Created
May 3, 2018 01:29
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Passphrase compound collision - case analysis
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- 3 word passphrases | |
- 1000 word list, with one collision: dog, under, underdog | |
Compounding: | |
under dog x: 1000 | |
x under dog: 1000 | |
Total loss: 2 * 1000 out of 1000^3 | |
- 5 word passhrases | |
under dog x x x: 1000^3 - 2 * 1000 | |
x under dog x x: 1000^2 - 1 | |
x x under dog x: 1000^2 - 1 | |
x x x under dog: 1000^3 - 2 * 1000 | |
under dog under dog x: 1000 | |
under dog x under dog: 1000 | |
x under dog under dog: 1000 | |
3 * 1000 + 2 * (1000^2 - 1) + 2 * (1000^3 - 2 * 1000) = 2001998998 ~= 2e9 | |
1000^5 = 1000000000000000 = 1e15 |
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Just to check my first assumption: is the number to the right of the colons the number of possible passphrases that have that location of compounding? I think that's the case, but just spelling it out.
So if that's the case, can you walk me through
x under dog x x: 1000^2 - 1
? Why is it not just1000^3
? Or maybe1000^3 - 1000
if we don't want to include the pattern ofx under dog under dog
?