Bitcoin Address Generation

A Bitcoin address is generated starting from the public key, following this algorithm:

1. A public key is generated
2. The private key $k$ associated to that public key is generated
3. The private key is multiplied by a number $G$ (ECDSA), which generates $K$.
4. $H=\text{RIPEMD160}(\text{SHA256}(K))$ is generated by double hashing
5. A version is generated, which is a hex number (0x03 for private key and 0x00 for public key).
6. The checksum is computed by double hashing $version$ concatenated to $H$ with SHA256.$\text{checksum}\leftarrow \text{SHA256}(\text{SHA256}(\text{version}\cdot H)$7. We take the first 4 bits of the checksum;$\text{chk}\leftarrow \text{checksum}[0,4]$8. We generate the address $A$ by doing $A=\text{Base58}(\text{version}\cdot H\cdot \text{chk})$ where $\cdot$ is the concatenation $A=\text{Base58}(\text{version}\cdot H\cdot \text{chk})$ The Base58 is equal to the Base64 encoding, but excluding the characters:

• Uppercase i (I)
• Lowercase L (l)
• Uppercase o (O)
• The zero (0)
• The symbols + and /.

Because those symbols can be confusing when inserted by hand.

The checksum is needed in order for the protocol to verify if the inserted address is a valid one, otherwise we might send money to an non existing address, and so money will be lost.

It’s possible to get $H$ from $A$, since both $chk$ adn $version$ are fixed length, and the $Base58$ operation is two way. Of course we cannot get the private key from $H$.

It’s also possible to personalize an address, if the address is not yet chose, but it’s not safe. The more random the address is, the better.