that when calculating `y calog (x), it is used for -log (x) is symmetrical around zero.
To illustrate this concept, consider an example in which we have an elliptical curve with (x, y) = (1, 2). By applying the transformation defined by the compression algorithm, we obtain (x ', y') = (1, -2). In this case, the initial coordination also y corresponds to a positive sign, while the transformed Odda coordination corresponds to a negative sign.
In conclusion, the choice whether a uniform or a strange coordinated in the compressed public keys is not arbitrary; It is deeply rooted in the mathematical structure of elliptical curves and encryption. The compression algorithm usually reduces the dimensions of coordinated x, while maintaining the integrity of the key, which leads to a uniform or strange coordinate corresponding to a positive or negative sign.
While we continue to explore the complications of public key systems, it is essential to understand how these mathematical choices affect the security and the ability to use these cryptographic protocols. By understanding the principles underlying the compression algorithms, we can better appreciate the importance of careful design and implementation in the creation of safe and reliable encryption systems such as Ethereum.