Mathematical Connection: As different addresses of the same private key are generated
In the field of cryptocurrency, especially Ethereum, understanding how various addresses of a private key are generated, it is crucial to capturing the underlying mathematics to mathematics. One of the concepts that comes to mind between the private keys and their relevant public clubs, which eventually translate into unique addresses for Blockchain.
For those who are unknown, let’s dive into details: When you create an Ethereum wallet, it generates two types of addresses:
- Private Key : Secret Code used to sign transactions (or «signature»).
- Public Key (or
Address ): An exclusive string that identifies and represents the Ethereum portfolio.
The relationship between private keys and public addresses lies in the mathematical concept of elliptical curves that are used to codify and verify blockchain cryptographic operations.
from a private key to the public address
Consider the following steps:
1.
2.
- Calculate K i n : These values are selected so that n is a product (P-1), Q, P and E.
From the public key to the address
The public key consists of four sixteen digits: `0x [base58 coded private key]. To translate it at an exclusive address on the Ethereum network:
1.
2.
Why many addresses of a private key?
Let’s deal now why you can get a lot of addresses by generating an Ethereum portfolio:
- Base58 Coding
: This step transforms the private key into a compact form that can be easily stored and sent (base 58 coded).
- Shortcut function : The coded public key is then transmitted by a shortcut function that generates a constant size.
This mathematical manipulation ensures that different addresses of a private key are random and unpredictable, providing an additional security layer before possible unauthorized attacks or transactions.
In short:
- The private key generates two types of Ethereum addresses: Public Key (or address) and another pair of numbers (P, Q) in the elliptical curve.
- The public key is still modified by subtracting 2 of the coded private key base58 and using module operations with a large number E.
- This process contains many exclusive addresses for each portfolio, ensuring safety and preventing attacks.
Understanding how Ethereum addresses are generated from a private key can help you navigate the cryptocurrency world more confidently.