Base58 encoder and decoder

How it works

Base58 writes bytes with 58 characters: the digits and letters without 0, O, I and l, which are easy to confuse, and without + and /, so that a double click selects the whole string. It was made for Bitcoin addresses, which people copy by hand.

Since 58 is not a power of 2, the bits cannot simply be cut into groups. Instead all the bytes are read as one big number $N$ (big-endian, base 256) and written in base 58, by dividing by 58 again and again: the remainders are the digits, last digit first. Each leading zero byte would vanish in the number, so it is written as the character 1 (the digit for 0).

Decoding goes the other way, with Horner’s rule $N \leftarrow 58N + d$. The repeated division makes Base58 slow for long data, but addresses and keys are short. Bitcoin adds a 4-byte checksum (Base58Check, the first bytes of a double SHA-256) before encoding.