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Co-authored-by: andrewtoth <andrewstoth@gmail.com>
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Pieter Wuille 2021-01-29 11:33:27 -08:00
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@ -220,7 +220,7 @@ For Bech32m, we aim to retain Bech32's guarantees for substitution errors, but m
===Error patterns & detection probability===
We define an error pattern as a sequence of first one or more deletions, then swaps of adjacent characters, followed by substitutions, insertions, and duplications, in that order, all in specific positions, applied to a string with valid checksum that is otherwise randomly chosen. For insertions and substitutions we assume a uniformly random new character. For example, "delete the 17th character, swap the 11th character with the 12th character, and insert a random character in the 24th position" is an error pattern. "Replace the 43th through 48th character with 'aardvark'" is not a valid error pattern, because the new characters are not random and there is no reason why this particular string is more likely than any other to be substituted.
We define an error pattern as a sequence of first one or more deletions, then swaps of adjacent characters, followed by substitutions, insertions, and duplications, in that order, all in specific positions, applied to a string with valid checksum that is otherwise randomly chosen. For insertions and substitutions we assume a uniformly random new character. For example, "delete the 17th character, swap the 11th character with the 12th character, and insert a random character in the 24th position" is an error pattern. "Replace the 43rd through 48th character with 'aardvark'" is not a valid error pattern, because the new characters are not random and there is no reason why this particular string is more likely than any other to be substituted.
A hash function-based checksum design with a 30-bit hash would have a probability of incorrectly accepting equal to ''2<sup>-30</sup>'', for every error pattern. Bech32 has a probability of 0 to incorrectly accept error patterns consisting of up to 4 substitutions—they are always detected. The 'q'-insertion issue shows that for Bech32 a simple error pattern ("insert a random character in the penultimate position") with probability ''2<sup>-10</sup>'' exists: it requires the final character to be 'p' (leaving only 1 in 32 strings), and requires the inserted character to be 'q' (permitting only 1 of 32 possible inserted characters).