Question regarding multiple SHA-256 rounds on a Bitcoin Brain Wallet passphrase…
This would hopefully eliminate the worry that somebody could reverse-engineer the process by which I generate the brain wallets.


By Kerckhoffs's principle, you should assume that the adversary already knows the algorithm, and the only thing unknown are the secret keys – in your case, the passphrases.

Therefore, the adversary by definition knows that you are generating the brain wallet passphrases by $w_i = h( h(k_1 || i) || k_2)$ (where $h(x)$ is something like $Hex(SHA2(ASCII(x)))$. So the only things your attacker has to "reverse-engineer" are the two passphrases $k_1$ and $k_2$.

For now, SHA-2 is assumed to be preimage-resistant, which means that the best way of finding $k_1$ and $k_2$ is to simply guess them and see if the result matches any captured output (or, if there is no captured output, see if the result helps unlocking any of your wallets).

Generating different $w_i$ with the same passphrases does not significantly help the attacker to break it, but if he breaks one, also all the others are broken. The encoding (hex, ascii, anything else) doesn't matter for the security, too.

If your two passphrases are good (i.e. having more than 100 bits of entropy together), an attacker has little chance of successing with this brute-force.

If your passphrase is bad (and this includes all passwords with less than 10 characters, or longer ones which can be found in dictionaries), your derivation can be brute-forced easily. Also, if other users are using your scheme too, and by chance have the same password, they'll have the same $w_i$s, which might be usable by an attacker.

Your scheme could be made better by using a slow password hash, and including a salt input which is unique to you, like your email address. The output of this slow hash you can then process with the counter to get the actual $w_i$.

If the attacker has a key-logger and captures your passwords, everything is already lost.