ALGORITHM_ABSTRACT.md

Basic32 Algorithm Abstraction

Basic32 encodes and decodes OTP (One-time passcode) tokens to and from a standard length Base32 string, effectively making them shorter. This abstraction is designed to walk through non-Javascript implementations.

Ideology

Basic32 should be extremely fault-tolerant, specifically to common letter transpositions and to

Utilized Characters

Basic32 utilizes characters 0123456789ACDEFGHJKMNPQRSTUVWXYZ specifically in that order. All lowercase letters correspond to their uppercase counterparts.

The remaining four letters are interpreted as follows:

User Writes	Interpreted
(Letter) O	(Number) 0
(Letter) I	(Number) 1
(Letter) L	(Number) 1
(Letter) B	(Number) 8

Encoding

1. Determine the number of digits of the OTP code.

2. Use outputLength = ceil(log10(10 ^ digits) / log10(32)) or outputLength = ceil(ln(10 ^ digits) / ln(32)) to find the number of characters to be output where digits is the number of digits of the OTP code.

3. Perform the following checks on the encoding input:

   • If a number, the encoding input must be less than 10 ^ digits.
   • If a string, the length must equal digits and the characters should only be numbers (Regular expression: /^\d{digits}$/ where digits is the number of digits of the OTP code).

4. Cast the input to a number.

5. Perform a base 32 encoding. This can be accomplished by looping from outputLength - 1 to 0, appending a string with the character in 0123456789ACDEFGHJKMNPQRSTUVWXYZ at the floor(input / (32 ^ loopIndex)), and reassigning input = input modulo (32 ^ loopIndex). This is represented below in pseudocode.

   characterSet = "0123456789ACDEFGHJKMNPQRSTUVWXYZ"
   encodedString = ""
   // Example given for input
   input = 123456
   digits = 6
   outputLength = ceil(log10(10 ^ 6) / log10(32)) = 4
   
   // This loop produces loopIndex = 3, 2, 1, 0 in that order
   for ((loopIndex = outputLength - 1) through (loopIndex is 0) change (loopIndex = loopIndex - 1))
     // Plus below is used to denote string concatenation
     // The characterAt operation considers 0 to be the starting position
     encodedString = encodedString + (characterSet characterAt floor(input / (32 ^ loopIndex)))
   
     // Input becomed the remainder, which can be found using a modulo operator, or manually
     input = input modulo (32 ^ loopIndex) = (input / (32 ^ loopIndex) - floor(input / (32 ^ loopIndex))) * (32 ^ loopIndex)
   

License

MIT © 2021 Russell Steadman. See LICENSE.