user109904: Is it possible to derive a new 12 word seed from a 12 word seed with passphrase (13th word) such that they both produce the same master key?

user7272: No, this is not possible.
The mnemonic and passphrase are put through PBKDF2. Any change in the input results in a completely different output.
While it is possible that there exists some 12 word mnemonic that just happens to hash to the same seed as your original mnemonic + passphrase, this would require bruteforcing all possible mnemonics to discover, and would not be derivable from the original mnemonic in any form - a hash collision would be completely unrelated.

109904: <p>Is it possible to derive a new 12 word seed from a 12 word seed with passphrase (13th word) such that they both produce the same master key?</p>
 7272: <p>No, this is not possible.</p>
<p>The mnemonic and passphrase are put through PBKDF2. Any change in the input results in a completely different output.</p>
<p>While it is possible that there exists some 12 word mnemonic that just happens to hash to the same seed as your original mnemonic + passphrase, this would require bruteforcing all possible mnemonics to discover, and would not be derivable from the original mnemonic in any form - a hash collision would be completely unrelated.</p>
