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| -rw-r--r-- | bip-0350.mediawiki | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/bip-0350.mediawiki b/bip-0350.mediawiki index 3ad41c8..d09ae6b 100644 --- a/bip-0350.mediawiki +++ b/bip-0350.mediawiki @@ -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). |