Quote from: xmready on Today at 09:48:48 PM

My reasoning is: if my 12 words are compromised via a physical intrusion, the extension stored in a separate location will guarantee that my wallet is not compromised. Simply splitting the 12 words in half and storing 6 words separately makes a brute force attack easier (I think). That is why I ask.

It will. The mnemonic passes through a HMAC-SHA512 hash function to produce 512 bits seed. Having a longer seed will increase your security, as long as it is under 512 bits.

Quote from: xmready on Today at 09:48:48 PM

If each Electrum seed is already extended with the word "electrum", then why don't we have to input that as a seed extension when recovering a wallet with Electrum or another Electrum compliant wallet?

If I'm not wrong, it isn't extended. The hash is salted by using "Electrum + passphrase". There isn't a lot of Electrum compliant wallet, they change the way to derive the addresses accordingly so long as they detect an Electrum seed. BIP39 generates addresses differently and they are incompatible.

Quote from: xmready on Today at 09:48:48 PM

Are you saying that an attacker would try to brute force the output of the PBKDF2 key derivation function, thus it would be the same difficulty? I would imagine if the attacker were trying to guess words and extension words, then it does double the difficulty.

It is more difficult. The length of the hash output is longer than the entropy given to it. If the attacker is finding the seed, then the complexity increases. However, addresses provides 128 bits of security, so if any attacker were to blindly bruteforce your addresses, they only need to break 128 bits of security. If they were finding your seed, the complexity is higher.