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Is it known the minimum amount of characters you need to mistype to get another valid address?
Addresses contain checksums, and also must follow some specific rules, so I guess this could be calculated: I wonder if someone did.
How many characters you need to mistype at minimum to get another valid address?
Answers
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Check sum is a result of 2 hash-functions: SHA256 and RIPEMD160. The length of checksum is 4 bytes. Hash functions are indistinguishable from random oracle, so it is possible, if you make 1 mistake in non-checksum character, you get the same checksum. But probability of this is 1/2^32.
Added later: not exactly correct due to base58 encoding. Correction in the another answer.
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Here's an example of a pair of valid addresses that differ by only one character.
1xxxxxxxxxxxxxxxxxxxy1wqmDWjatp7t
1xxxxxxxxxxxxxxxxxxxy1wqmDWgatp7t
another example pair
1xxxxxxxxxxxxxxxxxxxxyE4zW1N3nMx2
1xxxxxxxxxxxxxxxxxxxxyE4zW1U3nMx2
For both pairs, the 32-bit checksums are NOT the same, but they satisfy the condition that
(checksum1 % 656356768) == ((checksum2 + 356826688) % 656356768)
1To add to this: whether you make 1 mistake or 20, the probability that the address is valid is still 1/2^32. – Tim S. – 2014-02-28T12:54:28.773
1I'm afraid this is the wrong answer. The solution is NOT to find two addresses with the same checksum, but with the same sequence of base58-encoded characters for the large integer represented by the hash concatenated with checksum. See my answer for examples. – uminatsu – 2014-02-28T20:26:44.723
1I agree that you are right. Base58 encoding deforms last check sum bytes. But my calculation of probability is correct anyway. – Zergatul – 2014-03-01T21:06:14.697