The Missing Bit

Introducing Base24

TL;DR:
Base24 is a binary-to-text encoding aimed at encoding short keys (32-512 bits) for human usage.

Update:
I was somehow able to write the wrong alphabet in the initial article. This has now been corrected.

Update 2:
Implementations are now available for multiple languages. The list is at the end of the article.

Update 3:
I was surprised that my idea was very well received and I am very grateful for your interest.

I am working on a project where I need to give the user the possibility to recover its account with recovery codes. I generated a few codes and tried different encodings but I could not get something satisfying.

Comparison of some existing solutions

Plain numbers (base 10)

Pros:

  • No encoding necessary
  • Only numbers

Cons:

  • Longest
  • While it's only numbers, users might not realize it and mix 1 for l or I and 0 for O.
  • Hard to have a visual cursor while copying the code.
  • No visual identification without formatting.

Hex (base 16)

Pros:

  • Easy to encode and decode
  • Used everywhere in computing

Cons:

  • Same mix problem as with numbers, except with the presence of A-F users are even more confused and might think other letters are used.

Base32

Pros:

  • RFC 4648 is standard
  • Easy to encode and decode as 32 is power of 2

Cons:

  • Always the mix problem with I and 1. While 1 is not used by the alphabet, the user doesn't know that.

Base64

Pros:

  • The most compact

Cons:

  • Ugly, nearly impossible to write down by a human

How Base24 came together

The goal is to provide a way to encode and decode binary keys of cryptographic length (32-512 bits). Short keys can be used as recovery codes with key derivation while longer keys can be directly used.

To give an idea of the size of the numbers, here are a few numbers in base 10:

  • 32 bits: 4278190080
  • 64 bits: 18374686479671623680
  • 128 bits: 326374343753722343741285467180125988440

Those numbers are really hard to read directly.

The codes might be dictated over the phone or written down. As seen with credit cards numbers, it can be cumbersome. While a typo in a credit card will at worst lead to a failed transaction, a typo in a cryptographic key will make the data unreadable. Of course the typo can be "brute forced" by technical users, but it could be hard or even impossible for normal users. Which would lead to data loss.

The chosen encoding alphabet must be absolutely unambiguous. No similar characters. Present or not in the alphabet. The length of the alphabet is the minimum length required to store 32bit is 7 characters (instead of 8 for hex), which is 24. The alphabet must also be case insensitive.

A list of ambiguous characters (both cases are displayed for letters):

  • 1iIjJlL
  • oO0dDqQ
  • NNMnnm (double n mixed with m)
  • uUvU
  • gG6

The ambiguity is also taken into account when hand written.

The final alphabet I came up with is ZAC2B3EF4GH5TK67P8RS9WXY. As I required 24 characters, I kept G and 6 which are the least ambiguous in the list. The order of the characters is arbitrary, I just ensured the characters where not sorted, to ensure the string would stand out and not being seen as a full alphabet. I put the Z first so that a series of 0 would be ZZZ... which is snoring/sleeping and made me smile. This is of course technically irrelevant, but computers are made for people.

The data length must be multiple of 32 bits. There is no padding mechanism in the encoder.

Example

Let's take a 128 bit data:

  • Decimal: 49894920630459842177293598641814316632
  • Decimal with spaces: 49894 92063 04598 42177 29359 86418 14316 632
  • Hex (base16): 0x25896984125478546598563251452658
  • Base24: 2FC28KTA66WRST4XAHRRCF237S8Z
  • Base24 with spaces: 2FC2 8KTA6 6WRST 4XAHR RCF23 7S8Z
  • Base24 with spaces lowercase: 2fc2 8kta6 6wrst 4xahr rcf23 7s8z

Or 64 bit which is reasonable for recovery code when used with key derivation:

  • Uppercase A64KH WZ5W EPAGG
  • Lowercase a64kh wz5w epagg

As we can see, this is manageable by a human for copy on paper with a low risk of error.

Implementations

Licensing

If this is ever to used by anybody, consider it public domain.