How secure is a brain wallet with a randomly generated password?

[Welsh]

To expand on this for any future readers, there's been attempts in the past, success one's that have tried to demonstrate the security of a brain wallet, with a large randomly generated password, and they were never cracked. However, the problem with brain wallets is how you generate them, a lot of users will probably go to a website to generate it, and that introduces a number of attack vectors, which you wouldn't have if you generated your seed via a offline computer. You've first got to trust the website, then you've got to make sure there's no man in the middle attacks going on, and ultimately you have to either download the code or run it via the internet through your web browser.

Also, it's worth mentioning just because something is open source, it doesn't mean it's secure or isn't malicious.

[digaran]

To expand on this for any future readers, there's been attempts in the past, success one's that have tried to demonstrate the security of a brain wallet, with a large randomly generated password, and they were never cracked. However, the problem with brain wallets is how you generate them, a lot of users will probably go to a website to generate it, and that introduces a number of attack vectors, which you wouldn't have if you generated your seed via a offline computer. You've first got to trust the website, then you've got to make sure there's no man in the middle attacks going on, and ultimately you have to either download the code or run it via the internet through your web browser.

Also, it's worth mentioning just because something is open source, it doesn't mean it's secure or isn't malicious.

How would you explain some brainwallet passwords complicated enough like a bitcoin address or a long hex string which have been cracked already and people did use them with amounts as big as hundreds of bitcoins?

Brain wallet concept is a high risk method in general.
For security and privacy sake, it's better to generate several addresses with separate private keys, that way you could sever the links between wallets.

[Welsh]

I definitely don't agree with brain wallets, I just thought it was worth mentioning. The thing about brain wallets they encourage less secure standards, than traditional wallet software, and generally as humans we want to make it as easy as possible. I don't many people do use brain wallets, at least I'd hope not. However, there's been attempts in the past to try, and prove when a brain wallet is generated with high entropy they're just as safe. Now, I'm sure we could debate that until the cows go home, but it has been attempted in the past on the forum, and they didn't lose their coins.

Plus, sometimes it's not about the complexity of the password, since you can have some pretty substantial entropy to generate a brain wallet, it's the way you generate it, i.e doing it online in my opinion is a absolute no go or even doing it on a computer that has been exposed to the internet at some point, is a no go. Unless, you have the upmost confidence in its security.

[Saint-loup]

How would you explain some brainwallet passwords complicated enough like a bitcoin address or a long hex string which have been cracked already and people did use them with amounts as big as hundreds of bitcoins?

Brain wallet concept is a high risk method in general.
For security and privacy sake, it's better to generate several addresses with separate private keys, that way you could sever the links between wallets.

I don't think most people use brain wallets as their main wallet. It's just a convenient way offered by the Bitcoin technology to store, transport or transmit small amounts of funds without needing any physical or digital media. For example if you want to make a small donation to someone, or if you need to buy something from someone you trust, you can just give them the brain seed. You can even do the transaction with someone you don't trust, if he agrees to sweep the wallet in front of you or to not claim anything if something goes wrong.

[o_e_l_e_o]

However, there's been attempts in the past to try, and prove when a brain wallet is generated with high entropy they're just as safe. Now, I'm sure we could debate that until the cows go home, but it has been attempted in the past on the forum, and they didn't lose their coins.

It depends how you are defining a brain wallet. If I use a proper source of entropy such as Electrum pulling on /dev/urandom to generate a seed phrase, and then memorize that seed phrase, then technically that is a brain wallet which is completely secure against brute forcing (although still very fragile and at very high risk of loss, as is anything memorized). If you define brain wallet in the classical sense of I picked a string and then hashed it to generate a private key, then that will almost never be secure since the human brain cannot be random and will not pick a string with sufficient entropy.