Unlock Mathematics Behind Ethereum Private Keys: Base58 Codings
When it comes to cryptocurrency technology and blockchain, private keyys are used to ensure user accounts and transactions. . However, many people System of Ethereum, specifically
What is a private key?
. It is like a password, but instead of protecting your identity online, it protects the property of an asset. In the case of Ethereum, each user has a unique set of 256 -Bit keys, known as private keyys, which are used to sign transactions and verify their property.
Base58 Coding: A Base Coding Standard32
Ethereum uses base coding58, also known as P2PKH (Private Key Hash). This is a widely adopted standard to encode cryptographic keys in text chains. The coding scheme works by decomposing the components of the key in smaller parts and assigning unique numerical values to each part.
Based58, each component is represented by a 3 -digit hexadecimal chain, similar to how base coding works64 for text data. However, Unlike Base64, which Uses Ascii Characters, Base58 Uses a Different Set of Digits (0-9) and Letters (A-Z, A-Z). Long characters, with the first ‘5’ character.
Mathematical Breaks
Let’s take a closer look at How Private Keys are Encoded Based58.
Given a public key, denoted as x, we can divide it into three components:
R(Random Number): A 32 -Bit Integer
- S
(Signature): A 256 -Bit Random Numbers Chain
- N
(Network Hash): A 64 -Bit Integer
Then we combine these components using the following Formula:
x = r ⊕ s ⊕ n
where ⊕ Denotes Xor Bit and Bit.
To codify this public key on base58, Then we use a base coding scheme32 to compress the resulting chains.
Based32, each 4 -Digit characters sequence is represented by 6 bits. For example:
R(32 -bit integer) can be encoded as 3G2T7A4P3B1Q4D5c
S(256 bits chain) would be encoded using a different set of digits, results in a longer encoded chain.
Why 51 characters?
So why Ethereum's Private Keys Produce a 51 -Caracters Chain that begins with '5'? The answer is found in the way we build the coded chains. Since each component is represented by a unique numerical value (0-9) and letter (A-Z, A-Z), we can adjust 10 x 10 = 100 possible combinations.
Using the⊕operator, which Xor bitwise performs in the components of the public key, we can generate multiple coded chains. The number of possible coded chains.
The final encoded chain is chosen from the set:
5h | 5J | … (51 Long Characters)
where|` denotes concatenation. The first character ‘5’ ensures that all the resulting chains begin with this unique value.
Conclusion
(P2PKH), Base58 (P2PKH), is a complex mathematical process that implies decomposing public key in components and combining them using Xor Bitwise. By understanding how these coded chains are built,