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I assume Litecoin has different rules of generating addresses with Bitcoin, since all Litecoin addresses are 34-characters long which is different than Bitcoin.

Given that the rules for generating addresses are different, does Litecoin have a higher chance of address collision than Bitcoin?

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When encoding the 20 byte public key hash with base-58, a prefix for the version byte is prepended. In Bitcoin, this version byte is 0x00 so that bitcoin addresses always start with a 1. In Litecoin, this version byte is 0x48 so that addresses always start with an L. This also has the side effect that the base58 encoding of these hashes is 26-34 characters for Bitcoin, and always 34 characters for Litecoin. See https://en.bitcoin.it/wiki/List_of_address_prefixes

But this doesn't change the fact that there is 20 bytes of information being encoded (addresses are really just human readable short-hand for this 20 bytes of data), and each possible combination has a unique encoding. Therefore, the chance of address collision is exactly the same in the two coins.

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