Base 58 encoding and Bitcoin addresses

A few weeks ago I wrote about base32 and base64 encoding. I’ll review these quickly then discuss base58 and its use in Bitcoin.

Base32 and Base64

All three methods have the goal of compactly representing large numbers while maintaining readability. Douglas Crockford’s base32 encoding is the most conservative: it’s case-insensitive and it does not use the letters I, L, O, or U. The first three letters are omitted because of visual similarity to digits, and the last to avoid “accidental obscenities.”

Base 64 is not concerned with avoiding visual similarities, and uses the full upper and lower case alphabet, plus two more symbols, + and /.

Base58

Base58 is nearly as efficient as base64, but more concerned about confusing letters and numbers.The number 1, the lower case letter l, and the upper case letter I all look similar, so base58 retains the digit 1 and does not use the lower case letter l or the capital letter I.

The number 0 looks like the lower case letter o and the upper case letter O. Here base58 makes an unusual choice: it keeps the lower case letter o, but does not use the digit 0 or the capital letter O. This is odd because every other encoding that I can think of keep the 10 digits and differs over what letters to use.

Bases like 32 and 64 have the advantage of being trivial to convert back and forth with binary. To convert a binary number to base 2n, you start at the least significant end and convert groups of n bits. Since 58 is not a power of 2, converting to base 58 is more involved.

Bitcoin addresses

Bitcoin addresses are written in base58, and in fact base58 was developed for Bitcoin.

A Bitcoin address is a 25 byte (200 bit) number. Now

log582200 = 34.14

and so it may take up to 35 characters to represent a Bitcoin address in base58. Using base64 would have taken up to 34 characters, so base58 pays a very small price for preventing a class of errors relative to base64. Base32 would require 40 characters.

As noted above, converting between binary and base58 is more complicated than converting between binary and either base32 or base64. However, converting to base58 is trivial compared to everything else that goes into forming a Bitcoin address. The steps, documented here, involve taking an ECDSA public key, applying a secure hash function three times, and appending a checksum.

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